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A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of the dynamical variables into i) a fixed conformal 3-geometry, ii) a conformal factor possessing nonlinear dynamics and iii) transverse-traceless perturbations of the conformal 3-geometry.

In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra A defined on a transformation groupoid given by the action of a group G on a space E. Owing to the fact that G was assumed to be finite it was possible to compute the model in full details. In the present paper we develop the model in the case when G is a noncompact group. It turns out that also in this case the model works well. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model ``collapses'' to the usual quantum mechanics.

We propose a Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-splitting of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base manifold and a 2-dimensional fibre space. In this Kaluza-Klein formalism we find that general relativity of 4-dimensional spacetimes can be interpreted in a natural way as a (1+1)-dimensional gauge theory. In a gauge where the (1+1)-dimensional metric can be written as the Polyakov metric, the action is describable as a (1+1)-dimensional Yang-Mills type gauge theory action coupled to a (1+1)-dimensional non-linear sigma field and a scalar field, subject to the constraint equations associated with the diffeomorphism invariance of the (1+1)-dimensional base manifold. Diffeomorphisms along the fibre directions show up as the Yang-Mills type gauge symmetries, giving rise to the Gauss-law constraints. We also present the Einstein's equations in the Polyakov gauge and discuss them from the (1+1)-dimensional gauge theory point of view. Finally we show that this Kaluza-Klein formalism is closely related to the null hypersurface formalism of general relativity.

The longitudinal Doppler shift is a measure of hyperbolic distance. Transformations of uniform motion are determined by the Doppler shift, while its square root transforms to a uniformly accelerated frame. A time-velocity space metric is derived, by magnifying the Beltrami coordinates with the geometric time, which is similar to the one obtained by Friedmann using Einstein's equations in which the mass tensor describes a universe of dust at zero pressure. No such assumption nor any approximation in which the coordinates increase with time (i.e., constant velocities) need be made. The hyperbolic velocities are related to the sides of a Lambert quadrilateral. In the limit when the acute angle becomes an ideal point, the case of uniform acceleration arises. The relations to Hubble's law, and to the exponential red shift, are discussed.

Tracklist: 1. Incident At Harpham Flat 2. Eloi Lament 3. Lucky Life 4. The Pivot 5. Holy Waters 6. Round The Four Corners 7. Jiggle The Handle 8. Relativo 9. Taglioni 10. In A Child's Eyes

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

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The class of accelerated reference frames has been studied, on the basis of Fermi-Walker coordinates; both in the cases of uniform and arbitrary accelerations. In the first case, explicit formulae for the transformation of coordinates have been derived and, in both cases, we have also obtained the infinitesimal generators and their commutation relations. The outcome has been an extension of the Poincar\'e algebra (in 1+1 dimensions), which is infinite dimensional in the case of general acceleration. This extension turns out to be trivial, in the sense that it is Abelian.

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We investigate the possibility to recover a four-dimensional (4D) general theory of relativity, as embedded in a 5D spacetime where gravity is governed by a five-dimensional (5D) Brans-Dicke (BD) theory of gravity. Employing the Gauss-Codazzi-Ricci equations and some ideas of the induced matter theory, we obtain that when the 5D BD scalar field is only depending of the extra coordinate, it is possible to recover on every generic 4D hypersurface the usual Einstein field equations plus a cosmological constant term, with matter sources described by the energy-momentum tensor of induced matter and where the cosmological constant under certain conditions can vary with time. Finally to illustrate the formalism, we give an example in which we induced a cosmological constant from warped product spaces.

Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be rewritten as non-linear Poincare algebras with momentum-dependent deformations of commutators between boosts and time translations. In contrast to deformed special relativity, the deformations are derived for generators with an unambiguous physical role, following from the relationship between canonical constraints of gravity with stress-energy components. The original deformation does not appear in momentum space and does not give rise to non-locality issues or problems with macroscopic objects. Contact with deformed special relativity may help to test loop quantum gravity or restrict its quantization ambiguities.

In this paper we present an invariant formulation of special relativity, i.e., the ''true transformations relativity.'' It deals either with true tensor quantities (when no basis has been introduced) or equivalently with coordinate- based geometric quantities comprising both components and a basis (when some basis has been introduced). It is shown that this invariant formulation, in which special relativity is understood as the theory of a four-dimensional spacetime with the pseudo-Euclidean geometry, completely explains the results of the Michelson-Morley experiment. Two noncovariant approaches to the analysis of the Michelson-Morley experiment are discussed; the coventional one in which only the path lengths (optical or geometrical) are considered, and Driscoll's approach (R.B. Driscoll, Phys. Essays \QTR{bf}{10,}394 (1997)), in which the increment of phase is determined not only by the segment of geometric path length, but also by the wavelength in that segment. Because these analyses belong to the ''apparent transformations relativity,'' they do not agree with the results of the Michelson-Morley experiment.

The first regular exact black hole solution in General Relativity is presented. The source is a nonlinear electrodynamic field satisfying the weak energy condition, which in the limit of weak field becomes the Maxwell field. The solution corresponds to a charged black hole with |q| \leq 2 s_c m \approx 0.6 m, having the metric, the curvature invariants, and the electric field regular everywhere.

We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally observable quantum phase shifts in the wavefunction of an extended object due to the coupling of its multipole moments with the gravitational field are obtained. Also, since the theory may be quantized using the action, the present approach is useful in the interface between general relativity and quantum mechanics.

Rabbits in The Clouds - Demo, 12/2005

We propose a test of the principle of relativity, involving quantum signals between two inertial frames. If the principle is upheld, classical causality will appear to be split in a dramatic and emphatic way. We discuss the existence of quantum horizons, which are barriers to the transmission of any form of quantum information. These must occur in any finite time, inter-frame experiment if quantum causality holds. We conclude with some comments on such experiments involving entangled states.

We discuss high order absorbing constraint preserving boundary conditions for the Z4c formulation of general relativity coupled to the moving puncture family of gauges. We are primarily concerned with the constraint preservation and absorption properties of these conditions. In the frozen coefficient approximation, with an appropriate first order pseudo-differential reduction, we show that the constraint subsystem is boundary stable on a four dimensional compact manifold. We analyze the remainder of the initial boundary value problem for a spherical reduction of the Z4c formulation with a particular choice of the puncture gauge. Numerical evidence for the efficacy of the conditions is presented in spherical symmetry.

We discuss high order absorbing constraint preserving boundary conditions for the Z4c formulation of general relativity coupled to the moving puncture family of gauges. We are primarily concerned with the constraint preservation and absorption properties of these conditions. In the frozen coefficient approximation, with an appropriate first order pseudo-differential reduction, we show that the constraint subsystem is boundary stable on a four dimensional compact manifold. We analyze the remainder of the initial boundary value problem for a spherical reduction of the Z4c formulation with a particular choice of the puncture gauge. Numerical evidence for the efficacy of the conditions is presented in spherical symmetry.

This PhD thesis contains a collection of work related to the algebraic classification of spacetimes in higher dimensions, including an up-to-date review of various aspects of the field. The work discussed includes the higher-dimensional Geroch-Held-Penrose formalism, a partial generalization of the Goldberg-Sachs theorem to higher-dimensions, and applications of these results to studying the stability of extremal black holes.

We argue that a (slightly) curved space-time probed with a finite resolution, equivalently a finite minimal length, is effectively described by a flat non-commutative space-time. More precisely, a small cosmological constant (so a constant curvature) leads the kappa-deformed Poincar\'e flat space-time of deformed special relativity (DSR) theories. This point of view eventually helps understanding some puzzling features of DSR. It also explains how DSR can be considered as an effective flat (low energy) limit of a (true) quantum gravity theory. This point of view leads us to consider a possible generalization of DSR to arbitrary curvature in momentum space and to speculate about a possible formulation of an effective quantum gravity model in these terms. It also leads us to suggest a {\it doubly deformed special relativity} framework for describing particle kinematics in an effective low energy description of quantum gravity.

The next generation of weak lensing surveys will trace the growth of large scale perturbations through a sequence of epochs, offering an opportunity to test General Relativity (GR) on cosmological scales. We review in detail the parametrization used in MGCAMB to describe the modified growth expected in alternative theories of gravity and generalized dark energy models. We highlight its advantages and examine several theoretical aspects. In particular, we show that the same set of equations can be consistently used on super-horizon and sub-horizon linear scales. We also emphasize the sensitivity of data to scale-dependent features in the growth pattern, and propose using Principal Component Analysis to converge on a practical set of parameters which is most likely to detect departures from GR. The connection with other parametrizations is also discussed.

We describe a solitonic solution-generating technique for the five-dimensional General Relativity. Reducing the five-dimensional problem to the four-dimensional one, we can systematically obtain single-rotational axially symmetric vacuum solutions. Applying the technique for a simple seed solution, we have previously obtained the series of stationary solutions which includes $S^2$-rotating black ring. We analyze the qualitative features of these solutions, e.g., conical singularities, closed timelike curves, and spacetime curvatures. We investigate the rod structures of seed and solitonic solutions. We examine the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the C-metric coordinates.

Since it was theorized by Kerr in 1963, determining the spin of black holes from observed data was paid very little attention until few years back. The main reasons behind this were the unavailability of adequate data and the lack of appropriate techniques. In this article, we explore determining/predicting the spin of several black holes in X-ray binaries and in the center of galaxies, using X-ray and gamma-ray satellite data. For X-ray binaries, in order to explain observed quasi-periodic oscillations, our model predicts the spin parameter of underlying black holes. On the other hand, the nature of spin parameters of black holes in BL Lacs and Flat Spectrum Radio Quasars is predicted by studying the total luminosities of systems based on Fermi gamma-ray data. All sources considered here exhibit characteristics of spinning black holes, which verifies natural existence of the Kerr metric.

A general principle of non-equivalence for bodies and observers in different G potentials (GP) was derived from correspondence of the Einstein's equivalence principle either with optical physics or with gravitational experiments in which bodies and observers are in different GP. According to it some relative physical changes occur to any well defined part of an object after a change of GP.. Such changes cannot be measured by observers travelling with the object because his instruments change in identical proportions. The same principle was derived from a new gravitational theory based on a particle model made up of photons in stationary states. Such model accounts for the inertial and gravitational properties of matter. This principle is not consistent with both, the classical hypotheses on the relative invariability of the bodies after a change of GP and with the G field energy hypothesis. The two kinds of errors are of the same magnitude and opposite signs. Such errors are cancelled but only when the two hypotheses are used. This accounts for the good predictions of general relativity for the classical gravitational tests. The new properties of the universe derived from the new principle, are radically different from the classical ones. They are more clearly consistent with the astronomical observations.

A general principle of non-equivalence for bodies and observers in different G potentials (GP) was derived from correspondence of the Einstein's equivalence principle either with optical physics or with gravitational experiments in which bodies and observers are in different GP. According to it some relative physical changes occur to any well defined part of an object after a change of GP.. Such changes cannot be measured by observers travelling with the object because his instruments change in identical proportions. The same principle was derived from a new gravitational theory based on a particle model made up of photons in stationary states. Such model accounts for the inertial and gravitational properties of matter. This principle is not consistent with both, the classical hypotheses on the relative invariability of the bodies after a change of GP and with the G field energy hypothesis. The two kinds of errors are of the same magnitude and opposite signs. Such errors are cancelled but only when the two hypotheses are used. This accounts for the good predictions of general relativity for the classical gravitational tests. The new properties of the universe derived from the new principle, are radically different from the classical ones. They are more clearly consistent with the astronomical observations.

Observations of an apparent acceleration in the expansion rate of the universe, derived from measurements of high-redshift supernovae, have been used to support the hypothesis that the universe is permeated by some form of dark energy. We show that an alternative cosmological model, based on a linearly expanding universe with Omega=1, can fully account for these observations. This model is also able to resolve the other problems associated with the standard Big Bang model. A scale-invariant form of the field equations of General Relativity is postulated, based on the replacement of the Newtonian gravitational constant by an formulation based explicitly on Mach's principle. We derive the resulting dynamical equations, and show that their solutions describe a linearly expanding universe. Potential problems with non-zero divergencies in the modified field equations are shown to be resolved by adopting a radically different definition of time, in which the unit of time is a function of the scale-factor. We observe that the effects of the modified field equations are broadly equivalent to a Newtonian gravitational constant that varies both in time and in space, and show that this is also equivalent to Varying Speed of Light (VSL) theories using a standard definition of time. Some of the implications of this observation are discussed in relation to Black Holes, Planck scale phenomena, and the ultimate fate of the Universe.

We consider Friedmann-Lema\^{\i}tre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.

In this paper we recall the construction of scalar field action on $\kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $\Phi^4$ term we investigate the modified conservation laws. We show that the local interactions on $\kappa$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.

The gravitational behavior of antimatter is still unknown. While we may be confident that antimatter is self-attractive, the interaction between matter and antimatter might be either attractive or repulsive. We investigate this issue on theoretical grounds. Starting from the CPT invariance of physical laws, we transform matter into antimatter in the equations of both electrodynamics and gravitation. In the former case, the result is the well-known change of sign of the electric charge. In the latter, we find that the gravitational interaction between matter and antimatter is a mutual repulsion, i.e. antigravity appears as a prediction of general relativity when CPT is applied. This result supports cosmological models attempting to explain the Universe accelerated expansion in terms of a matter-antimatter repulsive interaction.

Changing choices psychological relativity theory unifying theory transformation parameters psychology psygologie koornstra choice dynamics The book contains a unifying theory on how the common object space is metrically transformed by individuals with different transformation parameters, due to their other previous experiences, to individually different psychological spaces for judgment on the one hand and preference on the other hand. Individual experiences also change generally, whereby the psychological spaces also change generally for each individual. The theory, therefore, is a psychological relativity theory of perception, judgment, preference, and choice dynamics. This book is a must read for all behavioural, economic, and social scientists with theoretical interest and some understanding of multidimensional data analyses. It integrates more than twenty theories on perception, judgment, preference, and risk decisions into one mathematical theory. Knowledge of advanced mathematics and modern geometry is not needed, because the mathematical subsections can be skipped without loss of understanding, due to their explanation and illustration by figures in the text.

Changing choices psychological relativity theory unifying theory transformation parameters psychology psygologie koornstra choice dynamics The book contains a unifying theory on how the common object space is metrically transformed by individuals with different transformation parameters, due to their other previous experiences, to individually different psychological spaces for judgment on the one hand and preference on the other hand. Individual experiences also change generally, whereby the psychological spaces also change generally for each individual. The theory, therefore, is a psychological relativity theory of perception, judgment, preference, and choice dynamics. This book is a must read for all behavioural, economic, and social scientists with theoretical interest and some understanding of multidimensional data analyses. It integrates more than twenty theories on perception, judgment, preference, and risk decisions into one mathematical theory. Knowledge of advanced mathematics and modern geometry is not needed, because the mathematical subsections can be skipped without loss of understanding, due to their explanation and illustration by figures in the text.

Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the associated algebroid bundle that is similar to Einstein field equation but contain Einstein field equation and Maxwell equations simultaneously and contain a new equation that may have new results.

Serious study on how memes [as in modern definition and usage] affect the mind and society.

The purpose of this contribution is to elucidate some of the properties of Shape Dynamics (SD) and is largely based on a recent longer article. We shall point out some of the key differences between SD and related theoretical constructions, illustrate the central mechanism of symmetry trading in electromagnetism and finally point out some new quantization strategies inspired by SD. We refrain from describing mathematical detail and from citing literature. For both we refer to the longer article.

There exist at least a few different kind of averaging of the differences of the energy-momentum and angular momentum in normal coordinates {\bf NC(P)} which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [1-8] giving the {\it canonical superenergy and angular supermomentum tensors}. In this paper we present one other averaging of the energy-momentum and angular momentum differences which gives tensorial quantities with proper dimensions of the energy-momentum and angular momentum densities. But these averaged energy-momentum and angular momentum tensors, closely related to the canonical superenergy and angular supermomentum tensors, {\it depend on some fundamental length L}. The averaged energy-momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent local (and also global) analysis of this field.

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In this presentation, I review physical principles behind a recently proposed \cite{smw-utr} Universal Theory of Relativity and speculate on the mathematical requirements implied by these physical principles. Some unresolved issues will also be discussed.

Michelson and Morley conducted an experiment in the year 1887 to measure the speed of earth in luminiferous aether.  In this experiment Michelson’s interferometer was used in which two waves are superimposed to generate interference fringes. Keeping in view known velocity of earth around the sun a fringe shift of 0.44 fringe was expected on the rotation of interferometer at an angle of 90 0 , but surprisingly no fringe shift was observed. The experiment was conducted so many times and at so many places but always null results were obtained. The null result of MMX could not be explained by classical mechanics. A number of explanations for null results were submitted but no one was found to be correct. George Fitzerald and Hendrick Lorentz proposed length contraction hypothesis in the direction of motion of earth, but it was also rejected being an adhoc hypothesis. Albert Einstein submitted his famous theory “The special theory of relativity” in the year 1905. The second postulate of the STR states that speed of light is constant in all directions of inertial frames of reference irrespective of motion of source of light or the observer and states that no luminiferous aether exist as a medium, light waves do not require any medium to propagate. As light travels with constant velocity in both the arms of interferometer irrespective of motion of interferometer and there involves no time difference between the two rays hence null results of MMX were explained by special theory of relativity.

Based on the Beltrami-de Sitter spacetime, we present the Newton-Hooke model under the Newton-Hooke contraction of the $BdS$ spacetime with respect to the transformation group, algebra and geometry. It is shown that in Newton-Hooke space-time, there are inertial-type coordinate systems and inertial-type observers, which move along straight lines with uniform velocity. And they are invariant under the Newton-Hooke group. In order to determine uniquely the Newton-Hooke limit, we propose the Galilei-Hooke's relativity principle as well as the postulate on Newton-Hooke universal time. All results are readily extended to the Newton-Hooke model as a contraction of Beltrami-anti-de Sitter spacetime with negative cosmological constant.

Matter-in-Space Destroys Theory of Relativity  Joseph George (Researcher & Author)  Einstein introduced the Theories of Relativity (Special and General) between 1905 and 1915, and he used them to explain many important phenomena in the Universe. Special Relativity is an explanation of how speed affects mass, time and space. General Relativity is the geometric theory of gravitation. However I have a different approach, which can provide an alternative and perhaps better explanations for all phenomena which are explained by relativity. Space is filled with a form of matter and the Michelson-Morley experiment has failed to detect it (please watch my other videos also). All kinds of mass defects in nature release this matter to space and the release of energy in a nuclear reaction is due to the rapid-huge expansion (or detonation) of missing mass to the above-stated matter. According to Einstein, gravity creates curvature in space (and time) and he used this idea to explain Starlight bending, Gravitational lensing, Precession of Mercury's orbit etc. However I believe that gravity of celestial bodies holds a denser region of the above-stated matter around the bodies (similar to the atmosphere). When light passes through these regions light will be refracted and bent. This can explain Starlight bending and Gravitational lensing. The presence of the denser region near the Sun exerts a buoyant force on the Mercury against gravity (this force will be maximum when the Mercury is in Perihelion). Because of this, each time when Mercury approaches the Perihelion, the planet's orbit will be slightly altered. This can explain Mercury's orbital anomaly. The density of matter-in-space decreases with increasing distance from a gravitational body. This results in the atoms in an atomic clock becoming slightly lighter. The frequency of photons that are emitted by the "lighter atoms" in the atomic clock will be different. This causes the Time dilation in the Satellite Navigation -GPS systems. When a particle moves through space its interaction with the matter-in-space causes the particle's mass to increase and its length (or thickness) to decrease in the direction of motion. These effects will become obvious as the particle's speed approaches the speed of light.  In fact I believe that there are better explanations for all phenomena which we currently deal with the Theory of Relativity. I think about the possibility that perhaps UFOs are taking advantage of the denser region around celestial bodies, for example, the Earth, to create an anti-gravity effect with the buoyant  force exerted by the matter-in-space. I also think about the possibility that perhaps there is a connection between the wave nature of matter and the presence of matter-in-space. Perhaps the constant collision of moving particles with the matter-in-space causes the wave nature of matter. Buy my books from kindle stores. Visit: https://www.amazon.com/author/atom     www.youtube.com/atommodel , www.facebook.com/j.thoduka   https://www.linkedin.com/in/atommodel , www.twitter.com/atommodel    

Matter-in-Space Destroys Theory of Relativity  Joseph George (Researcher & Author)  Einstein introduced the Theories of Relativity (Special and General) between 1905 and 1915, and he used them to explain many important phenomena in the Universe. Special Relativity is an explanation of how speed affects mass, time and space. General Relativity is the geometric theory of gravitation. However I have a different approach, which can provide an alternative and perhaps better explanations for all phenomena which are explained by relativity. Space is filled with a form of matter and the Michelson-Morley experiment has failed to detect it (please watch my other videos also). All kinds of mass defects in nature release this matter to space and the release of energy in a nuclear reaction is due to the rapid-huge expansion (or detonation) of missing mass to the above-stated matter. According to Einstein, gravity creates curvature in space (and time) and he used this idea to explain Starlight bending, Gravitational lensing, Precession of Mercury's orbit etc. However I believe that gravity of celestial bodies holds a denser region of the above-stated matter around the bodies (similar to the atmosphere). When light passes through these regions light will be refracted and bent. This can explain Starlight bending and Gravitational lensing. The presence of the denser region near the Sun exerts a buoyant force on the Mercury against gravity (this force will be maximum when the Mercury is in Perihelion). Because of this, each time when Mercury approaches the Perihelion, the planet's orbit will be slightly altered. This can explain Mercury's orbital anomaly. The density of matter-in-space decreases with increasing distance from a gravitational body. This results in the atoms in an atomic clock becoming slightly lighter. The frequency of photons that are emitted by the "lighter atoms" in the atomic clock will be different. This causes the Time dilation in the Satellite Navigation -GPS systems. When a particle moves through space its interaction with the matter-in-space causes the particle's mass to increase and its length (or thickness) to decrease in the direction of motion. These effects will become obvious as the particle's speed approaches the speed of light.  In fact I believe that there are better explanations for all phenomena which we currently deal with the Theory of Relativity. I think about the possibility that perhaps UFOs are taking advantage of the denser region around celestial bodies, for example, the Earth, to create an anti-gravity effect with the buoyant  force exerted by the matter-in-space. I also think about the possibility that perhaps there is a connection between the wave nature of matter and the presence of matter-in-space. Perhaps the constant collision of moving particles with the matter-in-space causes the wave nature of matter. Buy my books from kindle stores. Visit: https://www.amazon.com/author/atom     www.youtube.com/atommodel , www.facebook.com/j.thoduka   https://www.linkedin.com/in/atommodel , www.twitter.com/atommodel    

High-precision radial-velocity techniques, which enabled the detection of extrasolar planets are now sensitive to relativistic effects in the data of spectroscopic binary stars (SBs). We show how these effects can be used to derive the absolute masses of the components of eclipsing single-lined SBs and double-lined SBs from Doppler measurements alone. High-precision stellar spectroscopy can thus substantially increase the number of measured stellar masses, thereby improving the mass-radius and mass-luminosity calibrations.

We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations. Local Lorentz invariance is treated as a gauge theory with the spin connection field taken in the so(3,1) enveloping algebra. The resulting theory appears to be a noncommutative extension of the unimodular theory of gravitation. We compute the leading order noncommutative correction to the action and derive the noncommutative correction to the equations of motion of the weak gravitation field.

We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: (a) the interpretation of the weak equivalence principle and the relationship between gravity and inertia; (b) the connection between gravitational redshift results and spacetime curvature; and (c) the Einstein equivalence principle and the ability to "transform away" gravity in local inertial coordinate systems.

Following a bi-cylindrical model of geometrical dynamics, in the present study we show that Einstein gravitational equation leads to bi-geodesic description in an extended symmetrical time-space which fit Hubble expansion in a "microscopic" cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, as the squared Dirac equations of leptons and as a sub-solution with pseudo-axion. This result would serve an explicit approach to consistency between quantum mechanics and general relativity.

We consider one-loop effects in general relativity which result in quantum long-range corrections to the Newton law, as well as to the gravitational spin-dependent and velocity-dependent interactions. Some contributions to these effects can be interpreted as quantum corrections to the Schwarzschild and Kerr metric.

In this survey we review the progress made in the last ten years in understanding the Black Hole Rigidity problem in the setting of smooth spacetimes. We review both local and global results and discuss the main mathematical ideas behind them.

In this paper we will analyze the Fantappie group and its properties in connection with Cantorian space-time. Our attention will be focused on the possibility of extending special relativity. The cosmological consequences of such extension appear relevant, since thanks to the Fantappie group, the model of the Big Bang and that of stationary state become compatible. In particular, if we abandon the idea of the existence of only one time gauge, since we do not see the whole Universe but only a projection, the two models become compatible. In the end we will see the effects of the projective fractal geometry also on the galactic and extra-galactic dynamics.