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A space of kinematic quantum states for the Teleparallel Equivalent of General Relativity is constructed by means of projective techniques. The states are kinematic in this sense that their construction bases merely on the structure of the phase space of the theory and does not take into account constraints on it. The space of quantum states is meant to serve as an element of a canonical quantization of the theory.

The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property results in great simplification of the governing partial differential equations. In addition, some self-similar solutions can describe the asymptotic behaviors of more general solutions. Newtonian gravity contains only one dimensional constant, the gravitational constant, while the general relativity contains another dimensional constant, the speed of light, besides the gravitational constant. Due to this crucial difference, incomplete similarity can be more interesting in general relativity than in Newtonian gravity. Kinematic self-similarity has been defined and studied as an example of incomplete similarity in general relativity, in an effort to pursue a wider application of self-similarity in general relativity. We review the mathematical and physical aspects of kinematic self-similar solutions in general relativity.

The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property results in great simplification of the governing partial differential equations. In addition, some self-similar solutions can describe the asymptotic behaviors of more general solutions. Newtonian gravity contains only one dimensional constant, the gravitational constant, while the general relativity contains another dimensional constant, the speed of light, besides the gravitational constant. Due to this crucial difference, incomplete similarity can be more interesting in general relativity than in Newtonian gravity. Kinematic self-similarity has been defined and studied as an example of incomplete similarity in general relativity, in an effort to pursue a wider application of self-similarity in general relativity. We review the mathematical and physical aspects of kinematic self-similar solutions in general relativity.

The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property results in great simplification of the governing partial differential equations. In addition, some self-similar solutions can describe the asymptotic behaviors of more general solutions. Newtonian gravity contains only one dimensional constant, the gravitational constant, while the general relativity contains another dimensional constant, the speed of light, besides the gravitational constant. Due to this crucial difference, incomplete similarity can be more interesting in general relativity than in Newtonian gravity. Kinematic self-similarity has been defined and studied as an example of incomplete similarity in general relativity, in an effort to pursue a wider application of self-similarity in general relativity. We review the mathematical and physical aspects of kinematic self-similar solutions in general relativity.

It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the kinetic energy operator which relation with the ususal one is consistent with corresponding relation of kinetic energies in special relativity theory. The Schr\"odinger equation with this operator gives new interesting possibilities for quantum phenomena description.

This article gives a brief summary on recently obtained classical lagrangians for the nonminimal fermion sector of the Standard-Model Extension (SME). Such lagrangians are adequate descriptions of classical particles that are subject to a Lorentz-violating background field based on the SME. Explicitly, lagrangians were obtained for the leading nonminimal contributions of the m, a, c, e, and f coefficients. These results were then used to interpret classical, kinematic tests of Special Relativity in the framework of the nonminimal SME. This led to new constraints on certain nonminimal controlling coefficients. Although the experiments were very sophisticated in the era when they were carried out, their sensitivities for detecting Lorentz violation were still far away from the Planck scale. Obtaining the novel constraints can be considered as a proof-of-principle demonstrating the applicability of the classical lagrangians computed.

In this work, we test consistency relations between a kinematic probe, the observational Hubble data, and a dynamical probe, the growth rates for cosmic large scale structure, which should hold if general relativity is the correct theory of gravity on cosmological scales. Moreover, we summarize the development history of parametrization in testings and make an improvement of it. Taking advantage of the Hubble parameter given from both parametric and non-parametric methods, we propose three equations and test two of them performed by means of two-dimensional parameterizations, including one using trigonometric functions we propose. As a result, it is found that the consistency relations satisfies well at $1\sigma$ CL and trigonometric functions turn out to be efficient tools in parameterizations. Furthermore, in order to confirm the validity of our test, we introduce a model of modified gravity, DGP model and compare the testing results in the cases of $\Lambda$CDM, "DGP in GR" and DGP model with mock data. It can be seen that it is the establishing of consistency relations which dominates the results of the testing. Overall, the present observational Hubble data and growth rate data favor convincingly that the general relativity is the correct theory of gravity on cosmological scales.

Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation of the transformations between them. There are two consistent ways of defining the inputs and outputs to describe the transformations and relative motion between the systems. The standard approach uses a mixture of the two ways. By formulating the principle of special and general relativity as a symmetry principle we are able to specify these transformations to depend only on a constant. The transformations become Galilean if the constant is zero. Validity of the Clock Hypothesis for uniformly accelerated systems implies zero constant. If the constant is not zero, we can introduce a metric under which the transformations become self adjoint. In case of inertial systems, the metric is the Minkowski metric and we obtain a unique invariant maximal velocity. The ball of the relativistically admissible velocities is a bounded symmetric domain under projective maps. For uniformly accelerated systems the existence of an invariant \textit{maximal acceleration} is predicted. This is the only method of describing transformations between uniformly accelerated systems without assuming the Clock Hypothesis.

Book Source: Digital Library of India Item 2015.221558 dc.contributor.author: Milne, E. A dc.date.accessioned: 2015-07-09T22:17:34Z dc.date.available: 2015-07-09T22:17:34Z dc.date.digitalpublicationdate: 2005-05-19 dc.date.citation: 1948 dc.identifier.barcode: 2990140053861 dc.identifier.origpath: /data_copy/upload/0053/866 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/221558 dc.description.scannerno: 4 dc.description.scanningcentre: Osmania University dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 258 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: At The Clarendon Press dc.rights: Not Available dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.subject.classification: General Mechanics. Mechanics Of Solid And Rigid Bodies dc.title: Kinematic Relativity

1Trials and Confessions of a Housekeeper

By T. S. Arthur

Is housekeeping such a trial? Mrs. Smith thinks so and confesses all in this merry account of her escapades and near disasters! (Summary by Kehinde)

2Off-Hand Sketches

By T. S. Arthur

The reader cannot but smile at some of the phases of life presented in this volume. Yet the smile will, in no case, the author thinks, be at the expense of humanity, good feeling, or virtue. Many of the incidents given, are facts embellished by a few touches of fancy. In all, lessons may be read that some, at least, will do well to lay to heart. (Summary by the author)

3State of the Union Addresses by United States Presidents (1877 - 1884)

By Chester A. Arthur and Rutherford B. Hayes

The State of the Union address is a speech presented by the President of the United States to a joint session of the United States Congress, typically delivered annually. The address not only reports on the condition of the nation but also allows the President to outline his legislative agenda (for which he needs the cooperation of Congress) and national priorities. This album contains recordings of addresses from Rutherford B. Hayes and Chester A. Arthur. - Summary by Wikipedia