scholarly journals Some remarks on mathematical general relativity theory

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2403-2410
Author(s):  
Graham Hall
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Euclidean Geometry ◽  
Relativity Theory ◽  
Relativistic Cosmology ◽  
General Relativity Theory ◽  
Newtonian Theory

This paper gives a brief survey of the development of general relativity theory starting from Newtonian theory and Euclidean geometry and proceeding through to special relativity and finally to general relativity and relativistic cosmology.

VII.—On the Geometry of Dirac's Equations and their Expression in Tensor Form

1938 ◽  
Vol 57 ◽  
pp. 97-127 ◽  
Author(s):  
H. S. Ruse
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relativity Theory ◽  
Tensor Form ◽  
General Relativity Theory ◽  
Spinor Theory ◽  
Two Component

The purpose of the present paper is to give as simple an account as possible of the general-relativity theory of two-component spinors, and to investigate its geometrical and analytical consequences. The work was suggested by courses of lectures given at Edinburgh in 1932 and 1935 by Professor E. T. Whittaker, who, on the basis of the special-relativity spinor theory of van der Waerden (1929), obtained the completely tensorized form of Dirac's equations given by him in a recent paper (1937).

Energy transfer by gravitation in Newtonian theory

1960 ◽  
Vol 56 (4) ◽  
pp. 410-413 ◽  
Author(s):  
H. Bondi ◽  
W. H. McCrea
Keyword(s):  
General Relativity ◽  
Energy Transfer ◽  
Potential Energy ◽  
Gravitational Interaction ◽  
Empty Space ◽  
Relativity Theory ◽  
Gravitational Potential Energy ◽  
Mathematical Treatment ◽  
General Relativity Theory ◽  
Newtonian Theory

ABSTRACTThe problem is considered as to whether, in accordance with Newtonian theory, energy can be transferred from one system to another across empty space by gravitational interaction alone. Familiar examples of apparent energy transfer by this means do not give an unambiguous answer since they involve some net change of gravitational potential energy and this is not localized in the theory. Two examples are given here of systems in which the potential energy is the same at the beginning and end of an operation that does produce a resultant energy transfer. The establishment of this result is significant as a preliminary to the discussion of energy transfer according to general relativity theory. The appendix gives a particular illustration of one of the examples that admits exact mathematical treatment.

SOME CONSEQUENCES OF BORN'S RECIPROCAL RELATIVITY IN PHASE-SPACES

2011 ◽  
Vol 26 (21) ◽  
pp. 3653-3678 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
General Relativity ◽  
Time Delay ◽  
Phase Space ◽  
Special Relativity ◽  
Space Time ◽  
Relativity Theory ◽  
Relative Rotation ◽  
General Relativity Theory ◽  
Curved Space ◽  
Energy Dependent

We explore some novel consequences of Born's reciprocal relativity theory in flat phase-space and generalize the theory to the curved space–time scenario. We provide, in particular, six specific results resulting from Born's reciprocal relativity and which are not present in special relativity. These are: momentum-dependent time delay in the emission and detection of photons; energy-dependent notion of locality; superluminal behavior; relative rotation of photon trajectories due to the aberration of light; invariance of areas-cells in phase-space and modified dispersion relations. We finalize by constructing a Born reciprocal general relativity theory in curved space–time which requires the introduction of a complex Hermitian metric, torsion and nonmetricity. The latter procedure can be extended to the curved phase-space scenario.

scholarly journals Vaidya solutions in general covariant Hořava–Lifshitz gravity without projectability: Infrared limit

2014 ◽  
Vol 23 (08) ◽  
pp. 1450068 ◽  
Author(s):  
O. Goldoni ◽  
M. F. A. da Silva ◽  
G. Pinheiro ◽  
R. Chan
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Radiation Field ◽  
Relativity Theory ◽  
Covariant Theory ◽  
Spherically Symmetric ◽  
Theory U ◽  
General Relativity Theory ◽  
Infrared Limit ◽  
Symmetric Spacetime

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory (U(1) extension) of Hořava–Lifshitz (HL) gravity without the projectability condition and in the infrared (IR) limit. The Newtonian prepotential φ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava–Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field A should interact with the null radiation field of the Vaidya's spacetime in the HLT.

Propagators and commutators in general relativity

1962 ◽  
Vol 270 (1342) ◽  
pp. 342-345 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Relativity Theory ◽  
Quantum Field ◽  
General Relativity Theory ◽  
Free Fields

In this contribution, my purpose is to study a new mathematical instrument introduced by me in 1958-9: the tensor and spinor propagators. These propagators are extensions of the scalar propagator of Jordan-Pauli which plays an important part in quantum-field theory. It is possible to construct, with these propagators, commutators and anticommutators for the various free fields, in the framework of general relativity theory (see Lichnerowicz 1959 a, b, c , 1960, 1961 a, b, c ; and for an independent introduction of propagators DeWitt & Brehme 1960).

Seventeen Simple Lectures on General Relativity Theory

1983 ◽  
Vol 51 (1) ◽  
pp. 92-93 ◽  
Author(s):  
H. A. Buchdahl ◽  
Daniel M. Greenberger
Keyword(s):  
General Relativity ◽  
Relativity Theory ◽  
General Relativity Theory

Red shift of photon frequency in the gravitational field

2021 ◽  
Author(s):  
Jin Tong Wang ◽  
Jiangdi Fan ◽  
Aaron X. Kan
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Schrodinger Equation ◽  
Red Shift ◽  
Relativity Theory ◽  
Gravitational Redshift ◽  
General Relativity Theory ◽  
Photon Frequency

It has been well known that there is a redshift of photon frequency due to the gravitational potential. Scott et al. [Can. J. Phys. 44 (1966) 1639, https://doi.org/10.1139/p66-137 ] pointed out that general relativity theory predicts the gravitational redshift. However, using the quantum mechanics theory related to the photon Hamiltonian and photon Schrodinger equation, we calculate the redshift due to the gravitational potential. The result is exactly the same as that from the general relativity theory.

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