Screening vector field modifications of general relativity

A discussion is given of the sectional curvature function on a four-dimensional Lorentz manifold and, in particular, on the space–time of Einstein's general relativity theory. Its tight relationship to the metric tensor is demonstrated and some of its geometrical and algebraic properties evaluated. The concept of a sectional curvature preserving symmetry, in the form of a certain smooth vector field, is introduced and discussed.

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Homothetic vector field in plane symmetric Bianchi type-I cosmological model in Lyra geometry

Modern Physics Letters A ◽

10.1142/s0217732314501168 ◽

2014 ◽

Vol 29 (22) ◽

pp. 1450116 ◽

Cited By ~ 6

Author(s):

Ragab M. Gad ◽

A. S. Alofi

Keyword(s):

General Relativity ◽

Vector Field ◽

Riemannian Geometry ◽

Bianchi Type ◽

Displacement Vector ◽

Lyra Geometry ◽

Type I ◽

Bianchi Type I ◽

Plane Symmetric ◽

Homothetic Vector

In this paper, we obtain a homothetic vector field of a plane symmetric Bianchi type-I spacetime based on Lyra geometry. We discuss the cases when the displacement vector is function of t and when it is constant. We investigate the equation of state in both two cases. A comparison between the obtained results, using Lyra geometry, and that have obtained previously in the context of General Relativity (GR), based on Riemannian geometry, will be given.

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Conserved quantities of spinning test particles in general relativity. I

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1981.0046 ◽

1981 ◽

Vol 375 (1761) ◽

pp. 185-193 ◽

Cited By ~ 14

Keyword(s):

General Relativity ◽

Vector Field ◽

Tensor Field ◽

General Scheme ◽

Killing Vector ◽

Conserved Quantity ◽

General Linear ◽

Killing Vector Field ◽

Conserved Quantities ◽

Test Particles

This is the first of two papers devoted to conserved quantities of spinning test particles in general relativity. In this paper, a general scheme is described according to which these quantities can be investigated. It is shown that the general linear conserved quantity consists of a sum, the first term of which is the well known expression constructed from a Killing vector field, and the second term is of the form U kl S kl , where U* ab is a Killing-Yano tensor field, which is constrained by two additional equations.

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Total Conserved Charges of Kerr-Newman Spacetimes in Gravity Theory Using a Poincaré Gauge Version of the Teleparallel Equivalent of General Relativity

Advances in High Energy Physics ◽

10.1155/2013/692505 ◽

2013 ◽

Vol 2013 ◽

pp. 1-16

Author(s):

Gamal G. L. Nashed

Keyword(s):

General Relativity ◽

Angular Momentum ◽

Vector Field ◽

Gravity Theory ◽

Arbitrary Vector ◽

Conserved Charges ◽

Conserved Currents ◽

Total Conserved Charges

The total conserved charges of several tetrad spacetimes, generating the Kerr-Newman (KN) metric, are calculated using the approach of invariant conserved currents generated by an arbitrary vector field that reproduces a diffeomorphism on the spacetime. The accompanying charges of some tetrads give the known value of energy and angular momentum, while those of other tetrads give, in addition to the unknown format charges, a divergent entity. Therefore, regularized expressions are considered also to get the commonly known form of conserved charges of KN.

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Canonical transformation path to gauge theories of gravity-II: Space-time coupling of spin-0 and spin-1 particle fields

International Journal of Modern Physics E ◽

10.1142/s0218301319500071 ◽

2019 ◽

Vol 28 (01n02) ◽

pp. 1950007 ◽

Cited By ~ 2

Author(s):

J. Struckmeier ◽

J. Muench ◽

P. Liebrich ◽

M. Hanauske ◽

J. Kirsch ◽

...

Keyword(s):

General Relativity ◽

Gravitational Field ◽

Vector Field ◽

Vector Fields ◽

Energy Momentum Tensor ◽

Scalar Fields ◽

Momentum Tensor ◽

Space Time ◽

Complex Scalar ◽

Time Dynamics

The generic form of space-time dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the principle of general relativity. It was thus shown that Einstein’s general relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the “free” (uncoupled) gravitational field, and (ii) the energy–momentum tensor is that of scalar fields representing real or complex structureless (spin-[Formula: see text]) particles. It followed that all other source fields — such as vector fields representing massive and nonmassive spin-[Formula: see text] particles — need careful scrutiny of the appropriate source tensor. This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field. We show that different couplings emerge for massive and nonmassive vector fields. The massive vector field has the canonical energy–momentum tensor as the appropriate source term — which embraces also the energy density furnished by the internal spin. In this case, the vector fields are shown to generate a torsion of space-time. In contrast, the system of a massless and charged vector field is associated with the metric (Hilbert) energy–momentum tensor due to its additional [Formula: see text] symmetry. Moreover, such vector fields do not generate a torsion of space-time. The respective sources of gravitation apply for all models of the dynamics of the “free” (uncoupled) gravitational field — which do not follow from the gauge formalism but must be specified based on separate physical reasoning.

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