scholarly journals TELEPARALLEL KILLING VECTORS OF THE EINSTEIN UNIVERSE

2008 ◽  
Vol 23 (13) ◽  
pp. 963-969 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
General Relativity ◽  
Lie Derivative ◽  
Einstein Universe ◽  
Killing Vectors ◽  
Rank Tensor ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Definition Of

In this paper we establish the definition of the Lie derivative of a second rank tensor in the context of teleparallel theory of gravity and also extend it for a general tensor of rank p + q. This definition is then used to find Killing vectors of the Einstein universe. It turns out that Killing vectors of the Einstein universe in the teleparallel theory are the same as in general relativity.

scholarly journals TELEPARALLEL ENERGY–MOMENTUM DISTRIBUTION OF STATIC AXIALLY SYMMETRIC SPACETIMES

2008 ◽  
Vol 23 (37) ◽  
pp. 3167-3177 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Momentum Distribution ◽  
Coupling Constant ◽  
Axially Symmetric ◽  
Symmetric Spacetimes ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Comparison Of The Results ◽  
Special Case

This paper is devoted to discuss the energy–momentum for static axially symmetric spacetimes in the framework of teleparallel theory of gravity. For this purpose, we use the teleparallel versions of Einstein, Landau–Lifshitz, Bergmann and Möller prescriptions. A comparison of the results shows that the energy density is different but the momentum turns out to be constant in each prescription. This is exactly similar to the results available in literature using the framework of general relativity. It is mentioned here that Möller energy–momentum distribution is independent of the coupling constant λ. Finally, we calculate energy–momentum distribution for the Curzon metric, a special case of the above-mentioned spacetime.

scholarly journals Energy-momentum of the Friedmann models in General Relativity and the teleparallel theory of gravity

2008 ◽  
Vol 86 (11) ◽  
pp. 1297-1302 ◽  
Author(s):  
M Sharif ◽  
M Jamil Amir
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Spherical Shell ◽  
Momentum Density ◽  
Friedmann Universe ◽  
Coupling Constant ◽  
Dimensionless Coupling ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Dimensionless Coupling Constant

This paper is devoted to the evaluation of the energy-momentum density components for the Friedmann models. For this purpose, we have used Møller’s pseudotensor prescription in General Relativity and a certain energy-momentum density developed from Møller’s teleparallel formulation. We show that the energy density of the closed Friedmann universe vanishes on the spherical shell at the radius ρ = 2[Formula: see text]. This coincides with the earlier results available in the literature. We also discuss the energy of the flat and open models. A comparison shows a partial consistency between Møller’s pseudotensor for General Relativity and teleparallel theory. Further, we show that the results are independent of the free dimensionless coupling constant of the teleparallel gravity.PACS No.: 04.20.–q

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

INHERITING SPACELIKE CONFORMAL KILLING VECTORS IN STRING COSMOLOGY

2003 ◽  
Vol 12 (05) ◽  
pp. 885-892 ◽  
Author(s):  
HÜSNÜ BAYSAL
Keyword(s):  
General Relativity ◽  
Cosmic Strings ◽  
String Cosmology ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Conformal Killing Vectors

We study the consequences of the existence of spacelike conformal Killing vectors (SpCKV) parallel to xa for cosmic strings and string fluid in the context of general relativity. The inheritance symmetries of the cosmic strings and string fluid are discussed in the case of SpCKV. Furthermore we examine proper homothetic spacelike Killing vectors for the cosmic strings and string fluid.

scholarly journals What are the wild waves saying? Yet another meditation on the predictions, searches for, and detections of gravitational waves

2018 ◽  
Vol 27 (14) ◽  
pp. 1830009
Author(s):  
Virginia Trimble
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Point Of View ◽  
Large Majority ◽  
Laboratory Apparatus ◽  
New Information ◽  
Theory Of Gravity ◽  
To Come ◽  
The Universe

A large majority of the physics and astronomy communities are now sure that gravitational waves exist, can be looked for, and can be studied via their effects on laboratory apparatus as well as on astronomical objects. So far, everything found out has agreed with the predictions of general relativity, but hopes are high for new information about the universe and its contents and perhaps for hints of a better theory of gravity than general relativity (which even Einstein expected to come eventually). This is one version of the story, from 1905 to the present, told from an unusual point of view, because the author was, for 28.5 years, married to Joseph Weber, who built the first detectors starting in the early 1960s and operated one or more until his death on 30 September 2000.

scholarly journals Foundations of a Theory of Gravity with a Constraint and Its Canonical Quantization

2021 ◽  
Vol 52 (1) ◽  
Author(s):  
Alexander P. Sobolev
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Early Universe ◽  
Canonical Quantization ◽  
Entropy Density ◽  
Maximum Temperature ◽  
Past Century ◽  
Physical Point ◽  
Theory Of Gravity ◽  
The Universe

AbstractThe gravitational equations were derived in general relativity (GR) using the assumption of their covariance relative to arbitrary transformations of coordinates. It has been repeatedly expressed an opinion over the past century that such equality of all coordinate systems may not correspond to reality. Nevertheless, no actual verification of the necessity of this assumption has been made to date. The paper proposes a theory of gravity with a constraint, the degenerate variants of which are general relativity (GR) and the unimodular theory of gravity. This constraint is interpreted from a physical point of view as a sufficient condition for the adiabaticity of the process of the evolution of the space–time metric. The original equations of the theory of gravity with the constraint are formulated. On this basis, a unified model of the evolution of the modern, early, and very early Universe is constructed that is consistent with the observational astronomical data but does not require the hypotheses of the existence of dark energy, dark matter or inflatons. It is claimed that: physical time is anisotropic, the gravitational field is the main source of energy of the Universe, the maximum global energy density in the Universe was 64 orders of magnitude smaller the Planckian one, and the entropy density is 18 orders of magnitude higher the value predicted by GR. The value of the relative density of neutrinos at the present time and the maximum temperature of matter in the early Universe are calculated. The wave equation of the gravitational field is formulated, its solution is found, and the nonstationary wave function of the very early Universe is constructed. It is shown that the birth of the Universe was random.

Sign in / Sign up

Export Citation Format

Share Document