XXXVIII. Regraduation in spherically symmetric space-times of general relativity

1949 ◽  
Vol 40 (303) ◽  
pp. 428-434
Author(s):  
T.J. Willmore
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Spherically Symmetric

Stable wormhole models in general relativity under conformal symmetry

2021 ◽  
Vol 18 (03) ◽  
pp. 2150041
Author(s):  
Asifa Ashraf ◽  
Zhiyue Zhang
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Conformal Symmetry ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Shape Functions ◽  
The Stability ◽  
Tov Equation

In this study, we shall explore conformal symmetry to examine the wormhole models by considering traceless fluid. In this regard, we shall take anisotropic fluid with spherically symmetric space-time. Further, we shall calculate the properties of shape-functions, which are necessary for the existence of wormhole geometry. The presence of exotic matter is confirmed in all the cases through the violation of the Null Energy Condition. Furthermore, we have discussed the stability of wormhole solutions through the Tolman–Oppenheimer–Volkoff (TOV) equation. It is observed that our acquired solutions are stable under the particular values of involved parameters in different cases in conformal symmetry.

A REVIEW ON THE GEOMETRIC FORMULATION OF TOLMAN–BONDI EQUATIONS IN GENERAL RELATIVITY

2009 ◽  
Vol 06 (04) ◽  
pp. 595-617 ◽  
Author(s):  
IVANA BOCHICCHIO ◽  
MAURO FRANCAVIGLIA ◽  
ETTORE LASERRA
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Exact Solutions ◽  
Structural Properties ◽  
Spherically Symmetric ◽  
Principal Curvatures ◽  
Spherical Shells ◽  
Geometric Formulation ◽  
Dust Universe

This work is focused on spherically symmetric space-times. More precisely, geometric and structural properties of spatially spherical shells of a dust universe are analyzed in detail considering recent results of our research. Moreover, exact solutions, obtained for constant Ricci principal curvatures, are inferred and qualitatively analyzed through suitable classic analogies.

XIX.—A Theory of Regraduation in General Relativity

1946 ◽  
Vol 62 (2) ◽  
pp. 164-174
Author(s):  
A. G. Walker
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Special Form ◽  
The Other ◽  
Spherically Symmetric ◽  
Conservation Equations ◽  
Interesting Paper ◽  
Equivalence Theory ◽  
Two Alternatives

1. It was remarked by me a few years ago that temporal regraduations, other than trivial changes of zero and unit, had not so far been considered in General Relativity. An interesting paper by Dr G. C. McVittie has now appeared in which regraduations are examined in certain spherically symmetric space-times. Under the assumptions made by McVittie it is shown that regraduations can exist for some but not all space-times, those for which they can exist being of a very special form which excludes many space-times generally regarded as significant or interesting. In the present paper I take the matter further and discuss the problem with more generality. It will be shown that the existence of non-trivial regraduations depends firstly upon which theory is being assumed for the derivation of the conservation equations There are two alternatives, and regraduations are found to be excluded by one, the “geodesic” theory, but not necessarily by the other, the “equivalence” theory.

XVII.—The Regraduation of Clocks in Spherically Symmetric Space-times of General Relativity.

1946 ◽  
Vol 62 (2) ◽  
pp. 147-155
Author(s):  
G. C. McVittie
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Coordinate Transformation ◽  
Riemannian Space ◽  
Space Time ◽  
Spherically Symmetric ◽  
Dynamical Time

SummaryThe changes in his description of events brought about by an arbitrary regraduation of an observer's clock are examined, taking the axioms of general relativity as fundamental. It is shown that regraduation does not imply a change from one Riemannian space-time to another but merely a coordinate transformation within space-time. A generalisation of the “dynamical time” of kinematical relativity is a by-product of the investigation.

scholarly journals ENERGY OF SPHERICALLY SYMMETRIC SPACE–TIMES ON REGULARIZING TELEPARALLELISM

2010 ◽  
Vol 25 (14) ◽  
pp. 2883-2895 ◽  
Author(s):  
GAMAL G. L. NASHED
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Total Energy ◽  
Gravitational Energy ◽  
Spherically Symmetric ◽  
Tetrad Formulation ◽  
Spherically Symmetric Solutions

We calculate the total energy of an exact spherically symmetric solutions, i.e. Schwarzschild and Reissner–Nordström, using the gravitational energy–momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical. Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.

ISOMETRY HORIZONS IN SPHERICALLY SYMMETRIC SPACE–TIMES

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1263-1271
Author(s):  
J. SZENTHE
Keyword(s):  
Symmetric Space ◽  
Spherically Symmetric ◽  
Isometric Action ◽  
Event Horizons ◽  
Killing Horizons

Some event horizons in space–times that are invariant under an isometric action, considered first by Carter, are called isometry horizons, especially Killing horizons. In this paper, isometry horizons in spherically symmetric space–times are considered. It is shown that these isometry horizons are all Killing horizons.

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.

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