Projectively Flat Spherically Symmetric Metrics

2018 ◽  
pp. 67-79
Author(s):  
Enli Guo ◽  
Xiaohuan Mo
Keyword(s):  
Spherically Symmetric ◽  
Projectively Flat ◽  
Symmetric Metrics

scholarly journals A Note on the Transformability of Spherically Symmetric Metrics

1953 ◽  
Vol 9 (1) ◽  
pp. 13-16 ◽  
Author(s):  
Paul Kustaanheimo
Keyword(s):  
Spherically Symmetric ◽  
Symmetric Metrics ◽  
Spherically Symmetric Metric

SummaryIt is shown that every spherically symmetric metric can be transformed into the isotropic form. As illustration an example is given.

Conformal vector fields of static spherically symmetric space-times in f(R, G) gravity

2020 ◽  
Vol 17 (08) ◽  
pp. 2050120
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
M. Ramzan ◽  
S. F. Hussain ◽  
Sabiha Qazi
Keyword(s):  
Symmetric Space ◽  
Current Literature ◽  
Vector Fields ◽  
Spherically Symmetric ◽  
Direct Integration ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Symmetric Metrics

Assuming the most general form of static spherically symmetric space-times, we search for the conformal vector fields in [Formula: see text] gravity by means of algebraic and direct integration approaches. In this study, there exist six cases which on account of further study yield conformal vector fields of dimension four, six and fifteen. During this study, we also recovered some well-known static spherically symmetric metrics announced in the current literature.

Killing vectors of static spherically symmetric metrics

1990 ◽  
Vol 31 (6) ◽  
pp. 1463-1463 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Asghar Qadir
Keyword(s):  
Spherically Symmetric ◽  
Killing Vectors ◽  
Symmetric Metrics

Harmonic sections of vector bundles with spherically symmetric metrics

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed T. K. Abbassi ◽  
Ibrahim Lakrini
Keyword(s):  
Riemannian Manifold ◽  
Vector Bundle ◽  
Critical Points ◽  
Vector Bundles ◽  
Energy Functional ◽  
Spherically Symmetric ◽  
Arbitrary Vector ◽  
Smooth Maps ◽  
Symmetric Metrics ◽  
Spherically Symmetric Metric

Abstract We equip an arbitrary vector bundle over a Riemannian manifold, endowed with a fiber metric and a compatible connection, with a spherically symmetric metric (cf. [4]), and westudy harmonicity of its sections firstly as smooth maps and then as critical points of the energy functional with variations through smooth sections.We also characterize vertically harmonic sections. Finally, we give some examples of special vector bundles, recovering in some situations some classical harmonicity results.

HOLOGRAPHIC SPHERICALLY SYMMETRIC METRICS

2007 ◽  
Vol 16 (06) ◽  
pp. 1603-1641 ◽  
Author(s):  
MICHAEL PETRI
Keyword(s):  
Energy Density ◽  
Degrees Of Freedom ◽  
Mass Density ◽  
Entropy Density ◽  
Constant Factor ◽  
Spherically Symmetric ◽  
Scale Invariant ◽  
Total Energy Density ◽  
Boundary Area ◽  
Symmetric Metrics

The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.

scholarly journals Velocity and velocity bounds in static spherically symmetric metrics

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Ivan Arraut ◽  
Davide Batic ◽  
Marek Nowakowski
Keyword(s):  
Radial Velocity ◽  
Density Profile ◽  
Local Minimum ◽  
Naked Singularity ◽  
Massless Particle ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Naked Singularities ◽  
Symmetric Metrics

AbstractWe find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in the different metrics and find that in cases with naked singularity there always exists a region where the massless particle moves with a velocity greater than the velocity of light in vacuum. In the case of Reissner-Nordström-de Sitter we completely characterize the velocity and the metric in an algebraic way. We contrast the case of classical naked singularities with naked singularities emerging from metric inspired by noncommutative geometry where the radial velocity never exceeds one. Furthermore, we solve the Einstein equations for a constant and polytropic density profile and calculate the radial velocity of a photon moving in spaces with interior metric. The polytropic case of radial velocity displays an unexpected variation bounded by a local minimum and maximum.

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