A resolution of a metric singularity associated with the introduction of Λ into static spherically symmetric systems

2017 ◽  
Vol 26 (04) ◽  
pp. 1750039 ◽  
Author(s):  
Thomas E. Kiess
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Cosmological Parameters ◽  
Classical General Relativity ◽  
Spherically Symmetric ◽  
Astronomical Observations ◽  
Ordinary Matter ◽  
Physical Systems ◽  
General Relativistic ◽  
Symmetric Systems

We resolve a metric singularity at large [Formula: see text] that is due to the introduction of the cosmological constant [Formula: see text] in simple static spherically symmetric systems in classical general relativity for a mass bounded within a radius [Formula: see text]. For the metric to be nonsingular, we find that ordinary matter must exist beyond [Formula: see text], and that mass densities and [Formula: see text] must have spatial ranges. These features can be developed covariantly and can ameliorate discrepancies between theoretical values of [Formula: see text] and those derived from astronomical observations. Requiring a nonsingular metric in classical general relativistic modeling of this and other physical systems has the potential to offer suggestive insights into cosmological parameters.

Relativistic Stellar Dynamics in Rotating Axially Symmetric Systems

1968 ◽  
Vol 1 (3) ◽  
pp. 86-87 ◽  
Author(s):  
E.D. Fackerell
Keyword(s):  
General Relativity ◽  
Star Clusters ◽  
Stellar Dynamics ◽  
Spherically Symmetric ◽  
Axially Symmetric ◽  
Relativistic Star ◽  
General Relativistic ◽  
Stellar Sources ◽  
Symmetric Systems

Recently the possibility has been raised of using general relativistic star clusters as models for quasi-stellar sources. The theory of static, spherically symmetric, collisionless star clusters has been developed within the framework of general relativity. In particular, analogues have been found of the Newtonian polytropic models and of Woolley’s truncated Maxwellian systems. However, in view of the importance of rotation on stability in relativistic astrophysical problems, it is of considerable interest to include the effect of rotation in relativistic stellar dynamics.

scholarly journals SPHERICALLY SYMMETRIC GRAVITATIONAL COLLAPSE OF A DUST CLOUD IN EINSTEIN–GAUSS–BONNET GRAVITY

2011 ◽  
Vol 26 (28) ◽  
pp. 2135-2147 ◽  
Author(s):  
KANG ZHOU ◽  
ZHAN-YING YANG ◽  
DE-CHENG ZOU ◽  
RUI-HONG YUE
Keyword(s):  
Cosmological Constant ◽  
Gravitational Collapse ◽  
Dust Cloud ◽  
Spherically Symmetric ◽  
Relativistic Case ◽  
Bonnet Gravity ◽  
Profound Influence ◽  
Dimensional Spacetime ◽  
General Relativistic ◽  
Bonnet Term

We explore the gravitational collapse of a spherically symmetric dust cloud in the Einstein–Gauss–Bonnet gravity without a cosmological constant, and obtain three families of LTB-like solutions. It is shown that the Gauss–Bonnet term has a profound influence on the nature of singularities, and the global structure of spacetime changes drastically from the analogous general relativistic case. Interestingly, the formation of a naked, massive and uncentral singularity, allowed in five-dimensional spacetime, is forbidden if D≥6. Moreover, such singularity is gravitational strong and a serious counterexample to CCH.

HALOS OF MODIFIED GRAVITY

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2555-2562 ◽  
Author(s):  
KIRILL KRASNOV ◽  
YURI SHTANOV
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Cosmological Constant ◽  
Modified Gravity ◽  
Alternative Explanation ◽  
Gravitational Mass ◽  
Spherically Symmetric ◽  
Simple Modification ◽  
Type Ia ◽  
Supernova Type Ia

We describe how a certain simple modification of general relativity, in which the local cosmological constant is allowed to depend on the space–time curvature, predicts the existence of halos of modified gravity surrounding spherically symmetric objects. We show that the gravitational mass of an object weighed together with its halo can be much larger than its gravitational mass as seen from inside the halo. This effect could provide an alternative explanation of the dark-matter phenomenon in galaxies. In this case, the local cosmological constant in the solar system must be some six orders of magnitude larger than its cosmic value obtained in the supernova type Ia experiments. This is well within the current experimental bounds, but may be directly observable in future high-precision experiments.

scholarly journals NEUTRON STAR CORES IN THE GENERAL RELATIVISTIC THOMAS-FERMI TREATMENT

2013 ◽  
Vol 23 ◽  
pp. 185-192
Author(s):  
RICCARDO BELVEDERE ◽  
JORGE A. RUEDA ◽  
REMO RUFFINI
Keyword(s):  
General Relativity ◽  
Neutron Stars ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Strong Interactions ◽  
Spherically Symmetric ◽  
The Core ◽  
General Relativistic ◽  
The Mean

We introduce a new set of equations to describe the equilibrium of the core of neutron stars, composed by self-gravitating degenerate neutrons, protons and electrons in β-equilibrium. We take into account strong, weak, electromagnetic and gravitational interactions within the framework of general relativity. We extend the conditions of equilibrium based on the constancy of the Klein potentials to the strongly interactive case. The strong interactions between nucleons are modeled through the exchange of the σ, ω and ρ virtual mesons. The equations are solved numerically in the case of zero temperatures and for a non-rotating spherically symmetric neutron stars in the mean-field approximation.

scholarly journals Radar time delays in the dynamic theory of gravity

2004 ◽  
pp. 49-54
Author(s):  
I.I. Haranas
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Time Delays ◽  
Dynamic Theory ◽  
Dimensional Space ◽  
Gravity Potential ◽  
Spherically Symmetric ◽  
Time Element ◽  
General Relativistic ◽  
Theory Of Gravity

There is a new theory gravity called the dynamic theory, which is derived from thermodynamic principles in a five dimensional space, radar signals traveling times and delays are calculated for the major planets in the solar system, and compared to those of general relativity. This is done by using the usual four dimensional spherically symmetric space-time element of classical general relativistic gravity which has now been slightly modified by a negative inverse radial exponential term due to the dynamic theory of gravity potential.

SPHERICALLY SYMMETRIC SCALAR FIELD IN GENERAL RELATIVITY

1996 ◽  
Vol 11 (30) ◽  
pp. 2409-2415 ◽  
Author(s):  
FERNANDO KOKUBUN
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Scalar Field ◽  
Field Distribution ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Ordinary Matter ◽  
Spherically Symmetric Distribution

We analyze the presence of a scalar field around a spherically symmetric distribution of an ordinary matter, obtaining an exact solution for a given scalar field distribution.

scholarly journals THE CONSISTENT NEWTONIAN LIMIT OF EINSTEIN'S GRAVITY WITH A COSMOLOGICAL CONSTANT

2001 ◽  
Vol 10 (05) ◽  
pp. 649-661 ◽  
Author(s):  
MAREK NOWAKOWSKI
Keyword(s):  
Boundary Condition ◽  
General Relativity ◽  
Cosmological Constant ◽  
Mass Distribution ◽  
Newtonian Limit ◽  
Spherically Symmetric ◽  
Maximum Mass ◽  
Finite Range ◽  
Positive Cosmological Constant ◽  
The Poisson Equation

We derive the "exact" Newtonian limit of general relativity with a positive cosmological constant Λ. We point out that in contrast to the case with Λ=0, the presence of a positive Λ in Einsteins's equations enforces, via the condition |Φ|≪1 on the potential Φ, a range ℛ max (Λ)≫r≫ℛ min (Λ), within which the Newtonian limit is valid. It also leads to the existence of a maximum mass, ℳ max (Λ). As a consequence we cannot put the boundary condition for the solution of the Poisson equation at infinity. A boundary condition suitably chosen now at a finite range will then get reflected in the solution of Φ provided the mass distribution is not spherically symmetric.

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