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.

NUMERICAL STUDY OF THE INTERACTION BETWEEN POSITIVE AND NEGATIVE MASS OBJECTS IN GENERAL RELATIVITY

2012 ◽  
Vol 21 (07) ◽  
pp. 1250061 ◽  
Author(s):  
ZHOUJIAN CAO
Keyword(s):  
Boundary Condition ◽  
General Relativity ◽  
Numerical Study ◽  
Naked Singularity ◽  
Newtonian Limit ◽  
Computational Domain ◽  
Positive Mass ◽  
Negative Mass ◽  
Mass Particle ◽  
Causal Property

Based on Baumgarte–Shapiro–Shibata–Nakamura formalism and moving puncture method, we demonstrate the first numerical evolutions of the interaction between positive and negative mass objects. Using the causal property of general relativity, we set our computational domain around the positive mass black hole while excluding the region around the naked singularity introduced by the negative mass object. Besides the usual Sommerfeld numerical boundary condition, an approximate boundary condition is proposed for this nonasymptotically-flat computational domain. Careful checks show that either boundary condition introduces smaller error than the numerical truncation errors. This is consistent with the causal property of general relativity. Except for the numerical truncation error and round-off error, our method gives an exact solution to the full Einstein's equation for a portion of spacetime with two objects whose masses have opposite signs. So our method opens the door for numerical explorations with negative mass objects. Based on this method, we investigate the Newtonian limit of spacetime with two objects whose masses have opposite sign. Our result implies that this spacetime does have a Newtonian limit which corresponds to a negative mass particle chasing a positive mass particle. This result sheds some light on an interesting debate about the Newtonian limit of a spacetime with positive and negative point masses.

Five-dimensional spherical gravitational collapse of anisotropic fluid with cosmological constant

2017 ◽  
Vol 14 (02) ◽  
pp. 1750025 ◽  
Author(s):  
Suhail Khan ◽  
Hassan Shah ◽  
Ghulam Abbas
Keyword(s):  
Cosmological Constant ◽  
Apparent Horizon ◽  
Physical Significance ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Hole Size ◽  
Junction Conditions ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Exterior Regions

Our aim is to study five-dimensional spherically symmetric anisotropic collapse with a positive cosmological constant (PCC). For this purpose, five-dimensional spherically symmetric and Schwarzschild–de Sitter metrics are chosen in the interior and exterior regions respectively. A set of junction conditions is derived for the smooth matching of interior and exterior spacetimes. The apparent horizon is calculated and its physical significance is studied. It comes out that the whole collapsing process is influenced by the cosmological constant. The collapsing process under the influence of cosmological constant slows down and black hole size also reduced.

scholarly journals General Relativity with a Positive Cosmological Constant Λ as a Gauge Theory

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 24
Author(s):  
Marta Dudek ◽  
Janusz Garecki
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Cosmological Constant ◽  
Gauge Field ◽  
Geometrical Interpretation ◽  
Positive Cosmological Constant ◽  
Four Dimensions ◽  
Action Integral ◽  
Fields Equations

In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–Palatini (EP) action, and then we present how Einstein fields equations can be derived from it. In the next section, we study Einstein–Palatini action integral for general relativity with a positive cosmological constant Λ in terms of the corrected curvature Ω c o r . We see that in terms of Ω c o r this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω c o r .

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.

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.

scholarly journals General Relativity with a Positive Cosmological Constant as a Gauge Theory.

2018 ◽  
Author(s):  
Marta Dudek ◽  
Janusz Garecki
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Cosmological Constant ◽  
Gauge Field ◽  
Geometrical Interpretation ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Positive Cosmological Constant

In the paper we show that the general relativity in recent Einstein-Palatini formulation is equivalent to a gauge field. We begin with a bit of information of the Einstein-Palatini formulation and derive Einstein field equations from it. In the next section, we consider general relativity with a positive cosmological constant in terms of the corrected curvature. We show that in terms of the corrected curvature general relativity takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature.

New Bondi-type outgoing boundary condition for the Einstein equations with cosmological constant

2015 ◽  
Vol 24 (10) ◽  
pp. 1550081 ◽  
Author(s):  
Xiaokai He ◽  
Zhoujian Cao
Keyword(s):  
Boundary Condition ◽  
Cosmological Constant ◽  
Minkowski Spacetime ◽  
Einstein Equations ◽  
Conformally Flat ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Original Boundary ◽  
Sitter Spacetime ◽  
The One

In the middle of last century, Bondi and his coworkers proposed an outgoing boundary condition for the Einstein equations. Recently, more and more observations imply that the Einstein equations should include a nonzero cosmological constant. A spacetime with a positive cosmological constant approaches to a de Sitter space asymptotically. Bondi's original boundary condition is not valid for these asymptotically de Sitter spacetimes. But the traditional conformally flat boundary condition excludes the gravitational radiation for the asymptotically de Sitter spacetimes. In this work, a new Bondi-type outgoing boundary condition based on Bondi–Sachs coordinates is considered. With this new boundary condition, the gravitational wave behavior for the asymptotically de Sitter spacetime is similar to the one for the asymptotically Minkowski spacetime. The traditional conformally flat boundary condition falls into a special subclass of the new boundary condition.

scholarly journals The shape of bouncing universes

2017 ◽  
Vol 26 (12) ◽  
pp. 1743016 ◽  
Author(s):  
John D. Barrow ◽  
Chandrima Ganguly
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Cosmological Constant ◽  
Inflexion Point ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Entropy Increase

What happens to the most general closed oscillating universes in general relativity? We sketch the development of interest in cyclic universes from the early work of Friedmann and Tolman to modern variations introduced by the presence of a cosmological constant. Then we show what happens in the cyclic evolution of the most general closed anisotropic universes provided by the Mixmaster universe. We show that in the presence of entropy increase its cycles grow in size and age, increasingly approaching flatness. But these cycles also grow increasingly anisotropic at their expansion maxima. If there is a positive cosmological constant, or dark energy, present then these oscillations always end and the last cycle evolves from an anisotropic inflexion point towards a de Sitter future of everlasting expansion.

Sign in / Sign up

Export Citation Format

Share Document