scholarly journals Sakharov Curvature in Rowlands Duality Spacetime: Do vacuum ‘spacetime forces’ curve matter?

2018 ◽  
Vol 1051 ◽  
pp. 012017
Author(s):  
S E Karam
Keyword(s):  
Vacuum Spacetime

scholarly journals CONSTRUCTING HYPERBOLIC SYSTEMS IN THE ASHTEKAR FORMULATION OF GENERAL RELATIVITY

2000 ◽  
Vol 09 (01) ◽  
pp. 13-34 ◽  
Author(s):  
GEN YONEDA ◽  
HISA-AKI SHINKAI
Keyword(s):  
General Relativity ◽  
Hyperbolic System ◽  
Hyperbolic Systems ◽  
Equations Of Motion ◽  
Well Posedness ◽  
Symmetric Hyperbolic System ◽  
The Cauchy Problem ◽  
Long Time ◽  
Vacuum Spacetime ◽  
Gauge Conditions

Hyperbolic formulations of the equations of motion are essential technique for proving the well-posedness of the Cauchy problem of a system, and are also helpful for implementing stable long time evolution in numerical applications. We, here, present three kinds of hyperbolic systems in the Ashtekar formulation of general relativity for Lorentzian vacuum spacetime. We exhibit several (I) weakly hyperbolic, (II) diagonalizable hyperbolic, and (III) symmetric hyperbolic systems, with each their eigenvalues. We demonstrate that Ashtekar's original equations form a weakly hyperbolic system. We discuss how gauge conditions and reality conditions are constrained during each step toward constructing a symmetric hyperbolic system.

scholarly journals Asymptotically flat vacuum solution in modified theory of Einstein’s gravity

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Surajit Kalita ◽  
Banibrata Mukhopadhyay
Keyword(s):  
General Relativity ◽  
Vacuum Solution ◽  
Compact Objects ◽  
Schwarzschild Solution ◽  
Asymptotically Flat ◽  
Symmetric Vacuum ◽  
Theory Of Gravity ◽  
Bound Orbits ◽  
Vacuum Spacetime ◽  
The Universe

Abstract A number of recent observations have suggested that the Einstein’s theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to surpass the general relativity which explains a number of phenomena where Einstein’s theory of gravity fails. In the f(R) gravity, behaviour of the spacetime is modified as compared to that of given by the Einstein’s theory of general relativity. This theory has already been explored for understanding various compact objects such as neutron stars, white dwarfs etc. and also describing evolution of the universe. Although researchers have already found the vacuum spacetime solutions for the f(R) gravity, yet there is a caveat that the metric does have some diverging terms and hence these solutions are not asymptotically flat. We show that it is possible to have asymptotically flat spherically symmetric vacuum solution for the f(R) gravity, which is different from the Schwarzschild solution. We use this solution for explaining various bound orbits around the black hole and eventually, as an immediate application, in the spherical accretion flow around it.

scholarly journals Dark matter effects in vacuum spacetime

2010 ◽  
Vol 82 (2) ◽  
Author(s):  
Luca Rizzi ◽  
Sergio L. Cacciatori ◽  
Vittorio Gorini ◽  
Alexander Kamenshchik ◽  
Oliver F. Piattella
Keyword(s):  
Dark Matter ◽  
Matter Effects ◽  
Vacuum Spacetime

scholarly journals Is classical flat Kasner spacetime flat in quantum gravity?

2016 ◽  
Vol 25 (08) ◽  
pp. 1642001 ◽  
Author(s):  
Parampreet Singh
Keyword(s):  
Quantum Gravity ◽  
Minkowski Spacetime ◽  
Quantum Geometry ◽  
Classical Level ◽  
Bianchi I ◽  
Spacetime Curvature ◽  
Loop Quantization ◽  
Universal Bounds ◽  
Vacuum Spacetime ◽  
Geometric Effects

Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology (LQC). We find that even though the spacetime curvature vanishes at the classical level, nontrivial quantum gravitational effects can arise. For the standard loop quantization of Bianchi-I spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a physical solution of the effective spacetime description, except in a limit. The lack of a flat Kasner metric at the quantum level results from a novel feature of the loop quantum Bianchi-I spacetime: quantum geometry induces nonvanishing spacetime curvature components, making it not Ricci flat even when no matter is present. The noncurvature singularity of the classical flat Kasner spacetime is avoided, and the effective spacetime transits from a flat Kasner spacetime in asymptotic future, to a Minkowski spacetime in asymptotic past. Interestingly, for an alternate loop quantization which does not share some of the fine features of the standard quantization, flat Kasner spacetime with expected classical features exists. In this case, even with nontrivial quantum geometric effects, the spacetime curvature vanishes. These examples show that the character of even a flat classical vacuum spacetime can alter in a fundamental way in quantum gravity and is sensitive to the quantization procedure.

scholarly journals Maximal slicing ofD-dimensional spherically symmetric vacuum spacetime

2009 ◽  
Vol 80 (8) ◽  
Author(s):  
Ken-ichi Nakao ◽  
Hiroyuki Abe ◽  
Hirotaka Yoshino ◽  
Masaru Shibata
Keyword(s):  
Spherically Symmetric ◽  
Symmetric Vacuum ◽  
Vacuum Spacetime

c-boundary of Taub’s plane-symmetric static vacuum spacetime

1986 ◽  
Vol 33 (6) ◽  
pp. 1533-1537 ◽  
Author(s):  
Kuang zhi-quan ◽  
Li jian-zeng ◽  
Liang can-bin
Keyword(s):  
Static Vacuum ◽  
Plane Symmetric ◽  
Vacuum Spacetime

scholarly journals New tensorial estimates in Besov spaces for time-dependent (2 + 1)-dimensional problems

2014 ◽  
Vol 11 (04) ◽  
pp. 821-908
Author(s):  
Arick Shao
Keyword(s):  
Primary Objective ◽  
Null Cone ◽  
Trace Theorems ◽  
Einstein Vacuum ◽  
Bondi Mass ◽  
Vacuum Spacetime ◽  
Bondi Energy ◽  
Funct Anal ◽  
Invent Math ◽  
Causal Geometry

In this paper, we consider various tensorial estimates in geometric Besov-type norms on a one-parameter foliation of surfaces with evolving geometries. Moreover, we wish to accomplish this with only very weak control on these geometries. Several of these estimates were proved in [S. Klainerman and I. Rodnianski, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math. 159 (2005) 437–529; S. Klainerman and I. Rodnianski, Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux, Geom. Funct. Anal. 16(3) (2006) 164–229], but in very specific settings. A primary objective of this paper is to significantly simplify and make more robust the proofs of the estimates. Another goal is to generalize these estimates to more abstract settings. In [S. Alexakis and A. Shao, On the geometry of null cones to infinity under curvature flux bounds, Class. Quantum Grav. 31 (2014) 195012], we will apply these estimates in order to consider a variant of the problem in [S. Klainerman and I. Rodnianski, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math. 159 (2005) 437–529], that of a truncated null cone in an Einstein-vacuum spacetime extending to infinity. This analysis will then be used in [S. Alexakis and A. Shao, Bounds on the Bondi energy by a flux of curvature, to appear in J. Eur. Math. Soc.] to study and to control the Bondi mass and the angular momentum under minimal conditions.

scholarly journals LEVI–CIVITA SPACETIMES IN MULTIDIMENSIONAL THEORIES

2009 ◽  
Vol 24 (21) ◽  
pp. 1659-1667 ◽  
Author(s):  
J. PONCE DE LEON
Keyword(s):  
Dimensional Reduction ◽  
Separation Of Variables ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Reduction Procedure ◽  
Cylindrically Symmetric ◽  
Static Solutions ◽  
Symmetric Vacuum ◽  
Vacuum Spacetime ◽  
Vacuum Solutions

We obtain the most general static cylindrically symmetric vacuum solutions of the Einstein field equations in (4 + N) dimensions. Under the assumption of separation of variables, we construct a family of Levi–Civita–Kasner vacuum solutions in (4 + N) dimensions. We discuss the dimensional reduction of the static solutions. Depending on the reduction procedure, they can be interpreted either as a scalar-vacuum generalization of Levi–Civita spacetimes, or as the effective 4D vacuum spacetime outside of an idealized string in braneworld theory.

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