Republication of: A new class of vacuum solutions of the Einstein field equations

2009 ◽  
Vol 41 (10) ◽  
pp. 2485-2499 ◽  
Author(s):  
R. P. Kerr ◽  
A. Schild
Keyword(s):  
Einstein Field Equations ◽  
Field Equations ◽  
New Class ◽  
Vacuum Solutions

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.

CREATION OF A WORMHOLE DUE TO NONLINEAR ELECTRODYNAMICS

2002 ◽  
Vol 17 (20) ◽  
pp. 1305-1314 ◽  
Author(s):  
CARLA FONSECA-BARBATTI ◽  
M. NOVELLO ◽  
J. M. SALIM ◽  
REGINA C. ARCURI
Keyword(s):  
Magnetic Field ◽  
Quantum Electrodynamics ◽  
Nonlinear Electrodynamics ◽  
Einstein Field Equations ◽  
Field Equations ◽  
New Class ◽  
Effective Lagrangian ◽  
The One

We obtain a new class of solutions for the Einstein field equations which describe wormholes by using the one-loop effective Lagrangian of quantum electrodynamics. We also show that the derived wormholes can be maintained only by means of a magnetic field.

scholarly journals REMARKS ON PAPAPETROU CLASS OF VACUUM SOLUTIONS OF EINSTEIN EQUATIONS

2004 ◽  
Vol 13 (09) ◽  
pp. 1823-1830 ◽  
Author(s):  
A. V. KHUGAEV ◽  
B. J. AHMEDOV
Keyword(s):  
Gravitational Field ◽  
General Solution ◽  
Einstein Equations ◽  
Physical Application ◽  
Axially Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Spacetime Metric ◽  
Vacuum Solutions ◽  
Class Of Functions

Class of axially symmetric solutions of vacuum Einstein field equations including the Papapetrou solution as particular case has been found. It has been shown that the derived solution describes the external axial symmetric gravitational field of the source with nonvanishing mass. The general solution is obtained for this class of functions. As an example of physical application, the spacetime metric outside a line gravitomagnetic monopole has been obtained from Papapetrou solution of vacuum equations of gravitational field.

scholarly journals BULK VISCOUS SOLUTIONS TO THE FIELD EQUATIONS AND THE DECELERATION PARAMETER-REVISITED

2002 ◽  
Vol 11 (09) ◽  
pp. 1419-1434 ◽  
Author(s):  
ANIRUDH PRADHAN ◽  
I. AOTEMSHI
Keyword(s):  
Deceleration Parameter ◽  
Gravitational Constant ◽  
Mass Density ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Variable Cosmological Constant ◽  
New Class ◽  
Bulk Viscous Fluid ◽  
Bulk Viscous ◽  
Viscous Solutions

We utilise a form for the Hubble parameter to generate a number of solutions to the Einstein field equations with variable cosmological constant and variable gravitational constant in the presence of a bulk viscous fluid. The Hubble law utilised yields a constant value for the deceleration parameter. A new class of solutions is presented in the Robertson–Walker spacetimes. The coefficient of bulk viscosity is assumed to be a power function of the mass density. For a class of solutions, the deceleration parameter is negative which is consistent with the supernovae Ia observations.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals Geometries with mismatched branes

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Andreas Karch ◽  
Lisa Randall
Keyword(s):  
Boundary Conditions ◽  
Effective Action ◽  
Cosmological Models ◽  
Time Dependent ◽  
De Sitter ◽  
Stabilization Mechanism ◽  
New Class ◽  
Vacuum Solutions ◽  
Single Coordinate

Abstract We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

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