A SOLUTION OF THE EINSTEIN FIELD EQUATIONS

1960 ◽  
Vol 38 (12) ◽  
pp. 1661-1664
Author(s):  
Peter Rastall
Keyword(s):  
Empty Space ◽  
Time Dependent ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Gravitational Field Equations ◽  
Axis Of Symmetry ◽  
Time Dependent Solution ◽  
Empty Universe ◽  
Number Of Particles

An exact, cylindrically symmetric, time-dependent solution of the Einstein gravitational field equations for empty space is derived. A particular case of the solution has singularities only on the axis of symmetry and may represent a number of particles in an otherwise empty universe.

scholarly journals TRAPPING PHOTONS BY A LINE SINGULARITY

2003 ◽  
Vol 12 (06) ◽  
pp. 1095-1112 ◽  
Author(s):  
METIN ARIK ◽  
OZGUR DELICE
Keyword(s):  
Energy Density ◽  
Thin Shell ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Static Solutions ◽  
Line Singularity ◽  
Thick Shells

We present cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells. Positivity of the energy density of the thin shell and the line singularity is discussed. It is also shown that thick shells containing mostly radiation are possible in a numerical solution.

scholarly journals Emergence of a cosmological constant in anisotropic fluid cosmology

2021 ◽  
pp. 2150156
Author(s):  
M. Cadoni ◽  
A. P. Sanna
Keyword(s):  
Cosmological Constant ◽  
Large Scale ◽  
Spatial Scales ◽  
Time Dependent ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Coincidence Problem ◽  
Order Of Magnitude ◽  
Natural Way

In this paper, we investigate anisotropic fluid cosmology in a situation where the space–time metric back-reacts in a local, time-dependent way to the presence of inhomogeneities. We derive exact solutions to the Einstein field equations describing Friedmann–Lemaítre–Robertson–Walker (FLRW) large-scale cosmological evolution in the presence of local inhomogeneities and time-dependent backreaction. We use our derivation to tackle the cosmological constant problem. A cosmological constant emerges by averaging the backreaction term on spatial scales of the order of 100 Mpc, at which our universe begins to appear homogeneous and isotropic. We find that the order of magnitude of the “emerged” cosmological constant agrees with astrophysical observations and is related in a natural way to baryonic matter density. Thus, there is no coincidence problem in our framework.

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.

scholarly journals ON TIME-DEPENDENT BLACK HOLES AND COSMOLOGICAL MODELS FROM A KALUZA–KLEIN MECHANISM

2009 ◽  
Vol 24 (07) ◽  
pp. 1383-1415
Author(s):  
C. CASTRO ◽  
J. A. NIETO ◽  
L. RUIZ ◽  
J. SILVAS
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Model ◽  
Black Hole Entropy ◽  
Time Dependent ◽  
Einstein Field Equations ◽  
Schwarzschild Black Hole ◽  
Field Equations ◽  
Newman Black Hole ◽  
Kaluza Klein

Novel static, time-dependent and spatial–temporal solutions to Einstein field equations, displaying singularities, with and without horizons, and in several dimensions, are found based on a dimensional reduction procedure widely used in Kaluza–Klein-type theories. The Kerr–Newman black hole entropy as well as the Reissner–Nordstrom, Kerr and Schwarzschild black hole entropy are derived from the corresponding Euclideanized actions. A very special cosmological model based on the dynamical interior geometry of a black hole is found that has no singularities at t = 0 due to the smoothing of the mass distribution. We conclude with another cosmological model equipped also with a dynamical horizon and which is related to Vaidya's metric (associated with the Hawking radiation of black holes) by interchanging t ↔ r, which might render our universe a dynamical black hole.

scholarly journals Approximate Solutions of the Relativistic Gravitational Field Equations to Describe Clusters of Galaxies

1972 ◽  
Vol 25 (3) ◽  
pp. 299 ◽  
Author(s):  
MW Cook
Keyword(s):  
Gravitational Field ◽  
Approximate Solutions ◽  
Spherically Symmetric ◽  
Clusters Of Galaxies ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Stellar Objects ◽  
Gravitational Field Equations ◽  
Local Fluctuations ◽  
Region 10

Approximate solutions to the Einstein field equations are found which describe a spherically symmetric inhomogeneity in a general Robertson?Walker model, i.e. one with an arbitrary equation of state. The approximation hypothesis is that the pressure deviates only slightly from uniformity, and it is found that the density may have quite large local fluctuations, e.g. by a factor of 106 over a region 10-2 Mpc in diameter. Reference is made to observed data to determine which categories of stellar objects may be described by the results.

scholarly journals Quantum Theory of Gravitation

1998 ◽  
Vol 51 (3) ◽  
pp. 459
Author(s):  
H. S. Green
Keyword(s):  
Quantum Theory ◽  
Wave Equations ◽  
Algebraic Method ◽  
Empty Space ◽  
Space Time ◽  
Field Equations ◽  
Gauge Groups ◽  
Gravitational Field Equations ◽  
Non Euclidean Geometry ◽  
Curvature Tensors

It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein’s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein"s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) ⊗ SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation.

scholarly journals Relativistic models of thin disks immersed in a Robertson-Walker type spacetime

2013 ◽  
Vol 9 (18) ◽  
pp. 131-140
Author(s):  
Gonzalo García Reyes ◽  
Edwin García-Quintero
Keyword(s):  
Perfect Fluid ◽  
Time Dependent ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Ricci Collineations ◽  
Walker Metric ◽  
Relativistic Models ◽  
Thin Disks

Using the well known “displace, cut and reflect” method used to generate disks from given solutions of Einstein field equations, we construct somerelativistic models of time dependent thin disks of infinite extension made of a perfect fluid based on the Robertson-Walker metric. Two simple families of models of disks based on Robertson-Walker solutions admitting Matter and Ricci collineations are presented. We obtain disks that are inagreement with all the energy conditions.

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