scholarly journals INHOMOGENEOUS MULTIDIMENSIONAL COSMOLOGIES

2000 ◽  
Vol 15 (08) ◽  
pp. 531-539 ◽  
Author(s):  
SANTIAGO E. PEREZ BERGLIAFFA
Keyword(s):  
Space Time ◽  
Time Development ◽  
Energy Conditions ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
The Way

Einstein's equations for a (4 + n)-dimensional inhomogeneous space–time are presented, and a special family of solutions is exhibited for an arbitrary n. The solutions depend on two arbitrary functions of time. The time development of a particular member of this family is studied. This solution exhibits a singularity at t = 0 and dynamical compactification of the n dimensions. It is shown that the behavior of the system in the four-dimensional(i.e. post-compactification) phase is constrained by the way in which the compactified dimensions are stabilized. The fluid that generates this solution is analyzed by means of the energy conditions.

Physics as an Art Form

2018 ◽  
pp. 1-4
Author(s):  
Alvaro De Rújula
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Space Time ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Ockham’S Razor ◽  
Art Form ◽  
Ockham's Razor ◽  
The Universe ◽  
The Way

Beauty and simplicity, a scientist’s view. A first encounter with Einstein’s equations of General Relativity, space-time, and Gravity. Ockham’s Razor. Why the Universe is the way it is: The origin of the laws of Nature.

scholarly journals Einstein's equations and a cosmology with finite matter

2015 ◽  
Vol 30 (13) ◽  
pp. 1550068
Author(s):  
L. Clavelli ◽  
Gary R. Goldstein
Keyword(s):  
Infinite Number ◽  
Total Mass ◽  
Delta Function ◽  
Big Bang ◽  
Space Time ◽  
Matter Density ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
The Big Bang

We discuss various space–time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass.1 In this alternative cosmology, the matter density was postulated to be a spatial delta function at the time of the big bang thereafter diffusing outward with constant total mass. This proposal explores a departure from standard assumptions that the big bang occurred everywhere at once or was just one of an infinite number of previous and later transitions.

scholarly journals TOPOLOGICAL PROPERTIES FROM EINSTEIN'S EQUATIONS

2011 ◽  
Vol 03 ◽  
pp. 98-103
Author(s):  
EDMUNDO M. MONTE
Keyword(s):  
Dimensional Space ◽  
Computing System ◽  
Second Fundamental Form ◽  
Space Time ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Higher Dimensional ◽  
Algebraic Computing ◽  
Normal Vectors ◽  
Static Space

In this work we propose a new procedure on how to extract global information of a space-time. We consider a space-time immersed in a higher dimensional space and formulate the equations of Einstein through the Frobenius conditions of immersion. Through an algorithm and implementation into algebraic computing system we calculate normal vectors from the immersion to find the second fundamental form. We make an application for a static space-time with spherical symmetry. We solve Einstein's equations in the vacuum and obtain space-times with different topologies.

scholarly journals General Relativistic Wormhole Connections from Planck-Scales and the ER = EPR Conjecture

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 3 ◽  
Author(s):  
Fabrizio Tamburini ◽  
Ignazio Licata
Keyword(s):  
Physical Property ◽  
Space Time ◽  
The Novel ◽  
De Sitter ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Conformal Field ◽  
Low Energies ◽  
General Relativistic ◽  
Non Local

Einstein’s equations of general relativity (GR) can describe the connection between events within a given hypervolume of size L larger than the Planck length L P in terms of wormhole connections where metric fluctuations give rise to an indetermination relationship that involves the Riemann curvature tensor. At low energies (when L ≫ L P ), these connections behave like an exchange of a virtual graviton with wavelength λ G = L as if gravitation were an emergent physical property. Down to Planck scales, wormholes avoid the gravitational collapse and any superposition of events or space–times become indistinguishable. These properties of Einstein’s equations can find connections with the novel picture of quantum gravity (QG) known as the “Einstein–Rosen (ER) = Einstein–Podolski–Rosen (EPR)” (ER = EPR) conjecture proposed by Susskind and Maldacena in Anti-de-Sitter (AdS) space–times in their equivalence with conformal field theories (CFTs). In this scenario, non-traversable wormhole connections of two or more distant events in space–time through Einstein–Rosen (ER) wormholes that are solutions of the equations of GR, are supposed to be equivalent to events connected with non-local Einstein–Podolski–Rosen (EPR) entangled states that instead belong to the language of quantum mechanics. Our findings suggest that if the ER = EPR conjecture is valid, it can be extended to other different types of space–times and that gravity and space–time could be emergent physical quantities if the exchange of a virtual graviton between events can be considered connected by ER wormholes equivalent to entanglement connections.

scholarly journals A NEW PERSPECTIVE ON GRAVITY AND DYNAMICS OF SPACE–TIME

2005 ◽  
Vol 14 (12) ◽  
pp. 2263-2269 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Thermodynamic Limit ◽  
Space Time ◽  
Mathematical Framework ◽  
Surface Term ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Time Dynamics ◽  
New Perspective ◽  
Hilbert Action

The Einstein–Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self-contained, perspective on gravity and (ii) a concrete mathematical framework in which the description of space–time dynamics by Einstein's equations is similar to the description of a continuum solid in the thermodynamic limit.

scholarly journals FORM INVARIANT TRANSFORMATIONS BETWEEN n- AND m-DIMENSIONAL FLAT FRIEDMANN–ROBERTSON–WALKER COSMOLOGIES

2008 ◽  
Vol 17 (11) ◽  
pp. 1981-1989 ◽  
Author(s):  
MAURICIO CATALDO ◽  
LUIS P. CHIMENTO
Keyword(s):  
Energy Density ◽  
Space Time ◽  
Expansion Rate ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Duality Transformations ◽  
Isotropic Pressure ◽  
Symmetry Transformations ◽  
Friedmann Robertson Walker

We illustrate how a group of symmetry transformations, which preserve the form of the n-dimensional flat Friedmann–Robertson–Walker cosmologies satisfying Einstein's equations, act in any dimension. This group relates the energy density and the isotropic pressure of the cosmic fluid to the expansion rate. The freedom associated with the dimension of the space–time yields assisted inflation even when the energy density of the fluid is a dimensional invariant and enriches the set of duality transformations leading to phantom cosmologies.

scholarly journals GRAVITATIONAL TRAPPING FOR EXTENDED EXTRA DIMENSION

2002 ◽  
Vol 11 (10) ◽  
pp. 1639-1642 ◽  
Author(s):  
MERAB GOGBERASHVILI
Keyword(s):  
Cosmological Constant ◽  
Extra Dimension ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Newton's Law ◽  
Newton’S Law

The solution of Einstein's equations for 4-brane embedded in five-dimensional Anti-de Sitter space–time is found. It is shown that the cosmological constant can provide the existence of ordinary four-dimensional Newton's law and trapping of a matter on the brane.

On the analyticity of static vacuum solutions of Einstein's equations

1970 ◽  
Vol 67 (2) ◽  
pp. 415-421 ◽  
Author(s):  
H. Müller zum Hagen
Keyword(s):  
Coordinate System ◽  
Space Time ◽  
Coordinate Systems ◽  
Einstein’S Equations ◽  
Static Vacuum ◽  
Einstein's Equations ◽  
Vacuum Solutions ◽  
Vacuum Space

AbstractIt is shown that around each point of a C3static vacuum space-time there is a neighbourhood in which the metric is, in a certain suitable coordinate system, analytic. If two of these neighbourhoods overlap, then the transformation betweea these suitable coordinate systems is analytic (in the overlapping domain).

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