Einstein Equations Of Gravity Research Articles

Thermal spectrum of pseudo-scalar glueballs and Debye screening mass from holography

The finite temperature spectrum of pseudo-scalar glueballs in a plasma is studied using a holographic model. The 0^{-+} glueball is represented by a pseudo-scalar (axion) field living in a five dimensional geometry that comes from a solution of Einstein equations for gravity coupled with a dilaton scalar field. The spectral function obtained from the model shows a clear peak corresponding to the quasi-particle ground state. Analyzing the variation of the position of the peak with temperature, we describe the thermal behavior of the Debye screening mass of the plasma. As a check of consistency, the zero temperature limit of the model is also investigated. The glueball masses obtained are consistent with previous lattice results.

Time-parallel gravitational collapse simulation

This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar field. To account for the shrinking of the spatial domain in time, a tailored load balancing scheme is proposed and compared to load balancing based on number of time steps alone. The performance of Parareal is studied for both the sub-critical and black hole case; our experiments show that Parareal generates substantial speedup and, in the super-critical regime, can reproduce Choptuik's black hole mass scaling law.

Non-equilibrium thermodynamics of gravitational screens

We study the Einstein gravity equations projected on a timelike surface, which represents the time evolution of what we call a gravitational screen. We show that such a screen behaves like a viscous bubble with a surface tension and an internal energy, and that the Einstein equations take the same forms as non-equilibrium thermodynamic equations for a viscous bubble. We provide a consistent dictionary between gravitational and thermodynamic variables. In the non-viscous cases there are three thermodynamic equations that characterize a bubble dynamics: these are the first law, the Marangoni flow equation and the Young–Laplace equation. In all three equations the surface tension plays a central role: in the first law it appears as a work term per unit area, in the Marangoni flow its gradient drives a force, and in the Young–Laplace equation it contributes to a pressure proportional to the surface curvature. The gravity equations appear as a natural generalization of these bubble equations when the bubble itself is viscous and dynamical. In particular, this approach shows that the mechanism of entropy production for the viscous bubble is mapped onto the production of gravitational waves. We also review the relationship between surface tension and temperature, and discuss black-hole thermodynamics.

Absolute Maximum Proper Time to an Initial Event, the Curvature of Its Gradient along Conflict Strings and Matter

Einstein equation of gravity has on one side the momentum energy density tensor and on the other, Einstein tensor which is derived from Ricci curvature tensor. A better theory of gravity will have both sides geometric. One way to achieve this goal is to develop a new measure of time that will be independent of the choice of coordinates. One natural nominee for such time is the upper limit of measurable time form an event back to the big bang singularity. This limit should exist despite the singularity, otherwise the cosmos age would be unbounded. By this, the author constructs a scalar field of time. Time, however, is measured by material clocks. What is the maximal time that can be measured by a small microscopic clock when our curve starts at near the “big bang” event and ends at an event within the nucleus of an atom? Will our tiny clock move along geodesic curves or will it move in a non geodesic curve within matter? It is almost paradoxical that a test particle in General Relativity will always move along geodesic curves but the motion of matter within the particle may not be geodesic at all. For example, the ground of the Earth does not move at geodesic velocity. Where there is no matter, we choose a curve from near “big bang” to an event such that the time measured is maximal. Without assuming force fields, the gravitational field which causes that two or more such curves intersect at events, would cause discontinuity of the gradient of the upper limit of measurable time scalar field. The discontinuity can be avoided only if we give up on measurement along geodesic curves where there is matter. In other words, our tiny test particle clock will experience force when it travels within matter or near matter.

Some cosmological solutions of 5D Einstein equations with dark spinor condensate

We study the 5D Einstein gravity equations with dark spinor condensate, and under the cylinder condition we find an exponentially expanding cosmological solution for the scale factor of our universe, even without a cosmological constant. The stability condition for the solution is given. Some power-law cosmological solutions are also derived when bulk matter sources in the form of a perfect fluid are additionally introduced.

Thermodynamics of Black Holes from an Entropy Functional: An Other Approach Using Generalized Elasticity

In a series of recent papers Padmanabhan et al. derived Einstein equations for gravity by introducing an entropy functional for space-time viewed as an elastic medium. They showed that the same entropy functional applied to the thermodynamics of horizons yields an entropy that is always proportional to the area of the horizon. Following the same philosophy as theirs we first note that it may be arrived at Einstein equations, with a cosmological constant as an integration constant, using a slightly different route from theirs that also results in the same final expression for the entropy functional. We generalize the fundamental equations of three-dimensional elasticity to four dimensions and propose that the elastic deformation of space-time be constrained by those equations. A general Lagrangian describing the elastic deformation of space-time is deduced. When applied to the special case of a Schwarzschild black hole, viewed as an infinite line defect in space-time, the approach developed here permits to recover the black hole’s mass from the elastic deformation it caused to space-time, to reproduce the Hawking temperature, and to yield an entropy that is also in agreement with the Bekenstein-Hawking formula.

*‐Lie derivative, *‐covariant derivative and *‐gravity

AbstractThe Lie algebra of infinitesimal diffeomorphisms on noncommutative space allows to develop differential and Riemannian noncommutative geometry. Noncommutative Einstein's gravity equations are formulated.

Gauge theory of gravity and supergravity

We present a formulation of gravity in terms of a theory based on complex SU(2) gauge fields with a general coordinate invariant action functional quadratic in the field strength. Self-duality or anti-self-duality of the field strength emerges as a constraint from the equations of motion of this theory. This in turn leads to Einstein gravity equations for a dilaton and an axion conformally coupled to gravity for the self-dual constraint. The analysis has also been extended to N=1 and 2 super Yang-Mills theory of complex SU(2) gauge fields. This leads to, besides other equations of motion, self-duality/anti-self-duality of generalized supercovariant field strengths. The self-dual case is then shown to yield as its solutions N=1, 2 supergravity equations, respectively.

A NEW LOOK INTO THE GRAVITON MASS

We analyze the concept of graviton mass in the presence of a "cosmological" Λ term in Einstein equations of gravity. We point out a connection between the mass of the graviton and Λ.

Mach’s principle and hidden matter

According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor\(\hat \Theta _{ik}\) satisfying the relation\(\hat \Theta _{i;k}^k = 0\). The tensor\(\hat \Theta _{ik}\) is formed from the Einstein-Cartan torsion field given by the anholonomy objects, FAik=2hA[i,k], and appears together with Hilbert’s energy-momentum tensor T* ik and Poincare’s pressure λgik on the right-hand side of Einstein’s equations so that one has $$R_{ik} - (1/2)g_{ik} R = - \kappa T*_{ik} - \lambda g_{ik} - \hat \Theta _{ik}$$ According to this theory, in the universe and in cosmic systems one must excep “invisible masses” described by the Poincare and Einstein-Cartan terms to exist. The torsion field FAik makes the space-time a Machian universe; it is of the same nature as the “weak interacting matter” discussed in astrophysics.