Related papers: Topological Properties from Einstein's Equations?
We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well…
We show that for any perfect fluid in a static spacetime, if the Einstein constraint equation is satisfied and the temperature of the fluid obeys Tolman's law, then the other components of Einstein's equation are implied by the assumption…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…
The purpose of this paper is to demonstrate a new method of generating exact solutions to the Einstein's equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged…
The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\alpha\beta}$ of a spacetime with vanishing Ricci curvature $R_{\alpha,\beta}$ and prescribed initial data. Under the harmonic gauge condition, the…
In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively.…
All classes of spatially homogeneous space-time models are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of complete separation of variables according to type (2.1).…
In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
We present two methods for describing, from a pedagogical point of view, the solutions of Einstein's equations applied to a homogeneous and isotropic universe. In the first method, we define an effective gravitational potential of the…
We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…
We present a topological classification of vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology…
Motivated by the corrected form of the entropy-area law, and with the help of von Neumann entropy of quantum matter, we construct an emergent spacetime by the virtue of the geometric language of statistical information manifolds. We discuss…
It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…
We perform simulations in a gravitational collapsing model using the Einstein equations. In this paper, we review the equations for constructing the initial values and the evolution form of the Einstein equations called the BSSN…
We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve…
A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with…
We apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions…
We define the stretched future light cone, a timelike hypersurface composed of the worldlines of radially accelerating observers with constant and uniform proper acceleration. By attributing temperature and entropy to this hypersurface, we…
The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the…