相关论文: Solving Einstein's Equations With Dual Coordinate …
The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper…
Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial…
We present black hole type solutions in the scalar-tensor theory with nonminimal derivative coupling to the Einstein tensor. The effects of the nonminimal derivative coupling appear in the large scales, while the solutions approach those in…
A method of solving the Einstein equations with a scalar field is presented. It is applied to find higher dimensional vacuum metrics invariant under the group SO(n + 1) acting on n-dimensional spheres.
It is argued that, in order for the gravitational field to be propagated as a wave, it is necessary for it to satisfy a further set of field equations, in addition to those of Einstein and Hilbert, and these equations mean there is a…
We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We accomplish this by gluing Schwarzschild-de Sitter or Kerr-de…
Motivated by integrability of the sine-Gordon equation, we investigate a technique for constructing desired solutions to Einstein's equations by combining a dressing technique with a control-theory approach. After reviewing classical…
Recently one and two-parameter deformed Einstein equations have been studied for extremal quantum black holes which have been proposed to obey deformed statistics by Strominger. In this study, we give a deeper insight to the deformed…
The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon…
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be…
In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to…
We study the instability of Schwarzschild black holes and the appearance of scalarized solutions in Einstein-scalar-Gauss-Bonnet gravity performing a time-domain analysis in a perturbative scheme. First we consider a quadratic coupling…
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
The advancement in gravitational wave detection has made it possible to study the nonlinear effects in black hole perturbations, the modeling of which requires the full knowledge of the linear order perturbation of the metric. For the most…
This paper explores ``black hole'' solutions of various Einstein-wave matter systems admitting an isometry of their domain of outer communications taking every point to its future. In the first two parts, it is shown that such solutions,…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
Einstein's equations for stationary axisymmetric fields are reformulated as the equations for affine geodesics in a two--dimensional space. The affine collineations of this space are investigated and used to relate explicit solutions of…
We explore whether a new method to solve the constraints of Einstein's equations, which does not involve elliptic equations, can be applied to provide initial data for black holes. We show that this method can be successfully applied to a…