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We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we…
The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of…
A classical model for the extension of singular spacetime geometries across their singularities is presented. The regularization introduced by this model is based on the following observation. Among the geometries that satisfy Einstein's…
The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the…
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by…
We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…
Wormholes are non-trivial topological structures that arise as exact solutions to Einstein's field equations, theoretically connecting distinct regions of spacetime via a throat-like geometry. While static traversable wormholes necessarily…
We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases…
In this work, we introduce an analytical approximate black hole solution in Einstein-Cubic gravity. To obtain complete solutions, we construct the near horizon and asymptotic solutions as the first step. Then, the approximate analytic…
In this work we analyze traversable wormhole spacetimes in the framework of a covariant generalization of Einstein's General Relativity known as energy-momentum squared gravity, or $f\left(R,\mathcal T\right)$ gravity, where $R$ is the…
Solutions of an optimization problem are sensitive to changes caused by approximations or parametric perturbations, especially in the nonconvex setting. This paper shows that solutions of substitute problems, constructed from Rockafellian…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
Within a semiclassical framework, we investigate spherically symmetric solutions of the Einstein equations that (i) develop a trapped region within a finite time as measured by distant observers, and (ii) remain sufficiently regular at the…
In this thesis, we wish to examine the black-hole solutions of modified gravity theories inspired by String Theory or Cosmology. Namely, these modifications will take the guise of additional gauge and scalar fields for the so-called…
The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
Recent perturbative studies have shown the existence of long-lived, quasi-stationary configurations of scalar fields around black holes. In particular, such configurations have been found to survive for cosmological timescales, which is a…