相关论文: Perturbative Solutions of the Extended Constraint …

More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein - Maxwell equations were made and gave rise to constructions of…

Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this…

A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…

We study the Einstein-Lichnerowicz constraints system, obtained through the conformal method when addressing the initial data problem for the Einstein equations in a scalar field theory. We prove that this system is stable with respect to…

Einstein field equations with a cosmological constant are approximated to the second order in the perturbation to a flat background metric. The final result is a set of Einstein-Maxwell-Proca equations for gravity in the weak field regime.…

We explore black hole solutions and some of its physical properties in Einstein's theory in 4D, modified by a cubic gravity term and in the presence of non-linear electrodynamics. In the context of Effective Field Theories (EFT) and under…

The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved…

We first show that the connected sum along submanifolds introduced by the second author for compact initial data sets of the vacuum Einstein system can be adapted to the asymptotically Euclidean and to the asymptotically hyperbolic context.…

We show that the class of hyperelliptic solutions to the Ernst equation (the stationary axisymmetric Einstein equations in vacuum) previously discovered by Korotkin and Neugebauer and Meinel can be derived via Riemann-Hilbert techniques.…

We study in some detail the "extended Kerr-Schild" formulation of general relativity, which decomposes the gauge-independent degrees of freedom of a generic metric into two arbitrary functions and the choice of a flat background tetrad. We…

In this paper we perform systematic investigation of all possible exponential solutions in Einstein-Gauss-Bonnet gravity with the spatial section being a product of two subspaces. We describe a scheme which always allow to find solution for…

It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…

We consider the background cosmological solutions in the $6D$ (six-dimensional) model with one time and five space coordinates. The theory of our interest has the action composed by the Einstein term, cosmological constant, and two…

All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat…

In this paper we perform systematic investigation of all possible solutions with static compact extra dimensions and expanding three-dimensional subspace (``our Universe''). Unlike previous papers, we consider extra-dimensional subspace to…

The Einstein-Maxwell (E-M) equations in a curved spacetime that admits at least one Killing vector are derived, from a Lagrangian density adapted to symmetries. In this context, an auxiliary space of potentials is introduced, in which, the…

In this work, we use the global analysis and degree-theoretic methods introduced by Smale to study the existence and multiplicity of solutions of the vacuum Einstein constraint equations given by the conformal method of…

We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…

Using perturbative expansion in terms of powers of the rotation parameter $a$ we construct the axisymmetric and asymptotically flat black-hole metric in the $D$-dimensional Einstein-Gauss-Bonnet theory. In five-dimensional spacetime we find…