相关论文: A Minkowski inequality for the static Einstein-Max…

We obtain a two-parameter set of solutions, which represents a spherically symmetric space-time with a superposition of a neutral fluid and an electric field. The electromagnetic four-potential of this Einstein-Maxwell space-time is taken…

In the framework of the nonlinear stability of Minkowski spacetime, we show that if the radiation field of the curvature tensor vanishes, the spacetime must be flat.

The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of…

Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to…

If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…

We obtain Harnack estimates for a class of curvature flows in Riemannian manifolds of constant non-negative sectional curvature as well as in the Lorentzian Minkowski and de Sitter spaces. Furthermore, we prove a Harnack estimate with a…

In this note we consider the issue of the classical equivalence of scale-invariant gravity in the Einstein and in the Jordan frames. We first consider the simplest example $f(R)=R^{2}$ and show explicitly that the equivalence breaks down…

In this paper the application of the $M$-projective curvature tensor in the general theory of relativity has been studied. Firstly, we have proved that an $M$-projectively flat quasi-Einstein spacetime is of a special class with respect to…

A general relativistic model of a parallel-plate electrostatic capacitor is presented. The spacetime is a solution to the Einstein--Maxwell equations and involves class of solution previously studied by Vesel\'{y} and \v{Z}ofka (V\v{Z}). In…

We prove that the Inverse Mean Curvature Flow of a non-star-shaped, mean-convex embedded sphere in $\mathbb{R}^{n+1}$ with symmetry about an axis and sufficiently long, thick necks exists for all time and homothetically converges to a round…

Minkowski spacetime is a convenient setting for the study of the relativistic dynamics of particles and fields in the vacuum. In order to study events that occur in a dielectric or other linear medium, we adopt the familiar continuum…

We discuss quantum inequalities for minimally coupled scalar fields in static spacetimes. These are inequalities which place limits on the magnitude and duration of negative energy densities. We derive a general expression for the quantum…

We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the…

In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…

We prove global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindblad-Taylor, in which the Vlasov part is assumed to have…

In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space…

The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…

In this paper we study the static Einstein-Maxwell space when it is conformal to an $n$-dimensional pseudo-Euclidean space, which is invariant under the action of an $(n-1)$-dimensional translation group. We also provide a complete…

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the…