Related papers: The Stability of Lorentzian Space-Time
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
The Lorentzian metric structure used in any field theory allows one to implement the relativistic notion of causality and to define a notion of time dimension. This article investigates the possibility that at the microscopic level the…
We provide a short introduction to ``Lorentzian metric spaces" i.e., spacetimes defined solely in terms of the two-point Lorentzian distance. As noted in previous work, this structure is essentially unique if minimal conditions are imposed,…
In this short note we argue that, even if, as sometimes remarked, a Lorentzian manifold does not model correctly the structure of the spatio-temporal continuum as it is, yet a Lorentzian manifold should describe its macroscopic structure as…
In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that…
I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a…
The requirements for stability of a Lorentz violating theory are analyzed. In particular we conclude that Einstein-aether theory can be stable when its modes have any phase velocity, rather than only the speed of light as was argued in a…
In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…
We consider a Lorentzian metric in $\mathbb{R}\times\mathbb{R}^n$. We show that if we know the lengths of the space-time geodesics starting at $(0,y,\eta)$ when $t=0$, then we can recover the metric at $y$. We prove the rigidity of…
Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric…
Let g be a G-invariant Einstein metric on a compact homogeneous space M=G/K. We use a formula for the Lichnerowicz Laplacian of g at G-invariant TT-tensors to study the stability type of g as a critical point of the scalar curvature…
We study the Lorentzian metric independent of the time variable in the cylinder $\mathbb{R}\times\Omega$ where $x_0\in\mathbb{R}$ is the time variable and $\Omega$ is a bounded smooth domain in $\mathbb{R}^n$. We consider forward…
We investigate the local regularity of pointed spacetimes, that is, time-oriented Lorentzian manifolds in which a point and a future-oriented, unit timelike vector (an observer) are selected. Our main result covers the class of Einstein…
We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein equations together with the energy-momentum tensor of a barotropic perfect fluid.…
On a smooth $n$-manifold $M$ with $n \geq 3$, we study pairs $(g,T)$ consisting of a Riemannian metric $g$ and a unit length closed vector field $T$. Motivated by how Ricci solitons generalize Einstein metrics via a distinguished vector…
In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric…
In a previous paper [gr-qc/0104001; Class. Quant. Grav. 18 (2001) 3595-3610] we have shown that the occurrence of curved spacetime ``effective Lorentzian geometries'' is a generic result of linearizing an arbitrary classical field theory…
We prove that a globally hyperbolic smooth spacetime endowed with a $\smash{\mathrm{C}^1}$-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike…
The classification of compact homogeneous spaces of the form $M=G/K$, where $G$ is a non-simple Lie group, such that the standard metric is Einstein is still open. The only known examples are $4$ infinite families and $3$ isolated spaces…
We prove a local well-posedness theorem for the (n+1)-dimensional Einstein equations in Lorentzian signature, with initial data $(\tilde g, K)$ whose asymptotic geometry at infinity is similar to that anti-de Sitter (AdS) space, and…