Boundary conditions for coupled quasilinear wave equations with application to isolated systems

We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate reduction to a first order symmetric hyperbolic system with maximal dissipative boundary conditions, well posedness of such problems is established for a large class of boundary conditions on $\partial\Sigma$. We show that our class of boundary conditions is sufficiently general to allow for a well posed formulation for different wave problems in the presence of constraints and artificial, nonreflecting boundaries, including Maxwell's equations in the Lorentz gauge and Einstein's gravitational equations in harmonic coordinates. Our results should also be useful for obtaining stable finite-difference discretizations for such problems.Comment: 22 pages, no figure

Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates

In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the harmonic version of the Einstein equations. Here we show that these results can also be obtained via standard energy estimates, thus establishing strong well-posedness of the harmonic Einstein problem in the classical sense.Comment: More explanatory material and title, as will appear in the published article in Classical and Quantum Gravit

The Initial-Boundary Value Problem in General Relativity

In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.Comment: 11 pages, 2 figures. Contribution to a special volume for Mario Castagnino's seventy fifth birthda

On the linear stability of solitons and hairy black holes with a negative cosmological constant: the odd-parity sector

Using a recently developed perturbation formalism based on curvature quantities, we investigate the linear stability of black holes and solitons with Yang-Mills hair and a negative cosmological constant. We show that those solutions which have no linear instabilities under odd- and even- parity spherically symmetric perturbations remain stable under odd-parity, linear, non-spherically symmetric perturbations.Comment: 26 pages, 1 figur

Critical bubbles and implications for critical black strings

We demonstrate the existence of gravitational critical phenomena in higher dimensional electrovac bubble spacetimes. To this end, we study linear fluctuations about families of static, homogeneous spherically symmetric bubble spacetimes in Kaluza-Klein theories coupled to a Maxwell field. We prove that these solutions are linearly unstable and posses a unique unstable mode with a growth rate that is universal in the sense that it is independent of the family considered. Furthermore, by a double analytical continuation this mode can be seen to correspond to marginally stable stationary modes of perturbed black strings whose periods are integer multiples of the Gregory-Laflamme critical length. This allow us to rederive recent results about the behavior of the critical mass for large dimensions and to generalize them to the charged black string case.Comment: A reference to unpublished work for the case q=2, by J. Hovdebo adde