General matching across Killing horizons of zero order

Abstract

Null shells are a useful geometric construction to study the propagation of infinitesimally thin concentrations of massless particles or impulsive waves. After recalling the necessary and sufficient conditions obtained in [28] that allow for the matching of two spacetimes with null embedded hypersurfaces as boundaries, we will address the problem of matching across Killing horizons of zero order in the case when the symmetry generators are to be identified. The results are substantially different depending on whether the boundaries are non-degenerate or degenerate, and contain or not fixed points (in particular, in the former case the shells have zero pressure but non-vanishing energy density and energy flux in general). We will present the explicit form of the so-called step function in each situation. We will then concentrate on the case of actual Killing horizons admitting a bifurcation surface, where a complete description of the shell and its energy-momentum tensor can be obtained. We will conclude particularizing to the matching of two spacetimes with spherical, plane or hyperbolic symmetry without imposing this symmetry on the shell itself.

38 pages, 2 figures

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• Lorentzian and signature changing branes
• Massless charged particles: Cosmic censorship, and Third law of Black Hole Mechanics
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• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The geometric picture
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Cited by in corpus (4)

• Covariant definition of Double Null Data and geometric uniqueness of the characteristic initial value problem
• Transverse expansion of the metric at null hypersurfaces I. Uniqueness and application to Killing horizons
• Vacuum-dual static perfect fluid obeying $p=-(n-3)\rho /(n+1)$ in $n(\ge 4)$ dimensions
• Transverse expansion of the metric at null hypersurfaces II. Existence results and application to Killing horizons