Topology of the Causal Boundary for Standard Static Spacetimes

Abstract

The topology of the causal boundary for standard static spacetimes--spacetimes time-invariantly conformal to a metric product of the Lorentz line and a Riemannian manifold--is studied in depth. As this is given in terms of a set of real-valued functions on the Riemannian factor, one could use a function-space topology, but physical reasons recommend a chronological topology instead. The function-space topology has a simple product structure, while the chronological topology might not. This paper examines when the chronological topology coincides with the function-space topology and when it has a simple product structure. A class of standard static spacetimes is examined, all of which yield a simple product structure for the causal boundary; the conformal class of these spacetimes includes classical spacetimes such as external Schwarzschild or Reissner-Nordstrom.

arXiv comment50 pages, AMS-TeX; submitted to Class. Quantum Grav

References in corpus (5)

• Topology of the Future Chronological Boundary: Universality for Spacelike Boundaries
• A new recipe for causal completions
• Universality of the Future Chronological Boundary
• Discrete Group Actions on Spacetimes: Causality Conditions and the Causal Boundary
• Ricci Fall-off in Static, Globally Hyperbolic, Non-singular Spacetimes

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