Topology of the Causal Boundary for Standard Static Spacetimes

Details Topology of the Causal Boundary for Standard Static Spacetimes Topology of the Causal Boundary for Standard Static Spacetimes

2006-07-11

arxiv.org/abs/gr-qc/0607049v1

Class.Quant.Grav.24:1211-1260,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/24/5/010

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.

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