Global Structure of Certain Static Spacetimes (I)

TL;DR

This paper investigates the global structure of static spacetimes with a specific topological form, demonstrating that positive surface gravity guarantees a Killing horizon with a cross section homeomorphic to N, encompassing Schwarzschild and Reissner-Nordstrom as special cases.

Contribution

It establishes a general topological and geometric condition linking surface gravity to the existence of Killing horizons in static spacetimes with R^2 imes N topology.

Findings

Positive surface gravity implies the existence of a Killing horizon.

Schwarzschild and Reissner-Nordstrom spacetimes are special cases.

Cross section of the horizon is homeomorphic to N.

Abstract

In this paper, static spacetimes with a topological structure of R^2 \times N is studied, where N is an arbitrary manifold. Well known Schwarzschild spacetime and Reissner-Nordstrom spacetime are special cases. It is shown that the existence of a constant and positive surface gravity $\kappa$ ensures the existence of the Killing horizon, with the cross section homeomorphic to N.