科研之友
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摘要
The theory of nonexpanding horizons (NEHs) geometry and the theory of near-horizon geometries (NHGs) are two mathematical relativity frameworks generalizing the black hole theory. From the point of view of the NEHs theory, a NHG is just a very special case of a spacetime containing a NEH of many extra symmetries. It can be obtained as the Horowitz limit of a neighborhood of an arbitrary extremal Killing horizon. An unexpected relation between the two of them was discovered in the study of spacetimes foliated by a family of NEHs. The class of four-dimensional NHG solutions (either vacuum or coupled to a Maxwell field) was found as a family of examples of spacetimes admitting a NEH foliation. In the current paper, we systematically investigate geometries of the NEHs foliating a spacetime for arbitrary matter content and in arbitrary spacetime dimensions. We find that each horizon belonging to the foliation satisfies a condition that may be interpreted as an invitation for a transversal NEH to exist and to admit the structure of an extremal isolated horizon. Assuming the existence of a transversal extremal isolated horizon, we derive all the spacetime metrics satisfying the vacuum Einstein's equations. In this case, the NEHs become bifurcated Killing horizons.
- 出版日期2016-9-8
