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Multiple Killing horizons
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DOI：10.1088/1361-6382/aacd2c.png)
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Abstract
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Killing horizons which can be such for two or more linearly independent Killing vectors are studied. We provide a rigorous definition and then show that the set of Killing vectors sharing a Killing horizon is a Lie algebra Ali of dimension at most the dimension of the spacetime. We prove that one cannot attach different surface gravities to such multiple Killing horizons, as they have an essentially unique nonzero surface gravity (or none). Ali always contains an Abelian (sub)algebra-whose elements all have vanishing surface gravity-of dimension equal to or one less than dim A. There arise only two inequivalent possibilities, depending on whether or not the nonzero surface gravity exists. We show the connection with near-horizon geometries, and also present a linear system of PDEs, the master equation, for the proportionality function on the horizon between two Killing vectors of a multiple Killing horizon, with its integrability conditions. We provide explicit examples of all possible types of multiple Killing horizons, as well as a full classification of them in maximally symmetric spacetimes.
Keywords:
Killing horizon
surface gravity
near horizon geometry
bifurcate horizon
Killing vector
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