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arXiv · 1103.1171

Geometric Properties of Static EMdL Horizons

Shohreh Abdolrahimi·Andrey A. Shoom
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Abstract

We study non-degenerate and degenerate (extremal) Killing horizons of arbitrary geometry and topology within the Einstein-Maxwell-dilaton model with a Liouville potential (the EMdL model) in d-dimensional (d>=4) static space-times. Using Israel's description of a static space-time, we construct the EMdL equations and the space-time curvature invariants: the Ricci scalar, the square of the Ricci tensor, and the Kretschmann scalar. Assuming that space-time metric functions and the model fields are real analytic functions in the vicinity of a space-time horizon, we study behavior of the space-time metric and the fields near the horizon and derive relations between the space-time curvature invariants calculated on the horizon and geometric invariants of the horizon surface. The derived relations generalize the similar relations known for horizons of static four and 5-dimensional vacuum and 4-dimensional electrovacuum space-times. Our analysis shows that all the extremal horizon surfaces are Einstein spaces. We present necessary conditions for existence of static extremal horizons within the EMdL model.

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Shohreh Abdolrahimi, Andrey A. Shoom. 2011-03-06. Geometric Properties of Static EMdL Horizons. https://doi.org/10.1103/physrevd.83.104023

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