Geometric Properties of Static EMdL Horizons

TL;DR

This paper investigates the geometric and curvature properties of static horizons in Einstein-Maxwell-dilaton models with Liouville potential across various dimensions, revealing that extremal horizons are Einstein spaces and establishing conditions for their existence.

Contribution

It generalizes known relations for horizons to higher dimensions and complex models, providing new insights into extremal horizon geometry in the EMdL framework.

Findings

Extremal horizon surfaces are Einstein spaces.

Derived relations between curvature invariants and horizon geometry.

Established necessary conditions for static extremal horizons.

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.