Magnetic and Electric Black Holes in Arbitrary Dimension

TL;DR

This paper compares electric and magnetic black holes in arbitrary dimensions, analyzing their moduli spaces and extremal geometries, revealing similarities in their gravitational solutions despite fundamental differences.

Contribution

It provides a detailed comparison of electric and magnetic black holes across dimensions, highlighting their geometric similarities and differences in moduli space.

Findings

Electric and magnetic black holes have similar extremal geometries.

The moduli space for both types of black holes is bounded and well-characterized.

Gravity solutions unify many differences between electric and magnetic cases.

Abstract

In this work, we compare two different objects: electric black holes and magnetic black holes in arbitrary dimension. The comparison is made in terms of the corresponding moduli space and their extremal geometries. We treat parallelly the magnetic and the electric cases. Specifically, we discuss the gravitational solution of these spherically symmetric objects in the presence of a positive cosmological constant. Then, we find the bounded region of the moduli space allowing the existence of black holes. After identifying it in both the electric and the magnetic case, we calculate the geometry that comes out between the horizons at the coalescence points. Although the electric and magnetic cases are both very different (only dual in four dimensions), gravity solutions seem to clear up most of the differences and lead to very similar geometries.