SL(n,R)-Toda Black Holes

TL;DR

This paper constructs explicit multi-charge black hole solutions in higher-dimensional Einstein gravity coupled with vector fields and scalars, using SL(n,R) Toda equations, and analyzes their thermodynamics and extremal properties.

Contribution

It introduces a method to reduce Einstein-Maxwell-dilaton equations to SL(n,R) Toda equations, enabling explicit multi-charge black hole solutions with novel thermodynamic features.

Findings

Derived explicit black hole solutions with multiple charges.

Analyzed near-horizon geometry and extremal limits.

Established universal entropy product formula.

Abstract

We consider D-dimensional Einstein gravity coupled to (n-1) U(1) vector fields and (n-2) dilatonic scalars. We find that for some appropriate exponential dilaton couplings of the field strengths, the equations of motion for the static charged ansatz can be reduced to a set of one-dimensional SL(n,R) Toda equations. This allows us to obtain a general class of explicit black holes with mass and (n-1) independent charges. The near-horizon geometry in the extremal limit is AdS_2 x S^{D-2}. The n=2 case gives the Reissner-Nordstrom solution, and the n=3 example includes the Kaluza-Klein dyon. We study the global structure and the black hole thermodynamics and obtain the universal entropy product formula. We also discuss the characteristics of extremal multi-charge black holes that have positive, zero or negative binding energies.