# New five-dimensional Bianchi type magnetically charged hairy topological black hole solutions in string theory

## TL;DR

This paper constructs five-dimensional string theory black hole solutions with unusual asymptotics, involving Bianchi geometries, and analyzes their thermodynamics and T-duality properties.

## Contribution

It introduces new topological black hole solutions with Bianchi geometries and secondary dilaton hair, expanding the landscape of string theory black holes.

## Key findings

- Solutions have non-standard asymptotics, neither flat nor (A)dS.
- Thermodynamic quantities satisfy the first law.
- Entropy remains invariant under T-duality.

## Abstract

We construct black hole solutions to the leading order of string effective action in five dimensions with the source given by dilaton and magnetically charged antisymmetric gauge $B$-field. Presence of the considered $B$-field leads to the unusual asymptotic behavior of solutions which are neither asymptotically flat nor asymptotically (A)dS. We consider the three-dimensional space part to correspond to the Bianchi classes and so the horizons of these topological black hole solutions are modeled by seven homogeneous Thurston geometries of $E^3$, $S^3$, $H^3$, $H^2 \times E^1$, $\widetilde{{SL_2R}}$, nilgeometry, and solvegeometry. Calculating the quasi-local mass, temperature, entropy, dilaton charge, and magnetic potential, we show that the first law of black hole thermodynamics is satisfied by these quantities and the dilaton hair is of the secondary type. Furthermore, for Bianchi type $V$, the $T$-dual black hole solution is obtained which carries no charge associated with $B$-field and possesses a dilaton hair of secondary kind. Also, the entropy turns to be invariant under the $T$-duality.