# Hairy black holes in cubic quasi-topological gravity

## TL;DR

This paper constructs five-dimensional hairy black hole solutions in cubic quasi-topological gravity, revealing novel phase transitions and critical points, including the second example of black hole λ-lines and unique phase structures.

## Contribution

It introduces new hairy black hole solutions with conformal scalar hair and uncovers novel thermodynamic phase behaviors, including λ-lines and isolated critical points, in five-dimensional cubic quasi-topological gravity.

## Key findings

- Discovery of black hole λ-lines indicating second order phase transitions.
- Identification of isolated critical points in spherical black holes.
- Observation of complex phase structures including reentrant transitions.

## Abstract

We construct a class of five dimensional black hole solutions to cubic quasi-topological gravity with conformal scalar hair and study their thermodynamics. We find these black holes provide the second example of black hole $\lambda$-lines: a line of second order (continuous) phase transitions, akin to the fluid/superfluid transition of $^4$He. Examples of isolated critical points are found for spherical black holes, marking the first in the literature to date. We also find various novel and interesting phase structures, including an isolated critical point occurring in conjunction with a double reentrant phase transition. The AdS vacua of the theory are studied, finding ghost-free configurations where the scalar field takes on a non-zero constant value, in notable contrast to the five dimensional Lovelock case.