Thermodynamics of de Sitter black holes with conformally coupled scalar fields

We investigate the thermodynamic properties of 3+1 dimensional black holes in asymptotically de Sitter spacetimes, conformally coupled to a real scalar field. We use a Euclidean action approach, where boundary value data is specified at a finite radius 'cavity' outside the black hole, working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. For the MTZ subclass of solutions, we find Hawking-Page-like phase transitions from a black hole spacetime to thermal de Sitter with a scalar field. In the more general case, Hawking-Page-like phase transitions are also present, whose existence depends further on a particular cosmic censorship bound.

Automated summary

The thermodynamic properties of 3+1 dimensional black holes conformally coupled to a real scalar field in asymptotically de Sitter spacetimes were investigated using a Euclidean action approach. By treating the cosmological constant as a thermodynamic pressure in the extended phase space, phase transitions resembling Hawking-Page transitions were observed in the black hole solutions, with the existence of these transitions further depending on a specific cosmic censorship bound.