Excited States of Maximal Warm Holes

Abstract

Recently, the Einstein–Maxwell–scalar model with a non-minimal coupling between the scalar and Maxwell fields was explored. As a result, a new class of black hole solutions with scalar hair was discovered. By fixing the mass of a black hole and taking the maximum allowable charge, an extremal black hole was obtained. Interestingly, this extremal black hole not only possesses an event horizon with a non-zero surface area but also exhibits a non-zero Hawking temperature. This unique type of extremal black hole is referred to as a maximal warm hole (MWH). In this paper, we revisit this model and examine these black holes with highly excited state fields. We discovered that an excited state MWH solution can also be obtained under extremal conditions. We investigate the range of existence for excited states and analyze their relevant physical properties.