Regular Article - Theoretical Physics
Black hole thermodynamics from logotropic fluids
Dipartimento di Fisica “E. Pacini”, Università di Napoli “Federico II”, Via Cinthia 9, 80126, Naples, Italy
2 Scuola Superiore Meridionale, Largo San Marcellino 10, 80138, Naples, Italy
3 Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, 80126, Naples, Italy
4 Divisione di Fisica, Università di Camerino, Via Madonna delle Carceri 9, 62032, Camerino, Italy
5 Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy
6 Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, 050040, Almaty, Kazakhstan
Accepted: 12 February 2023
Published online: 23 February 2023
We show that the Einstein field equations with a negative cosmological constant can admit black hole solutions whose thermodynamics coincides with that of logotropic fluids, recently investigated to heal some cosmological and astrophysical issues. For this purpose, we adopt the Anton–Schmidt equation of state, which represents a generalized version of logotropic fluids. We thus propose a general treatment to obtain an asymptotic anti-de Sitter metric, reproducing the thermodynamic properties of both Anton–Schmidt and logotropic fluids. Hence, we explore how to construct suitable spacetime functions, invoking an event horizon and fulfilling the null, weak, strong and dominant energy conditions. We further relax the strong energy condition to search for possible additional solutions. Finally, we discuss the optical properties related to a specific class of metrics and show how to construct an effective refractive index depending on the spacetime functions and the thermodynamic quantities of the fluid under study. We also explore possible departures with respect to the case without the fluid.
© The Author(s) 2023
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