Eur. Phys. J. C (2019) 79: 229
https://doi.org/10.1140/epjc/s10052-019-6745-0

Regular Article - Theoretical Physics

Quasi-homogeneous black hole thermodynamics

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, AP 70543, Ciudad de México, 04510, Mexico
² Dipartimento di Fisica and ICRA, Università di Roma “Sapienza”, 00185, Rome, Italy
³ Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
⁴ Departamento de Matemáticas, Universidad Militar Nueva Granada, Cra 11 No. 101-80, Bogotá, DE, Colombia
⁵ Departamento de posgrado, CIIDET, AP752, Querétaro, QRO, 76000, Mexico

^* e-mail: quevedo@nucleares.unam.mx

Received: 26 December 2018
Accepted: 4 March 2019
Published online: 13 March 2019

Abstract

Although the fundamental equations of ordinary thermodynamic systems are known to correspond to first-degree homogeneous functions, in the case of non-ordinary systems like black holes the corresponding fundamental equations are not homogeneous. We present several arguments, indicating that black holes should be described by means of quasi-homogeneous functions of degree different from one. In particular, we show that imposing the first-degree condition leads to contradictory results in thermodynamics and geometrothermodynamics of black holes. As a consequence, we show that in generalized gravity theories the coupling constants like the cosmological constant, the Born–Infeld parameter or the Gauss–Bonnet constant must be considered as thermodynamic variables.