Eur. Phys. J. Plus (2022) 137: 383
https://doi.org/10.1140/epjp/s13360-022-02569-y

Regular Article

Black hole solution and thermal properties in 4DAdS Gauss–Bonnet massive gravity

¹ Department of Physics, K. L. S. College, 805110, Nawada, Bihar, India
² Department of Physics, Magadh University, 824234, Bodh Gaya, Bihar, India
³ Inter-University Centre for Astronomy and Astrophysics (IUCAA), 411007, Pune, Maharashtra, India
⁴ School of Physics, Damghan University, P.O. Box 3671641167, Damghan, Iran
⁵ Department of Physics, Institute of Applied Science and Humanities, GLA University, 281406, Mathura, India

Received: 18 November 2021
Accepted: 6 March 2022
Published online: 22 March 2022

Abstract

We consider an Einstein–Gauss–Bonnet massive gravity model in 4DAdS spacetime to obtain a possible black hole solution and discuss the horizon structure of this black hole. The real roots of the vanishing metric function lead to various types of horizons. Furthermore, we derive various thermodynamic quantities, thus insuring the validity of the first law of thermodynamics and the Smarr relation. The thermodynamic quantities are modified in the presence of the massive gravity parameter and also discuss the stability of the system from the heat capacity. Black hole space times can not only possess standard thermodynamics, but also possess phase structures when the cosmological constant is treated as the thermodynamic pressure. The effects of massive parameter and GB parameter on phase transition are also discussed. We also examine the phase structure through Maxwell’s equal area law. The first-order phase transition occurs only when pressure is lower than its critical value. At critical pressure, the first-order phase transition terminates, and the second-order phase transition occurs. No phase transition occurs when pressure is greater than its critical value.