https://doi.org/10.1140/epjc/s10052-025-15235-1
Regular Article - Theoretical Physics
Restricted phase space thermodynamics of charged static and charged rotating black holes in f(R) gravity
1
Department of Physics, Dibrugarh University, 786004, Dibrugarh, Assam, India
2
Theoretical Physics Division, Centre for Atmospheric Studies, Dibrugarh University, 786004, Dibrugarh, Assam, India
a
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Received:
7
October
2025
Accepted:
18
December
2025
Published online:
29
December
2025
Abstract
In this work, we study the restricted phase space thermodynamics (RPST) of charged static and rotating black holes in f(R) gravity. By keeping the cosmological constant fixed and introducing the central charge C with its conjugate chemical potential 
, RPST allows the black-hole mass to be interpreted as internal energy. We compute the corresponding thermodynamic quantities and analyse the T–S and F–T behaviours, which show the characteristic non-monotonicity and swallow-tail structures associated with first-order phase transitions, along with a second-order critical point. To confirm these results, we use the Legendre-invariant framework of geometrothermodynamics (GTD) and show that divergences of the GTD scalar curvature coincide with those of the specific heat, providing geometric confirmation of the phase structure in f(R) gravity.
© The Author(s) 2025
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