The Specific Heat for Black Holes

https://doi.org/10.65770/EVEU2446

ABSTRACT

Specific heat (C_v) is an important thermodynamic parameter that has been used to study phase transition and to calculate the transition temperature (T_c) from one phase (that may be unstable) to another phase (that may be stable). The specific heat of a Black Hole could be negative or positive depending on its type and the thermodynamic variables kept constant. Negative C_v means that the Black Hole gets hotter as it radiates energy and this indicates instability and evaporation via Hawking radiation. Whereas in the case of larger Reissner-Nord-Strom and anti-de-Sitter (Ads) Black Holes, the specific heat can be positive, allowing them to achieve stable thermal equilibrium with their environment or surrounding atmosphere. Thus, the stability of the Black Hole is determined by the sign of the specific heat. With negative C_v, it may radiate energy and become smaller Black Hole, whereas with positive C_v, it may be large Black Hole with some phase transition. Calculations of C_v are done for two types of Black Holes. In one it is treated as a huge gravitational mass while in the second calculation, Black Hole is treated as a quantum gravitational mass. In both cases C_v is negative but in the quantum gravitational case C_v is less negative within intermediate temperatures. At higher temperatures of the order 10³¹K both cases display a unified behavior signifying stability. Quantum gravity considerations lead to increase in T_c and this means a more stable system.

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WSN 213 (2026) 170-179