New black hole solutions in f(P) gravity and their thermodynamic nature

Abstract

Black holes are the fascinating objects in the universe. They represent extreme deformations in spacetime geometry. Here, we construct $f\left(P\right)$ gravity and the first example of static-spherically symmetric black hole solution in $f\left(P\right)$ gravity and discuss their thermodynamics. Using the numerical approach and series solution, we discover the solution and demonstrate that it is a generalization of Schwarzschild. The solution is characterized by a single function that satisfies a non-linear fourth-order differential equation. Interestingly, we can analytically calculate the solution's specific heat, Wald entropy, and Hawking temperature as a function of horizon radius. After analyzing the specific heat, we discovered that the black hole is thermodynamically stable over a small horizon radius.