Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities

We explore the quadratic form of the f (R) = R + bR(2) gravitational theory to derive rotating N-dimensions black hole solutions with a(i), i >= 1 rotation parameters. Here, R is the Ricci scalar and b is the dimensional parameter. We assumed that the N-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter b, whereas, in the case of N > 4, it depends on parameter b, owing to the contribution of the correction R-2 term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter b to be b < 1/16 Lambda to obtain a positive entropy.

Automated summary

By exploring the rotating black hole solutions in N-dimensions with specific parameters and studying the relationships between physical quantities, we investigated the effects of the parameter b on black holes in multi-dimensional cases depend on the contribution of the correction R-2 term. Through calculating thermodynamic quantities and analyzing stability, we demonstrated that these black hole solutions exhibit thermodynamic stability.