Irreducible mass of a regular rotating black hole

This article presents an analysis of regular rotating black hole solutions within the framework of teleparallel equivalent to general relativity. The study evaluates the total energy and derives an analytical expression for the irreducible mass of a regular black hole. The results reveal the significance of these regular black holes as approximations of real astrophysical objects. The investigation explores the behavior of the total energy for different surfaces and its value at spatial infinity. Additionally, the article addresses the instability of the inner horizon and examines the inertial acceleration of an observer inside the inner horizon.

Figure 1

Numerical integration of the energy (39) for surfaces of distinct radii $R>r_{+}$. The outer horizon is at $r_{+}=1.99499$, and the parameters are $M=10$, $a=1$, and $e=0$. The continuous line represents the regular black hole ($b=1$), and the dotted one represents the Kerr black hole ($b=0$).

Figure 2

Numerical integration of the energy (39) for surfaces of distinct radii $R>r_{+}$. The outer horizon is at $r_{+}=1.99499$, and the parameters are $M=10$, $a=1$, and $b=0$. The continuous line represents the regular black hole ($e=1.9$), and the dotted one represents the Kerr black hole ($e=0$).

Figure 3

Inertial acceleration of the observer inside the inner horizon, comparing the cases with a Kerr deviation parameter (continuous line) and without a Kerr regularization parameter (dashed line). The chosen parameters for the plot are $M=10$, $a=0.6$, and $b=0.5$.

Figure 4

Inertial acceleration of the observer inside the inner horizon, with the Kerr deviation parameter represented by the continuous line and without the Kerr regularization parameter shown by the dashed line. The chosen parameters for the plot are $M=10$, $a=0.6$, and $b=0.5$.

Figure 5

Irreducible mass as a function of $a$ for different values of the regularization parameter $b$.

Figure 6

Irreducible mass as a function of $b$ for different values of the rotation parameter $a$.