Entropy inside the Kerr–Sen black holes

Abstract

In this paper, we consider the Kerr–Sen black hole. Unlike the AdS black hole, it is actually an exact solution for the heterotic string theory in the low energy effective field theory in four dimensions. Starting from the black hole metric in the Boyer–Lindquist coordinates, we calculate the maximal interior volume by introducing the advanced time. Further, we present the rate of change of the interior volume with the advanced time on the radius of the black hole and observe that it has a maximal value for a specific value of the radius of the black hole. It is also shown from the graph that the maximal value increases with the increase of mass, and the position of the maxima shifts towards the large radius. Moreover, we calculate the rate of loss of mass due to Hawking radiation and interpret it graphically. Finally, we compute the interior entropy and show from its variations with mass and outer horizon radius of the black hole that in the interior, the entropy decreases with mass and becomes negative, whereas, in the exterior, the entropy increases with mass and remains positive. This is further proof of the argument that was proposed in Azuma and Subramanian (2020). In this investigation, an interesting feature is that the low-mass Kerr–Sen black hole behaves like a reversible process, whatever its outer horizon also reveals.