Thermodynamic studies of a rotating polytropic black hole: Outer and interior regions

Abstract

In this letter, considering the metric of a rotating polytropic black hole in the Boyer-Lindquist coordinates, at first, we derive the thermodynamic parameters such as entropy S, Helmholtz free energy F, internal energy U and Gibbs free energy G and study its dependence on the outer horizon by depicting suitable graphs. Then after reconstruction of the metric of the same in the Eddington-Finkelstein coordinates, we establish the interior volume of the black hole. We further analyze the variations of the interior volume with the small change of the advanced time with respect to the radius. Here we show the existence of a certain value of the radius for which this variation becomes maximum. Moreover, we show the dependence of this maximum value of the radius on the mass of the black hole. We derive the differential form of the interior volume for this limit of the radius and hence the maximal interior volume of the said black hole. Finally, we analyze the same thermodynamic parameters inside the black hole and present a comparative study between the parameters in the outer and interior regions of the black hole.