Entropy of the Kerr black hole arising from Rarita--Schwinger field
In the present work, the author computes the entropy of the Kerr black hole due to the massless Rarita-Schwinger field. He applies the brick-wall model and the Newman-Penrose formalism. He starts by writing down the massless Rarita-Schwinger field equation in the background of the Kerr black hole. He uses the Newman-Penrose formalism in order to write the above equation and the WKB approximation to solve it. In this approximation, he determines initially an expression for the radial wave number (\(k_s\)). Then, integrating \(k_s\) over the appropriate variables he obtains the total number of modes of the Rarita-Schwinger field with energy less than \(E\) (\(n(E)\)). After that, introducing \(n(E)\) in the usual formula for the fermions free energy (\(F\)), he computes \(F\). Finally, from the standard statistical mechanical equation which gives the entropy once one knows \(F\), he derives the entropy (\(S\)) for the Rarita-Schwinger field. \(S\) has two terms. The first one depends on the Kerr black hole event horizon area. The second is a logarithmic correction to the first one. The author compares the above expression for \(S\) with the entropy of the Kerr Black hole, computed with the brick-wall model, due to massless fields of spin \(1/2\), \(1\) and \(2\) in references [\textit{J. Jing} and \textit{M. L. Yan}, Phys. Rev. D 63, 084028 (2001); Phys. Rev. D. 64, 064015 (2001)]. The first term of \(S\) agrees with the one in Jing-Yan, on the other hand, the logarithmic correction does not entirely agree with the one in those references.
scientific article; zbMATH DE number 1879730