Kerr and Kerr-AdS black shells and black hole entropy

by Xun Wang

Institution: University of Victoria
Year: 2007
Keywords: general relativity; thin shell; black hole thermodynamics; Bekenstein-Hawking entropy; Israel's junction conditions; ZAM; Kerr; Kerr-AdS; AdS/CFT; UVic Subject Index::Sciences and Engineering::Physics
Record ID: 1795817
Full text PDF: http://hdl.handle.net/1828/241


As an operational approach to the Bekenstein-Hawking formula S_{BH}=A/4l_{Pl}^{2} for the black hole entropy, we consider the reversible contraction of a spinning thin shell to its event horizon and find that its thermodynamic entropy approaches $S_{\mathrm{BH}}$. In this sense the shell, called a "black shell", imitates and is externally indistinguishable from a black hole. Our work is a generalization of the previous result [10] for the spherical case. We assume the exterior space-time of the shell is given by the Kerr metric and match it to two different interior metrics, a vacuum one and a non-vacuum one. We find the vacuum interior embedding breaks down for fast spinning shells. The mechanism is not clear and worth further exploring. We also examine the case of a Kerr-AdS exterior, without trying to find a detailed interior solution. We expect the same behavior of the shell when the horizon limit is approached.