Entropy of an extremal electrically charged thin shell and the extremal black hole

Abstract

There is a debate as to what is the value of the the entropy $S$ of extremal black holes. There are approaches that yield zero entropy $S=0$, while there are others that yield the Bekenstein-Hawking entropy $S=A_{+}/4$, in Planck units. There are still other approaches that give that $S$ is proportional to $r_{+}$ or even that $S$ is a generic well-behaved function of $r_{+}$. Here $r_{+}$ is the black hole horizon radius and $A_{+}=4\pi r_{+}^2$ is its horizon area. Using a spherically symmetric thin matter shell with extremal electric charge, we find the entropy expression for the extremal thin shell spacetime. When the shell's radius approaches its own gravitational radius, and thus turns into an extremal black hole, we encounter that the entropy is $S=S(r_{+})$, i.e., the entropy of an extremal black hole is a function of $r_{+}$ alone. We speculate that the range of values for an extremal black hole is $0\le S(r_{+})\le A_{+}/4$.

11 pages, minor changes, added references, matches the published version

References in corpus (5)

• Entropy of extremal black holes from entropy of quasiblack holes
• Entropy of a self-gravitating electrically charged thin shell and the black hole limit
• Thermodynamics of rotating thin shells in the BTZ spacetime
• Extremal black holes, gravitational entropy and nonstationary metric fields
• Hamiltonian thermodynamics of d-dimensional (d=4 and d>4) Reissner-Nordström anti-de Sitter black holes with spherical, planar, and hyperbolic topology

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• Thermodynamics of extremal rotating thin shells in an extremal BTZ spacetime and the extremal black hole entropy
• Thermodynamics and entropy of self-gravitating matter shells and black holes in $d$ dimensions
• Compact objects in general relativity: From Buchdahl stars to quasiblack holes
• Junction conditions in gravity theories with extra scalar degrees of freedom
• Electrically charged spherical matter shells in higher dimensions: Entropy, thermodynamic stability, and the black hole limit
• Dynamical and thermodynamical stability of a charged thin-shell wormhole
• Thermodynamic Stability of a Schwarzschild Thin-Shell Wormhole
• Cosmological and astrophysical applications of modified theories of gravity