Abstract
We investigate the thermodynamic equilibrium states of a rotating thin shell, i.e., a ring, in the (2 + 1)-dimensional spacetime with a negative cosmological constant. The inner and outer regions with respect to the shell are given by pure anti-de Sitter (AdS) and the Banados-Teitelbom-Zanelli (BTZ) spacetimes, respectively. The first law of thermodynamics of the thin shell, together with three equations of state for the pressure, the local inverse temperature and the thermodynamic angular velocity of the shell, yields the entropy of the shell, which is shown to depend only on its gravitational radii. When the shell is pushed to its own gravitational radius and its temperature is taken to be the Hawking temperature of the corresponding black hole, the entropy of the shell coincides with the Bekenstein-Hawking entropy.
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