Thermodynamics of toroidal black holes

The thermodynamical properties of toroidal black holes in the grand canonic al ensemble are investigated using York's formalism. The black hole is encl osed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow one to compute the rele vant thermodynamical quantities, e.g., thermal energy, entropy, and specifi c heat. This black hole is thermodynamically stable and dominates the grand partition function. This means that there is no phase transition, such as the one encountered for spherical black holes. (C) 2000 American Institute of Physics. [S0022-2488(00)05805-9].