Black holes with unusual topology

The Einstein's equations with a negative cosmological constant admit solutions which are asymtotically anti-de Sitter space. Matter fields in anti-de Sitter can be in stable equilibrium even if the potential energy is unbounded from below, violating the weak energy condition. Hence there is no fundamental reason that black hole's horizons should have spherical topology. Here it is shown that in anti-de Sitter space the Einstein equations admit black hole solutions where the horizon can be a Riemann surface with genus $g$. The case $g=0$ is the asymptotically anti-de Sitter black hole first studied by Hawking-Page, which has spherical topology. The genus one black hole has a new free parameter entering the metric, the size of the torus. The genus $g>1$ black hole has no other free parameters apart from the mass. All such black holes exihibits a natural temperature which is identified as the period of its euclidean continuation and there is a mass formula connecting the mass with the surface gravity and the horizon area of the black hole. Due to a peculiar character of some of its properties it is unknown, to the author, whether the black hole could form as a result of gravitational collapse.