We investigate whether or not the Hawking-Page phase transition is possible to occur in three dimensions. Starting with the simplest class of LanczosLovelock action, thermodynamic behavior of all AdS-type black holes without charge falls into two classes: Schwarzschild-AdS black holes in even dimensions and Chern-Simons black holes in odd dimensions. The former class can provide the Hawking-Pag...

The topological structure of the event horizon has been considered in terms of the Morse theory. The elementary process of topology changes can be understood as a handle attachment. It has been found that there are certain constraints on the black hole topology changes: (i) There are n kinds of the handle attachment in the (n+1)-dimensional black hole space-times. (ii) The handle is further cla...

We study the apparent horizon for two boosted black holes in the asymptotically de Sitter space-time by solving the initial data on a space with punctures. We show that the apparent horizon enclosing both black holes is not formed if the conserved mass of the system (Abbott-Deser mass) is larger than a critical mass. The black hole with too large AD mass therefore cannot be formed in the asympt...

We prove non–existence of static, vacuum, appropriately regular, asymptotically flat black hole space–times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum, asymptotically flat domains of outer communication in an appropriate class of space–times, showing that the domains of outer communication of the Schwarzschild ...

The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and Stojkovic. We also show that five-dimensional AdS Kerr black holes are isosp...