We review recent developments in special geometry and explain its role in the theory of supersymmetric black holes. To make this article self-contained, a short introduction to black holes is given, with emphasis on the laws of black hole mechanics and black hole entropy. We also summarize the existing results on the para-complex version of special geometry, which occurs in Euclidean supersymme...

The Hessian of the entropy function can be thought of as a metric tensor on the state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study this geometry for some families of black holes. It is flat for the ...

In the standard methodology for evaluating the Hawking radiation emanating from a black hole, the background geometry is fixed. Trying to be more realistic we consider a dynamical geometry for a two-dimensional charged black hole and we evaluate the Hawking radiation as a tunneling process. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. We exlore th...

We review recent developments in special geometry and explain its role in the theory of supersymmetric black holes. To make this article self-contained, a short introduction to black holes is given, with emphasis on the laws of black hole mechanics and black hole entropy. We also summarize the existing results on the para-complex version of special geometry, which occurs in Euclidean supersymme...

In the standard methodology for evaluating the Hawking radiation emanating from a black hole, the background geometry is fixed. Trying to be more realistic we consider a dynamical geometry for a two-dimensional charged black hole and we evaluate the Hawking radiation as a tunneling process. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. We exlore th...