Luciano Vanzo

Hawking radiation as tunneling for extremal and rotating black holes

The issue concerning semi-classical methods recently developed in deriving the conditions for Hawking radiation as tunneling, is revisited and applied also to rotating black hole solutions as well as to the extremal cases. It is noticed how the tunneling method fixes the temperature of extremal black hole to be zero, unlike the euclidean regularity method that allows an arbitrary compactification period. A comparison with other approaches is presented.

Black holes with unusual topology

Einsteins equations with a negative cosmological constant admit solutions which are asymptotically anti\char21{}de Sitter space. Matter fields in anti\char21{}de Sitter space 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 horizons should have a spherical topology. In anti\char21{}de Sitter space Einsteins equations admit black hole solutions where the horizon can be a Riemann surface with genus

Quantum fields and extended objects in space-times with constant curvature spatial section

g.

Entropy and universality of Cardy-Verlinde formula in dark energy universe

The case

Fermion tunneling from dynamical horizons

g=0

Tunnelling methods and Hawking's radiation: achievements and prospects

is the asymptotically anti\char21{}de Sitter black hole first studied by Hawking and Page, which has a spherical topology. The genus one black hole has a new free parameter entering the metric, the conformal class to which the torus belongs. The genus

Local Hawking temperature for dynamical black holes

gg1

On the Hawking radiation as tunneling for a class of dynamical black holes

black hole has no other free parameters apart from the mass and the charge. All such black holes exhibit a natural temperature which is identified as the period of the Euclidean continuation and there is a mass formula connecting the mass with the surface gravity and the horizon area of the black hole. The Euclidean action and entropy are computed and used to argue that the mass spectrum of states is positive definite.

Zeta function regularization, the multiplicative anomaly and the Wodzicki residue

Abstract The heat-kernel expansion and ζ-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times with spatial section consisting in manifold with constant curvature are discussed in detail. Several mathematical results, relevant to physical applications are presented, including exact solutions of the heat-kernel equation, a simple exposition of hyperbolic geometry and an elementary derivation of the Selberg trace formula. With regard to the physical applications, the vacuum energy for scalar fields, the one-loop renormalization of a self-interacting scalar field theory on a hyperbolic space-time, with a discussion on the topological symmetry breaking, the finite-temperature effects and the Bose-Einstein condensation, are considered. Some attempts to generalize the results to extended objects are also presented, including some remarks on path-integral quantization, asymptotic properties of extended objects and a novel representation for the one-loop (super) string free energy.

Hawking radiation as tunnelling : the D-dimensional rotating case

We study the entropy of a FRW universe filled with dark energy (cosmological constant, quintessence, or phantom). For the general or time-dependent equation of state