Classical Quantum Gravity Research Articles

Highly damped quasinormal modes of Kerr black holes

Motivated by recent suggestions that highly damped black hole quasinormal modes (QNM's) may provide a link between classical general relativity and quantum gravity, we present an extensive computation of highly damped QNM's of Kerr black holes. We do not limit our attention to gravitational modes, thus filling some gaps in the existing literature. The frequency of gravitational modes with l=m=2 tends to \omega_R=2 \Omega, \Omega being the angular velocity of the black hole horizon. If Hod's conjecture is valid, this asymptotic behaviour is related to reversible black hole transformations. Other highly damped modes with m>0 that we computed do not show a similar behaviour. The real part of modes with l=2 and m<0 seems to asymptotically approach a constant value \omega_R\simeq -m\varpi, \varpi\simeq 0.12 being (almost) independent of a. For any perturbing field, trajectories in the complex plane of QNM's with m=0 show a spiralling behaviour, similar to the one observed for Reissner-Nordstrom (RN) black holes. Finally, for any perturbing field, the asymptotic separation in the imaginary part of consecutive modes with m>0 is given by 2\pi T_H (T_H being the black hole temperature). We conjecture that for all values of l and m>0 there is an infinity of modes tending to the critical frequency for superradiance (\omega_R=m) in the extremal limit. Finally, we study in some detail modes branching off the so--called ``algebraically special frequency'' of Schwarzschild black holes. For the first time we find numerically that QNM multiplets emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.

Symmetries of the Classical Integrable Systems and 2-Dimensional Quantum Gravity: a `Map'

Abstract We draw attention to the connections recently established by others between the classical integrable KdV and KP hierarchies in 1 + 1 and 2 + 1 dimensions respectively and the matrix models which relate to the partition functions of 2-dimensional (1 + 1 dimensional) quantum gravity. The symmetries of the classical KP hierarchy in 2 + 1 dimensions are fundamental to this connection.

Isotropic solutions of the Einstein-Vlasov equations with lowest-order quantum corrections

The author studies a model in between classical relativity and quantum gravity by considering the lowest-order quantum corrections to the classical Einstein-Vlasov equations. He proves that the isotropic solutions of this model are Robertson-Walker universes which are singularity-free, strictly periodic and symmetric for closed universes and which develop a singularity-free, symmetric bounce for open and flat universes.

Recent Developments in Gravitation, Cargèse 1978

This valuable collection of lectures is divided into three parts: classical relativity, quantum gravity and supergravity. The most useful contributions are probably the more didactic ones.