Asymptotically de Sitter and anti-de Sitter black holes with confining electric potential

We study gravity interacting with a special kind of QCD-inspired nonlinear gauge field system which earlier was shown to yield confinement-type effective potential (the “Cornell potential”) between charged fermions (“quarks”) in flat space-time. We find new static spherically symmetric solutions generalizing the usual Reissner-Nordström-de Sitter and Reissner-Nordström-anti-de Sitter black holes with the following additional properties: (i) appearance of a constant radial electric field (in addition to the Coulomb one); (ii) novel mechanism of dynamical generation of cosmological constant through the non-Maxwell gauge field dynamics; (iii) appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds.     

Magnetic dilaton strings in anti-de Sitter spaces

With an appropriate combination of three Liouville-type dilaton potentials, we construct a new class of spinning magnetic dilaton string solutions which produces a longitudinal magnetic field in the background of anti-de Sitter spacetime. These solutions have no curvature singularity and no horizon, but have a conic geometry. We find that the spinning string has a net electric charge which is proportional to the rotation parameter. We present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. We also calculate the conserved quantities of the solutions by using the counterterm method.     

Time-dependent fluctuations and particle production in cosmological de Sitter and anti-de Sitter spaces

We study the evolution of time-dependent fluctuations and particle production in an expanding dS and contracting AdS universe. Using the functional Schrödinger formalism we are able to probe the time-dependent regime which is out of the reach of the standard approximations like the Bogolyubov method. In both cases, the evolution of fluctuations is governed by the harmonic oscillator equation with time-dependent frequency. In the case of an expanding dS universe we explicitly show that the frequency of fluctuations produced at a certain moment diminish in time, while the distribution of the created particles quickly approaches the thermal radiation of the dS space. In the case of a contracting AdS universe we show that the frequency of fluctuations produced at a certain moment grow in time. Nominally, the temperature of radiation diverges as the Big Crunch is approaching, however, increasing oscillations of the spectrum make the temperature poorly defined, which is in agreement with the fact that AdS space does not have an event horizon which would cause thermal radiation. Unlimited growth of fluctuations indicates that an eventual tunneling into AdS vacuum would have catastrophic consequences for our universe.     

Quantum anti-de Sitter space

The quantum anti-de Sitter (AdS) group and the quantum AdS space are discussed. A differential calculus on the quantum AdS space is introduced. A conjugation on the quantum AdS algebra is deduced from the corresponding conjugation on the quantum AdS group. Received: 14 April 1999 / Revised version: 13 December 1999 / Published online: 25 September 2000     

Lorentz boosts in de Sitter and anti-de Sitter space-times

Symmetries of de Sitter and anti-de Sitter space-times are discussed. In particular, Lorentz boosts, which appear to be given previously only in the infinitesimal form, are presented here in closed finite forms.Dedicated to the memory of Professor Jozef Kvasnica.I would like to thank Prof. Jií Biák and Dr. Hans-Jürgen Schmidt for useful discussions.     

A note on conserved charges of asymptotically flat and anti-de Sitter spaces in arbitrary dimensions

The calculation of conserved charges of black holes is a rich problem, for which many methods are known. Until recently, there was some controversy on the proper definition of conserved charges in asymptotically anti-de Sitter (AdS) spaces in arbitrary dimensions. This paper provides a systematic and explicit Hamiltonian derivation of the energy and the angular momenta of both asymptotically flat and asymptotically AdS spacetimes in any dimension D  ≥  4. This requires as a first step a precise determination of the asymptotic conditions of the metric and of its conjugate momentum. These conditions happen to be achieved in ellipsoidal coordinates adapted to the rotating solutions. The asymptotic symmetry algebra is found to be isomorphic either to the Poincaré algebra or to the so(D − 1,2) algebra, as expected. In the asymptotically flat case, the boundary conditions involve a generalization of the parity conditions, introduced by Regge and Teitelboim, which are necessary to make the angular momenta finite. The charges are explicitly computed for Kerr and Kerr–AdS black holes for arbitrary D and they are shown to be in agreement with thermodynamical arguments. The author is a FRIA-FNRS bursar (National Fund for Scientific Research, Belgium).     

Electromagnetic quantum effects in anti-de Sitter spacetime

Physics of Atomic Nuclei - The two-point functions of the vector potential and of the field tensor for the electromagnetic field in the background of anti-de Sitter (AdS) spacetime are evaluated in...     

Accelerating black holes in anti-de Sitter universe

A physical interpretation of theC-metric with a negative cosmological constantΛ is suggested. Using a convenient coordinate system it is demonstrated that this class of exact solutions of Einstein’s equations describes uniformly accelerating (possibly charged) black holes in anti-de Sitter universe. Main differences from the analogous de Sitter case are emphasised. Dedicated to my academic teacher Prof. J. Bičák on the occasion of his 60th birthday. This work was supported by the grant GACR-202/99/0261 of the Czech Republic and GAUK 141/2000 of Charles University in Prague.     

Weakly turbulent instability of anti-de Sitter spacetime

We study the nonlinear evolution of a weakly perturbed anti-de?Sitter (AdS) space by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS space is unstable under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.     

Gott time machines in anti-de Sitter space

In 1991 Gott presented a solution of Einstein's field equations in 2+1 dimensions with =0 that contained closed timelike curves (ctc's). This solution was remarkable because at first it did not seem to be unphysical in any other respect. Later, however, it was shown that Gott's solution is tachyonic in a certain sense. Here the case <0 is discussed. We show that it is also possible to constructctc's in this case, in a way analogous to that used by Gott. We also show a special case of this construction to be tachyonic. <0 means that we are dealing with anti-de Sitter space, and since the CTC-construction necessitates some understanding of its structure, a few pages are devoted to this subject.     

Generic cosmic-censorship violation in anti-de Sitter space

We consider (four-dimensional) gravity coupled to a scalar field with potential V(phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti-de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of cosmic censorship in asymptotically flat spacetimes, but we do not have definite results.     

Remarks on quantum field theory on de Sitter and anti-de Sitter space-times

This is a short review of work done in common with Jacques Bros, Michel Gaudin, Ugo Moschella, and Vincent Pasquier. Among results are explicit K?llén?CLehmann representations for products of two free-field two-point functions in the de Sitter and the anti-de Sitter spaces and applications to particle decay.