Canonical quantization and black hole perturbations

We examine the possibility of a constraint-free quantization of linearized gravity, based on the Teukolsky equation for black hole perturbations. We exhibit a simple quadratic (but complex) Lagrangian for the Teukolsky equation, leading to the interpretation that the elementary excitations (gravitons bound to the Kerr black hole) are unstable.Comment: Contribution to the XIXth Max Born Symposium, Wroclaw. 10 pages, LaTeX, no figure

Solutions of the Regge Equations on some Triangulations of CP^2

Simplicial geometries are collections of simplices making up a manifold together with an assignment of lengths to the edges that define a metric on that manifold. The simplicial analogs of the Einstein equations are the Regge equations. Solutions to these equations define the semiclassical approximation to simplicial approximations to a sum-over-geometries in quantum gravity. In this paper, we consider solutions to the Regge equations with cosmological constant that give Euclidean metrics of high symmetry on a family of triangulations of CP^2 presented by Banchoff and Kuhnel. This family is characterized by a parameter p. The number of vertices grows larger with increasing p. We exhibit a solution of the Regge equations for p=2 but find no solutions for p=3. This example shows that merely increasing the number of vertices does not ensure a steady approach to a continuum geometry in the Regge calculus.Comment: 11 pages, uuencoded revtex w/ embedded ps figure. Replaces a submission which had corrupted ps fil

Charged black holes: Wave equations for gravitational and electromagnetic perturbations

A pair of wave equations for the electromagnetic and gravitational perturbations of the charged Kerr black hole are derived. The perturbed Einstein-Maxwell equations in a new gauge are employed in the derivation. The wave equations refer to the perturbed Maxwell spinor $\Phi_0$ and to the shear $\sigma$ of a principal null direction of the Weyl curvature. The whole construction rests on the tripod of three distinct derivatives of the first curvature $\kappa$ of a principal null direction.Comment: 12 pages, to appear in Ap.

The Speciality Index as invariant indicator in the BKL Mixmaster Dynamics

The speciality index, which has been mainly used in Numerical Relativity for studying gravitational waves phenomena as an indicator of the special or non-special Petrov type character of a spacetime, is applied here in the context of Mixmaster cosmology, using the Belinski-Khalatnikov-Lifshitz map. Possible applications for the associated chaotic dynamics are discussed

Cost Reduction by Means of Alternative Solutions

In some projects the offered remuneration is lower than the estimated total costs. There are three possibilities to handle this problem. The first two is either to resign from the implementation, or to accept it knowing that we will loose money, but can regain it later in another project. In this latter case we have to determine the optimal resource allocation with minimal total cost. In the scheduling phase we can use some cost minimizing method. After that we can determine the lower and the upper bound of the start time of the activities. The next step is to determine a feasible solution and then the optimal resource allocation. The third possibility is to accomplish the project and find alternative implementation of activities that requires lower variable costs. During the search for alternative implementation of activities the most important aspect should be the quality, the decrease of costs is only the second one. If the total cost is lower than the offered remuneration we have to find the optimal resource allocation for the problem. Sometimes we cannot find alternative implementations, e.g. when a minimal quality level is given. In this case we can decide to either refuse or accept the implementation based on the extent of possible loss of money