Do Killing-Yano tensors form a Lie Algebra?

Killing-Yano tensors are natural generalizations of Killing vectors. We investigate whether Killing-Yano tensors form a graded Lie algebra with respect to the Schouten-Nijenhuis bracket. We find that this proposition does not hold in general, but that it does hold for constant curvature spacetimes. We also show that Minkowski and (anti)-deSitter spacetimes have the maximal number of Killing-Yano tensors of each rank and that the algebras of these tensors under the SN bracket are relatively simple extensions of the Poincare and (A)dS symmetry algebras.Comment: 17 page

Tension term, interchange symmetry, and the analogy of energy and tension laws of the AdS soliton solution

In this paper, we reconsider the energy and tension laws of the Ricci flat black hole by taking the contribution of the tension term into account. After this considering and inspired by the interchange symmetry between the Ricci flat black hole and the AdS soliton solution which arises from the double analytic continuation of the time and compact spatial direction, we find out the analogy of the energy and tension laws of the AdS soliton solution. Moreover, we also investigate the energy and tension laws of the boosted Ricci flat black hole, and discuss the boosted AdS soliton solution. However, although there is the same interchange symmetry between the boosted Ricci flat black hole and boosted AdS soliton, the analogy of laws of the boosted AdS soliton solution may be of no sense for the existence of the closed timelike curves and conical singularity. In spite of that, the conserved charges such as the energy and momentum of the boosted AdS soliton are well-defined, and an interesting result is that its energy is lower than that of the static AdS soliton. On the other hand, note that although the laws obtained above are the same as those of the asymptotically flat case, the underlying deduced contents are different. Thus, our results could also be considered as a simple generalization to the asymptotically AdS case. Moreover, during the calculation, we find that there may be a new way to define the gravitational tension which can come from the quasi-local stress tensor of the counter-term method.Comment: V4: 15 pages, no figure, version to appear in JHE

A Probe Particle in Kerr-Newman-deSitter Cosmos

We consider the force acting on a spinning charged test particle (probe particle) with the mass m and the charge q in slow rotating the Kerr-Newman-deSitter(KNdS) black hole with the mass M and the charge Q. We consider the case which the spin vector of the probe particle is parallel to the angular momentum vector of the KNdS space-time. We take account of the gravitational spin-spin interaction under the slow rotating limit of the KNdS space-time. When Q=M and q=m, we show that the force balance holds including the spin-spin interaction and the motion is approximately same as that of a particle in the deSitter space-time. This force cancellation suggests the possibility of the existence of an exact solution of spinning multi-KNdS black hole.Comment: 7 pages, Classical and Quantum Gravity accepte

Are All Static Black Hole Solutions Spherically Symmetric?

The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples demonstrating that static black holes need not be spherically symmetric exist in theories, such as the standard electroweak model, with electrically charged massive vector fields. In such theories, a magnetically charged Reissner-Nordstrom solution with sufficiently small horizon radius is unstable against the development of a nonzero vector field outside the horizon. General arguments show that, for generic values of the magnetic charge, this field cannot be spherically symmetric. Explicit construction of the solution shows that it in fact has no rotational symmetry at all.Comment: 6 pages, plain TeX. Submitted to GRF Essay Competitio

The effectiveness of resource levelling tools for Resource Constraint Project Scheduling Problem

Abstract The PERT/CPM network techniques are based on the assumption that all needed resources will be available. The scarcity of resources is a usual reason for project delays. For the solution of the Resource Constrained Project Scheduling Problem (RCPSP) other methods have been applied. The objective of these methods consists in minimizing the project's duration by considering both the precedence and resource constraints. Project Management software packages solve the resource conflicts using resource levelling. The paper evaluates the effectiveness of resource levelling tools of three popular packages by comparing the results when levelling two real construction projects as case studies

Breaking cosmic strings without monopoles

It is shown that topologically stable cosmic strings can, in fact, appear to end or to break, even in theories without monopoles. This can occur whenever the spatial topology of the universe is nontrivial. For the case of Abelian-Higgs strings, we describe the gauge and scalar field configurations necessary for a string to end on a black hole. We give a lower bound for the rate at which a cosmic string will break via black hole pair production, using an instanton calculation based on the Euclidean C-metric

Separability of Gravitational Perturbation in Generalized Kerr-NUT-de Sitter Spacetime

Generalized Kerr-NUT-de Sitter spacetime is the most general spacetime which admits a rank-2 closed conformal Killing-Yano tensor. It contains the higher-dimensional Kerr-de Sitter black holes with partially equal angular momenta. We study the separability of gravitational perturbations in the generalized Kerr-NUT-de Sitter spacetime. We show that a certain type of tensor perturbations admits the separation of variables. The linearized perturbation equations for the Einstein condition are transformed into the ordinary differential equations of Fuchs type.Comment: 47 pages, LaTeX; v2: typos corrected; v3: a reference and comments added, details of calculations are moved to appendices, version accepted for publication in IJMP

SO(4) Invariant States in Quantum Cosmology

The phenomenon of linearisation instability is identified in models of quantum cosmology that are perturbations of mini-superspace models. In particular, constraints that are second order in the perturbations must be imposed on wave functions calculated in such models. It is shown explicitly that in the case of a model which is a perturbation of the mini-superspace which has $S^3$ spatial sections these constraints imply that any wave functions calculated in this model must be SO(4) invariant. (This replaces the previous corrupted version.)Comment: 15 page