Exact quasinormal modes for a special class of black holes

Analytic exact expressions for the quasinormal modes of scalar and electromagnetic perturbations around a special class of black holes are found in d\ge3 dimensions. It is shown that, the size of the black hole provides a bound for the angular momentum of the perturbation. Quasinormal modes appear when this bound is fulfilled, otherwise the excitations become purely damped.Comment: 8 pages, no figures. Slightly updated version of the plenary talk given at the General Relativity Conference: "50 Years of FaMAF and Workshop on Global Problems in Relativity", hosted during November 2006 at FaMAF, Universidad Nacional de Cordoba, Cordoba, Argentina

Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity

Asymptotically AdS rotating black holes for the Bergshoeff-Hohm-Townsend (BHT) massive gravity theory in three dimensions are considered. In the special case when the theory admits a unique maximally symmetric solution, apart from the mass and the angular momentum, the black hole is described by an independent "gravitational hair" parameter, which provides a negative lower bound for the mass. This bound is saturated at the extremal case and, since the temperature and the semiclassical entropy vanish, it is naturally regarded as the ground state. The absence of a global charge associated with the gravitational hair parameter reflects through the first law of thermodynamics in the fact that the variation of this parameter can be consistently reabsorbed by a shift of the global charges, giving further support to consider the extremal case as the ground state. The rotating black hole fits within relaxed asymptotic conditions as compared with the ones of Brown and Henneaux, such that they are invariant under the standard asymptotic symmetries spanned by two copies of the Virasoro generators, and the algebra of the conserved charges acquires a central extension. Then it is shown that Strominger's holographic computation for general relativity can also be extended to the BHT theory; i.e., assuming that the quantum theory could be consistently described by a dual conformal field theory at the boundary, the black hole entropy can be microscopically computed from the asymptotic growth of the number of states according to Cardy's formula, in exact agreement with the semiclassical result.Comment: 10 pages, no figure

Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum

The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in $d\geq5$ dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for $d>5$. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximally symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum

'Technical Safety’ or ‘System Safety’? Why Names Matter

By providing safety and risk management consulting services, we have the opportunity to be regularly involved with clients from a number of different industries. We often interact with professionals of varied trajectories and backgrounds, many of whom have never received comprehensive training in system safety. Those individuals are by no means less competent in their jobs; however, their schooling in system safety often comes from a senior colleague or mentor who held a safety-related position during a long career in a single industry. More often than not, the individual’s understanding of system safety is reduced to his or her limited exposure to this rich and diverse field

Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns

An exhaustive classification of certain class of static solutions for the five-dimensional Einstein-Gauss-Bonnet theory in vacuum is presented. The class of metrics under consideration is such that the spacelike section is a warped product of the real line with a nontrivial base manifold. It is shown that for generic values of the coupling constants the base manifold must be necessarily of constant curvature, and the solution reduces to the topological extension of the Boulware-Deser metric. It is also shown that the base manifold admits a wider class of geometries for the special case when the Gauss-Bonnet coupling is properly tuned in terms of the cosmological and Newton constants. This freedom in the metric at the boundary, which determines the base manifold, allows the existence of three main branches of geometries in the bulk. For negative cosmological constant, if the boundary metric is such that the base manifold is arbitrary, but fixed, the solution describes black holes whose horizon geometry inherits the metric of the base manifold. If the base manifold possesses a negative constant Ricci scalar, two different kinds of wormholes in vacuum are obtained. For base manifolds with vanishing Ricci scalar, a different class of solutions appears resembling "spacetime horns". There is also a special case for which, if the base manifold is of constant curvature, due to certain class of degeneration of the field equations, the metric admits an arbitrary redshift function. For wormholes and spacetime horns, there are regions for which the gravitational and centrifugal forces point towards the same direction. All these solutions have finite Euclidean action, which reduces to the free energy in the case of black holes, and vanishes in the other cases. Their mass is also obtained from a surface integral.Comment: 31 pages, 1 figure, minor changes and references added. Final version to be published in PR

Vacuum solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory

The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial base manifold. For arbitrary values of the Gauss-Bonnet coupling, the base manifold must be Einstein with an additional scalar restriction. The geometry of the boundary can be relaxed only when the Gauss-Bonnet coupling is related with the cosmological and Newton constants, so that the theory admits a unique maximally symmetric solution. This additional freedom in the boundary metric allows the existence of three main branches of geometries in the bulk, containing new black holes and wormholes in vacuum.Comment: Prepared for the proceedings of the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, July 2008, Joao Pessoa, Brasil. 4 pages, References adde

Static spherically symmetric solutions for conformal gravity in three dimensions

Static spherically symmetric solutions for conformal gravity in three dimensions are found. Black holes and wormholes are included within this class. Asymptotically the black holes are spacetimes of arbitrary constant curvature, and they are conformally related to the matching of different solutions of constant curvature by means of an improper conformal transformation. The wormholes can be constructed from suitable identifications of a static universe of negative spatial curvature, and it is shown that they correspond to the conformal matching of two black hole solutions with the same mass.Comment: Talk given at the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, Joao Pessoa, Brazil, 29 Jun - 5 Jul 2008. 4 pages and one figur

The Forced van der Pol Equation II: Canards in the reduced system

This is the second in a series of papers about the dynamics of the forced van der Pol oscillator [J. Guckenheimer, K. Hoffman, and W. Weckesser, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 1–35]. The first paper described the reduced system, a two dimensional flow with jumps that reflect fast trajectory segments in this vector field with two time scales. This paper extends the reduced system to account for canards, trajectory segments that follow the unstable portion of the slow manifold in the forced van der Pol oscillator. This extension of the reduced system serves as a template for approximating the full nonwandering set of the forced van der Pol oscillator for large sets of parameter values, including parameters for which the system is chaotic. We analyze some bifurcations in the extension of the reduced system, building upon our previous work in [J. Guckenheimer, K. Hoffman, and W. Weckesser, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 1–35]. We conclude with computations of return maps and periodic orbits in the full three dimensional flow that are compared with the computations and analysis of the reduced system. These comparisons demonstrate numerically the validity of results we derive from the study of canards in the reduced system