Symmetries at stationary Killing horizons

It has often been suggested (especially by Carlip) that spacetime symmetries in the neighborhood of a black hole horizon may be relevant to a statistical understanding of the Bekenstein-Hawking entropy. A prime candidate for this type of symmetry is that which is exhibited by the Einstein tensor. More precisely, it is now known that this tensor takes on a strongly constrained (block-diagonal) form as it approaches any stationary, non-extremal Killing horizon. Presently, exploiting the geometrical properties of such horizons, we provide a particularly elegant argument that substantiates this highly symmetric form for the Einstein tensor. It is, however, duly noted that, on account of a "loophole", the argument does fall just short of attaining the status of a rigorous proof.Comment: 11 pages, Revte

The horizon and its charges in the first order gravity

In this work the algebra of charges of diffeomorphisms at the horizon of generic black holes is analyzed within first order gravity. This algebra reproduces the algebra of diffeomorphisms at the horizon, (Diff(S^1)), without central extension

Introduction to Isolated Horizons in Numerical Relativity

We present a coordinate-independent method for extracting mass (M) and angular momentum (J) of a black hole in numerical simulations. This method, based on the isolated horizon framework, is applicable both at late times when the black hole has reached equilibrium, and at early times when the black holes are widely separated. We show how J and M can be determined in numerical simulations in terms of only those quantities which are intrinsic to the apparent horizon. We also present a numerical method for finding the rotational symmetry vector field (required to calculate J) on the horizon.Comment: 14 pages, revtex4, 7 figures. Final PRD versio

Asymptotic symmetries on Killing horizons

We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in the Einstein theory with or without the cosmological constant. Those asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of asymptotic Killing vectors and find that the group of the asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved under not only diffeomorphisms but also non-trivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the $\mathit{Diff}(S^1)$ subgroup, which results from the supertranslations dependent only on the null coordinate, it is shown that the Poisson bracket algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire non-trivial central charges. Finally, by considering extended symmetries, we discuss that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with non-trivial central charges, which will not be justified when we respect the spherical symmetry of Killing horizons.Comment: 28 page

Near-Horizon Conformal Symmetry and Black Hole Entropy in Any Dimension

Recently, Carlip proposed a derivation of the entropy of the two-dimensional dilatonic black hole by investigating the Virasoro algebra associated with a newly introduced near-horizon conformal symmetry. We point out not only that the algebra of these conformal transformations is not well defined on the horizon, but also that the correct use of the eigenvalue of the operator $L_0$ yields vanishing entropy. It has been shown that these problems can be resolved by choosing a different basis of the conformal transformations which is regular even at the horizon. We also show the generalization of Carlip's derivation to any higher dimensional case in pure Einstein gravity. The entropy obtained is proportional to the area of the event horizon, but it also depends linearly on the product of the surface gravity and the parameter length of a horizon segment in consideration. We finally point out that this derivation of black hole entropy is quite different from the ones proposed so far, and several features of this method and some open issues are also discussed.Comment: 14 pages, no figur

Poisson Algebra of Diffeomorphism Generators in a Spacetime Containing a Bifurcation

In this article we will analyze the possibility of a nontrivial central extension of the Poisson algebra of the diffeomorphism generators, which respect certain boundary conditions on the black hole bifurcation. The origin of a possible central extension in the algebra is due to the existence of boundary terms in the in the canonical generators. The existence of such boundary terms depend on the exact boundary conditions one takes. We will check two possible boundary conditions i.e. fixed bolt metric and fixed surface gravity. In the case of fixed metric the the action acquires a boundary term associated to the bifurcation but this is canceled in the Legendre transformation and so absent in the canonical generator and so in this case the possibility of a nontrivial central extension is ruled out. In the case of fixed surface gravity the boundary term in the action is absent but present in the Hamiltonian. Also in this case we will see that there is no nontrivial central extension, also if there exist a boundary term in the generator.Comment: LaTex 20 pages, some misprints corrected, 2 references added. Accepted for publication on Phys. Rev.

The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked Singularities in the Teukolsky Perturbation Theory

We give a new theoretical basis for examination of the presence of the Kerr black hole (KBH) or the Kerr naked singularity (KNS) in the central engine of different astrophysical objects around which astrophysical jets are typically formed: X-ray binary systems, gamma ray bursts (GRBs), active galactic nuclei (AGN), etc. Our method is based on the study of the exact solutions of the Teukolsky master equation for electromagnetic perturbations of the Kerr metric. By imposing original boundary conditions on the solutions so that they describe a collimated electromagnetic outflow, we obtain the spectra of possible {\em primary jets} of radiation, introduced here for the first time. The theoretical spectra of primary electromagnetic jets are calculated numerically. Our main result is a detailed description of the qualitative change of the behavior of primary electromagnetic jet frequencies under the transition from the KBH to the KNS, considered here as a bifurcation of the Kerr metric. We show that quite surprisingly the novel spectra describe linearly stable primary electromagnetic jets from both the KBH and the KNS. Numerical investigation of the dependence of these primary jet spectra on the rotation of the Kerr metric is presented and discussed.Comment: 18 pages, 35 figures, LaTeX file. Final version. Accepted for publication in Astrophysics and Space Science. Amendments. Typos corrected. Novel notion -"primary jet" is introduced. New references and comments adde

Intra‐clinothem variability in sedimentary texture and process regime recorded down slope profiles

Shelf‐margin clinothem successions can archive process interactions at the shelf to slope transition, and their architecture provides constraints on the interplay of factors that control basin‐margin evolution. However, detailed textural analysis and facies distributions from shelf to slope transitions remain poorly documented. This study uses quantitative grain‐size and sorting data from coeval shelf and slope deposits of a single clinothem that crops out along a 5 km long, dip‐parallel transect of the Eocene Sobrarbe Deltaic Complex (Ainsa Basin, south‐central Pyrenees, Spain). Systematic sampling of sandstone beds tied to measured sections has captured vertical and basinward changes in sedimentary texture and facies distributions at an intra‐clinothem scale. Two types of hyperpycnal flow‐related slope deposits, both rich in mica and terrestrial organic matter, are differentiated according to grain size, sorting and bed geometry: (i) sustained hyperpycnal flow deposits, which are physically linked to coarse channelized sediments in the shelf setting and which deposit sand down the complete slope profile; (ii) episodic hyperpycnal flow deposits, which are disconnected from, and incise into, shelf sands and which are associated with sediment bypass of the proximal slope and coarse‐grained sand deposition on the medial and distal slope. Both types of hyperpycnites are interbedded with relatively homogenous, organic‐free and mica‐free, well‐sorted, very fine‐grained sandstones, which are interpreted to be remobilized from wave‐dominated shelf environments; these wave‐dominated deposits are found only on the proximal and medial slope. Coarse‐grained sediment bypass into the deeper‐water slope settings is therefore dominated by episodic hyperpycnal flows, whilst sustained hyperpycnal flows and turbidity currents remobilizing wave‐dominated shelf deposits are responsible for the full range of grain sizes in the proximal and medial slope, thus facilitating clinoform progradation. This novel dataset highlights previously undocumented intra‐clinothem variability related to updip changes in the shelf process‐regime, which is therefore a key factor controlling downdip architecture and resulting sedimentary texture

On the selection of AGN neutrino source candidates for a source stacking analysis with neutrino telescopes

The sensitivity of a search for sources of TeV neutrinos can be improved by grouping potential sources together into generic classes in a procedure that is known as source stacking. In this paper, we define catalogs of Active Galactic Nuclei (AGN) and use them to perform a source stacking analysis. The grouping of AGN into classes is done in two steps: first, AGN classes are defined, then, sources to be stacked are selected assuming that a potential neutrino flux is linearly correlated with the photon luminosity in a certain energy band (radio, IR, optical, keV, GeV, TeV). Lacking any secure detailed knowledge on neutrino production in AGN, this correlation is motivated by hadronic AGN models, as briefly reviewed in this paper. The source stacking search for neutrinos from generic AGN classes is illustrated using the data collected by the AMANDA-II high energy neutrino detector during the year 2000. No significant excess for any of the suggested groups was found.Comment: 43 pages, 12 figures, accepted by Astroparticle Physic

Quantization of the interior Schwarzschild black hole

We study a Hamiltonian quantum formalism of a spherically symmetric space-time which can be identified with the interior of a Schwarzschild black hole. The phase space of this model is spanned by two dynamical variables and their conjugate momenta. It is shown that the classical Lagrangian of the model gives rise the interior metric of a Schwarzschild black hole. We also show that the the mass of such a system is a Dirac observable and then by quantization of the model by Wheeler-DeWitt approach and constructing suitable wave packets we get the mass spectrum of the black hole.Comment: 12 pages, 1 figure, revised versio