Regularization of odd-dimensional AdS gravity: Kounterterms

As an alternative to the Dirichlet counterterms prescription, I introduce the concept of Kounterterms as the boundary terms with explicit dependence on the extrinsic curvature K_{ij} that regularize the AdS gravity action. Instead of a Dirichlet boundary condition on the metric, a suitable choice of the boundary conditions --compatible with any asymptotically AdS (AAdS) spacetime-- ensures a finite action principle for all odd dimensions. Background-independent conserved quantities are obtained as Noether charges associated to asymptotic symmetries and their general expression appears naturally split in two parts. The first one gives the correct mass and angular momentum for AAdS black holes and vanishes identically for globally AdS spacetimes. Thus, the second part is a covariant formula for the vacuum energy in AAdS spacetimes and reproduces the results obtained by the Dirichlet counterterms method in a number of cases. It is also shown that this Kounterterms series regularizes the Euclidean action and recovers the correct black hole thermodynamics in odd dimensions.Comment: 35+6 pages, 8 references and an appendix added, improved discussion on boundary conditions and geometrical origin of Kounterterms. Version accepted in JHE

Generalized Area Law under Multi-parameter Rotating Black Hole Spacetime

We study the statistical mechanics for quantum scalar fields under the multi-parameter rotating black hole spacetime in arbitrary D dimensions. The method of analysis is general in the sense that the metric does not depend on the explicit black hole solutions. The generalized Stefan-Boltzmann's law for the scalar field is derived by considering the allowed energy region properly. Then the generalized area law for the scalar field entropy is derived by introducing the invariant regularization parameter in the Rindler spacetime. The derived area law is applied to Kerr-AdS black holes in four and five dimensions. Thermodynamic implication is also discussed.Comment: 27 pages, no figure

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 bigger or equal to 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 Poincare 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.Comment: 27 pages; v2 : references added, minor corrections; v3 : replaced to match published version forthcoming in General Relativity and Gravitatio

Transgression forms and extensions of Chern-Simons gauge theories

A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem.Comment: 28 pages, no figures. Minor changes in the introduction, final comments and reference

Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem

We present a detailed analysis of the 3+1-split formalism of gravity in the presence of a cosmological constant. The formalism helps revealing the intimate connection between holography and the initial value formulation of gravity. We show that the various methods of holographic subtraction of divergences correspond just to different transformations of the canonical variables, such that the initial value problem is properly set up at the boundary. The renormalized boundary energy momentum tensor is a component of the Weyl tensor.Comment: 28 pages; v2: minor improvements, references adde

Conserved charges for gravity with locally AdS asymptotics

A new formula for the conserved charges in 3+1 gravity for spacetimes with local AdS asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the limit of vanishing cosmological constant.Comment: 5 pages, 2 Columns, revtex. Last version for Phys. Rev. Let

Gauss-Bonnet brane-world cosmology without Z2Z_{2}-symmetry

We consider a single 3-brane situated between two bulk spacetimes that posses the same cosmological constant, but whose metrics do not posses a $Z_{2}$-symmetry. On each side of the brane, the bulk is a solution to Gauss-Bonnet gravity. This asymmetry modifies junction conditions, and so new terms arise in the Friedmann equation. If these terms become dominant, these behave cosmological constant at early times for some case, and might remove the initial singularity for other case. However, we show that these new terms can not become dominant ones under usual conditions when our brane is outside an event horizon. We also show that any brane-world scenarios of this type revert to a $Z_{2}$-symmetric form at late times, and hence rule out certain proposed scenarios.Comment: 8 pages, 3 figures; Minor typos corrected. References added. V3: Numerical errors are corrected. Fig.1 and Fig.3 are replaced. V4: published versio

Logarithmic correction to BH entropy as Noether charge

We consider the role of the type-A trace anomaly in static black hole solutions to semiclassical Einstein equation in four dimensions. Via Wald's Noether charge formalism, we compute the contribution to the entropy coming from the anomaly induced effective action and unveil a logarithmic correction to the Bekenstein-Hawking area law. The corrected entropy is given by a seemingly universal formula involving the coefficient of the type-A trace anomaly, the Euler characteristic of the horizon and the value at the horizon of the solution to the uniformization problem for Q-curvature. Two instances are examined in detail: Schwarzschild and a four-dimensional massless topological black hole. We also find agreement with the logarithmic correction due to one-loop contribution of conformal fields in the Schwarzschild background.Comment: 14 pages, JHEP styl

The Nuclear Stellar Cluster in the Seyfert~1 Galaxy NGC 3227: High Angular Resolution NIR Imaging and Spectroscopy

NIR high angular resolution speckle imaging and imaging spectroscopy of the nuclear region (10'' ~ 840pc) of the Seyfert1 galaxy NGC3227 are presented. A nuclear stellar cluster is slightly resolved in the J and H band with increasing contribution to the NIR continuum from the K to the J band. The stellar absorption lines are extended compared to the neighboring continuum suggesting a cluster size of ~ 70pc FWHM. Analysis of those lines suggests that the stars are contributing about 65% (40%) of the total continuum emission in the H (K) band in a 3.6'' aperture. Population synthesis in conjunction with NIR spectral synthesis indicates an age of 25 to 50 Myr when red supergiants contribute most to the NIR light. This is supported by published optical data on the MgIb line and the CaII triplet. Although a higher age of ~ 0.5 Gyr where AGB stars dominate the NIR light can not be excluded, the observed parameters are at the limit of those expected for a cluster dominated by AGB stars. However, in either case the resolved stellar cluster contributes only about ~ 15 % of the total dynamical mass in the inner 300pc implying another much older stellar population. Pure constant star formation over the last 10 Gyr can be excluded. Therefore, at least two star formation/starburst events took place in the nucleus of NGC3227. Since such sequences in the nuclear star formation history are also observed in the nuclei of other galaxies a link between the activity of the star formation and the AGN itself seems likely.Comment: accepted for publication in the Astrophysical Journal, 46 pages, 15 figure

Entropy function and attractors for AdS black holes

We apply Sen's entropy formalism to the study of the near horizon geometry and the entropy of asymptotically AdS black holes in gauged supergravities. In particular, we consider non-supersymmetric electrically charged black holes with AdS_2 xS^{d-2} horizons in U(1)^4 and U(1)^3 gauged supergravities in d=4 and d=5 dimensions, respectively. We study several cases including static/rotating, BPS and non-BPS black holes in Einstein as well as in Gauss-Bonnet gravity. In all examples, the near horizon geometry and black hole entropy are derived by extremizing the entropy function and are given entirely in terms of the gauge coupling, the electric charges and the angular momentum of the black hole.Comment: 27 pages, no figures, references adde