Entropy of Killing horizons from Virasoro algebra in D-dimensional extended Gauss-Bonnet gravity

We treat D-dimensional black holes with Killing horizon for extended Gauss-Bonnet gravity. We use Carlip method and impose boundary conditions on horizon what enables us to identify Virasoro algebra and evaluate its central charge and Hamiltonian eigenvalue. The Cardy formula allows then to calculate the number of states and thus provides for microscopic interpretation of entropy.Comment: 15 page

Axial gravity: a non-perturbative approach to split anomalies

In a theory of a Dirac fermion field coupled to a metric-axial-tensor (MAT) background, using a Schwinger-DeWitt heat kernel technique, we compute non-perturbatively the two (odd parity) trace anomalies. A suitable collapsing limit of this model corresponds to a theory of chiral fermions coupled to (ordinary) gravity. Taking this limit on the two computed trace anomalies we verify that they tend to the same expression, which coincides with the already found odd parity trace anomaly, with the identical coefficient. This confirms our previous results on this issue.Comment: 43 pages, some additions in section 6.3 and 6.5 plus minor correction

Axial gravity, massless fermions and trace anomalies

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms { and using dimensional regularization}, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones.Comment: 55 pages, comments added in section 2 and 5. Sections 6.4, 6.6, 7, 7.1, 7.2 and Appendices 5.3, 5.5 partially modifie

Conformal entropy and stationary Killing horizons

Using Virasoro algebra approach, black hole entropy formula for a general class of higher curvature Lagrangians with arbitrary dependence on Riemann tensor can be obtained from properties of stationary Killing horizons. The properties used are a consequence of regularity of invariants of Riemann tensor on the horizon. As suggested by an example Lagrangian, eventual generalisation of these results to Lagrangians with derivatives of Riemann tensor, would require assuming regularity of invariants involving derivatives of Riemann tensor and that would lead to additional restrictions on metric functions near horizon

Conformal entropy for generalised gravity theories as a consequence of horizon properties

We show that microscopic entropy formula based on Virasoro algebra follows from properties of stationary Killing horizons for Lagrangians with arbitrary dependence on Riemann tensor. The properties used are consequence of regularity of invariants of Riemann tensor on the horizon. Eventual generalisation of these results to Lagrangians with derivatives of Riemann tensor, as suggested by an example treated in the paper, relies on assuming regularity of invariants involving derivatives of Riemann tensor. This assumption however leads also to new interesting restrictions on metric functions near horizon.Comment: 9 pages, appendix adde

Hawking Fluxes, W∞W_\infty Algebra and Anomalies

We complete the analysis started in [arXiv:0804.0198] of the Hawking radiation calculated by means of anomaly techniques. We concentrate on a static radially symmetric BH, reduced to two dimensions. We compare the two methods used to derive the integrated Hawking radiation, based on the trace and diffeomorphism anomaly, respectively, and show that they can be reduced to the same basic elements. We then concentrate on higher moments of the Hawking radiation and on higher spin currents, and show that, similarly to trace anomalies, also diffeomorphism anomalies are absent from the conservation laws of higher spin currents. We show that the predictivity of the method is due to the $W_\infty$ current algebra underlying the effective model that describes matter around the black hole.Comment: 31 pages, two footnotes, references and minor corrections adde