Gravitational entropy of Kerr black holes

Classical invariants of General Relativity can be used to approximate the entropy of the gravitational field. In this work, we study two proposed estimators based on scalars constructed out from the Weyl tensor, in Kerr spacetime. In order to evaluate Clifton, Ellis and Tavakol's proposal, we calculate the gravitational energy density, gravitational temperature, and gravitational entropy of the Kerr spacetime. We find that in the frame we consider, Clifton et al.'s estimator does not reproduce the Bekenstein-Hawking entropy of a Kerr black hole. The results are compared with previous estimates obtained by the authors using the Rudjord-Gr$\varnothing$n-Hervik approach. We conclude that the latter represents better the expected behaviour of the gravitational entropy of black holes.Comment: 12 pages, 7 figures, accepted for publication in General Relativity and Gravitatio

Symplectic Regularization of Binary Collisions in the Circular N+2 Sitnikov Problem

We present a brief overview of the regularizing transformations of the Kepler problem and we relate the Euler transformation with the symplectic structure of the phase space of the N-body problem. We show that any particular solution of the N-body problem where two bodies have rectilinear dynamics can be regularized by a linear symplectic transformation and the inclusion of the Euler transformation into the group of symplectic local diffeomorphisms over the phase space. As an application we regularize a particular configuration of the circular N+2 Sitnikov problem.Comment: 23 pages, 5 figures. References to algorithmic regularization included, changes in References and small typographic corrections. Accepted in J. of Phys. A: Math. Theor 44 (2011) 265204 http://stacks.iop.org/1751-8121/44/26520

Accretion disks around black holes in modified strong gravity

Stellar-mass black holes offer what is perhaps the best scenario to test theories of gravity in the strong-field regime. In particular, f(R) theories, which have been widely discuss in a cosmological context, can be constrained through realistic astrophysical models of phenomena around black holes. We aim at building radiative models of thin accretion disks for both Schwarzschild and Kerr black holes in f(R) gravity. We study particle motion in f(R)-Schwarzschild and Kerr space-times. We present the spectral energy distribution of the accretion disk around constant Ricci scalar f(R) black holes, and constrain specific f(R) prescriptions using features of these systems. A precise determination of both the spin and accretion rate onto black holes along with X-ray observations of their thermal spectrum might allow to identify deviations of gravity from General Relativity. We use recent data on the high-mass X-ray binary Cygnus X-1 to restrict the values of the parameters of a class of f(R) models.Comment: 16 pages, 20 figures, accepted for publication in Astronomy & Astrophysic