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

Gravitational entropy of black holes and wormholes

Pure thermodynamical considerations to describe the entropic evolution of the universe seem to violate the Second Law of Thermodynamics. This suggests that the gravitational field itself has entropy. In this paper we expand recent work done by Rudjord, Gr{\O}n and Sigbj{\O}rn where they suggested a method to calculate the gravitational entropy in black holes based on the so-called `Weyl curvature conjecture'. We study the formulation of an estimator for the gravitational entropy of Reissner-Nordstr\"om, Kerr, Kerr-Newman black holes, and a simple case of wormhole. We calculate in each case the entropy for both horizons and the interior entropy density. Then, we analyse whether the functions obtained have the expected behaviour for an appropriate description of the gravitational entropy density.Comment: 11 pages, 11 figures, accepted for publication in International Journal of Theoretical Physic

Financial Restrictions, Personal Income Tax (PIT) and Demand for a Permanent Home in a Dynamic Model. An analysis with Panel Data for Spain

This paper analyzes the way in which income tax and liquidity determine the purchase or rental of a permanent home in Spain. To do this, we have developed a theoretical dynamic model based on Euler’s equation. This model is verified using a sample from the 1991-1995 Panel of income taxpayers. Results suggest that the degree of financial restriction is the most relevant variable when determining the possibility of purchasing a home, while tax incentives increase their relative weighting once this asset has been acquired. Incentives for renting a home are relatively insignificant particularly for taxpayers who habitually rent their homes.personal income tax, liquidity, permanent home, tax incentives

High-energy signatures of binary systems of supermassive black holes

Context. Binary systems of supermassive black holes are expected to be strong sources of long gravitational waves prior to merging. These systems are good candidates to be observed with forthcoming space-borne detectors. Only a few of these systems, however, have been firmly identified to date. Aims. We aim at providing a criterion for the identification of some supermassive black hole binaries based on the characteristics of the high-energy emission of a putative relativistic jet launched from the most massive of the two black holes. Methods. We study supermassive black hole binaries where the less massive black hole has carved an annular gap in the circumbinary disk, but nevertheless there is a steady mass flow across its orbit. Such a perturbed disk is hotter and more luminous than a standard thin disk in some regions. Assuming that the jet contains relativistic electrons, we calculate its broadband spectral energy distribution focusing on the inverse Compton up-scattering of the disk photons. We also compute the opacity to the gamma rays produced in the jet by photon annihilation with the disk radiation and take into account the effects of the anisotropy of the target photon field as seen from the jet. Results. We find that the excess of low-energy photons radiated by the perturbed disk causes an increment in the external Compton emission from the jet in the X-ray band, and a deep absorption feature at energies of tens of TeVs for some sets of parameters. According to our results, observations with Cherenkov telescopes might help in the identification of supermassive black hole binaries, especially those black hole binaries that host primaries from tens to hundreds of million of solar masses.Comment: 12 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Financial Restrictions, Personal Income Tax (PIT) and Demand for a Permanent Home in a Dynamic Model. An analysis with Panel Data for Spain

This paper analyzes the way in which income tax and liquidity determine the purchase or rental of a permanent home in Spain. To do this, we have developed a theoretical dynamic model based on Euler’s equation. This model is verified using a sample from the 1991-1995 Panel of income taxpayers. Results suggest that the degree of financial restriction is the most relevant variable when determining the possibility of purchasing a home, while tax incentives increase their relative weighting once this asset has been acquired. Incentives for renting a home are relatively insignificant particularly for taxpayers who habitually rent their homes.personal income tax, liquidity, permanent home, tax incentives

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

Cosmological black holes and the direction of time

Macroscopic irreversible processes emerge from fundamental physical laws of reversible character. The source of the local irreversibility seems to be not in the laws themselves but in the initial and boundary conditions of the equations that represent the laws. In this work we propose that the screening of currents by black hole event horizons determines, locally, a preferred direction for the flux of electromagnetic energy. We study the growth of black hole event horizons due to the cosmological expansion and accretion of cosmic microwave background radiation, for different cosmological models. We propose generalized McVittie co-moving metrics and integrate the rate of accretion of cosmic microwave background radiation onto a supermassive black hole over cosmic time. We find that for flat, open, and closed Friedmann cosmological models, the ratio of the total area of the black hole event horizons with respect to the area of a radial co-moving space-like hypersurface always increases. Since accretion of cosmic radiation sets an absolute lower limit to the total matter accreted by black holes, this implies that the causal past and future are not mirror symmetric for any spacetime event. The asymmetry causes a net Poynting flux in the global future direction; the latter is in turn related to the ever increasing thermodynamic entropy. Thus, we expose a connection between four different "time arrows": cosmological, electromagnetic, gravitational, and thermodynamic.Comment: 13 pages, 2 figures in Foundations of Science (2017