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K. H. C. Castello-Branco

Publications and source records attributed to K. H. C. Castello-Branco.

9 recordsLinked to original sources
arXiv2021

Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole

We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface of constant radius $r$, in the region $m\,<<\,r\,<<\infty$, where $m$ is the mass of the black hole. Considering the usual asymptotic expression for the perturbed metric components, we arrive at finite values for the energy spectrum. The perturbed energy depends on the two integers $n$ and $l$ that describe the quasinormal modes. In this sense, the energy perturbations are discretised. We also obtain a simple expression for the decrease of the flux of gravitational radiation of the perturbations.

gr-qc↗
arXiv2018

Gravitational Pressure and the Accelerating Universe

In the context of the Teleparallel Equivalent of General Relativity (TEGR) one can obtain an alternative insight into General Relativity, as has been shown in addressing properties as energy, momentum and angular momentum of the gravitational field. In this paper, we apply the definition, that arises from the field equation of the the TEGR, for the stress-energy-momentum tensor of the gravitational field, whose spatial components naturally lead to the definition of gravitational pressure, to compute the total space-time pressure, due to the gravitational and matter fields, over a spherical, space-like two-surface of a Friedman-Robertson-Walker (FRW) universe, for any curvature index. In particular, for a spatially flat FRW universe in the actual era (i.e., for "cold matter"), it resulted that the pressure (now due only to the gravitational field) is outwardly directed over any spherical, spatial two-surface. This surface can be, in particular, the apparent horizon of a spatially flat FRW universe (in this case, the apparent horizon coincides with the Hubble horizon). Assuming the validity of the first law of thermodynamics for matter and gravity, and taking into account the contribution of the gravitational field to both the energy and the pressure terms in the first law of the (gravitational) thermodynamics, as well as considering the thermal character of the apparent horizon of the spatially flat FRW universe, we have thus obtained a value of the gravitational pressure that is very close to the observed value. We interpret this result as a possibility that the accelerated expansion of the actual universe might be due to the effect of the pressure of the very gravitational field, instead of an totally unkown (dark) energy.

gr-qc↗
arXiv2013

Gravitational energy, gravitational pressure, and the thermodynamics of a charged black hole in teleparallel gravity

We investigate, in the case of a Reissner-Nordström black hole, the definitions of gravitational energy and gravitational pressure that naturally arise in the framework of the Teleparallel Equivalent of General Relativity. In particular, we calculate the gravitational energy enclosed by the event horizon of the black hole, E, and the radial pressure over it, p. With these quantities we then analyse the thermodynamic relation dE + pdV (as p turns out to be a density, dV is actually given by dV = dr dθdϕ, in spherically-type coordinates). We compare the latter with the standard first law of black hole dynamics. Also, by identifying TdS = dE + pdV, we comment on a possible modification of the standard, Bekenstein-Hawking entropy-area relation due to gravitational energy and gravitational pressure of the black hole. The infinitesimal variations in question refer to the Penrose process for a Reissner-Nordström black hole.

gr-qc↗
arXiv2012

Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach

We investigate the distribution of gravitational energy on the spacetime of a Schwarzschild black hole immersed in a cosmic magnetic field. This is done in the context of the {\it Teleparallel Equivalent of General Relativity}, which is an alternative geometrical formulation of General Relativity, where gravity is describe by a spacetime endowed with torsion, rather than curvature, with the fundamental field variables being tetrads. We calculate the energy enclosed by a two-surface of constant radius - in particular, the energy enclosed by the event horizon of the black hole. In this case we find that the magnetic field has the effect of increasing the gravitational energy as compared to the vacuum Schwarzschild case. We also compute the energy (i) in the weak magnetic field limit, (ii) in the limit of vanishing magnetic field, and (iii) in the absence of the black hole. In all cases our results are consistent with what should be expected on physical grounds.

gr-qc↗
arXiv2011

Free-fall in a uniform gravitational field in non-commutative quantum mechanics

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM.

hep-th↗
arXiv2005

High overtones of Dirac perturbations of a Schwarzschild black hole

Using the Frobenius method, we find high overtones of the Dirac quasinormal spectrum for the Schwarzschild black hole. At high overtones, the spacing for imaginary part of $ω_{n}$ is equidistant and equals to $\Im{ω_{n+1}}-\Im{ω_{n}} =i/8M$, ($M$ is the black hole mass), which is twice less than that for fields of integer spin. At high overtones, the real part of $ω_{n}$ goes to zero. This supports the suggestion that the expected correspondence between quasinormal modes and Barbero-Immirzi parameter in Loop Quantum Gravity is just a numerical coincidence.

hep-th↗
arXiv2003

Area Quantization in Quasi-Extreme Black Holes

We consider quasi-extreme Kerr and quasi-extreme Schwarzschild-de Sitter black holes. From the known analytical expressions obtained for their quasi-normal modes frequencies, we suggest an area quantization prescription for those objects.

gr-qc↗
arXiv2002

Support of dS/CFT correspondence from space-time perturbations

We analyse the spectrum of perturbations of the de Sitter space on the one hand, while on the other hand we compute the location of the poles in the Conformal Field Theory (CFT) propagator at the border. The coincidence is striking, supporting a dS/CFT correspondence. We show that the spectrum of thermal excitations of the CFT at the past boundary $I^{-}$ together with that spectrum at the future boundary $I^{+}$ is contained in the quasi-normal mode spectrum of the de Sitter space in the bulk.

hep-th↗