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.Comment: version to match the one to be published on General Relativity and Gravitatio

Neutron Stars in Teleparallel Gravity

In this paper we deal with neutron stars, which are described by a perfect fluid model, in the context of the teleparallel equivalent of general relativity. We use numerical simulations to find the relationship between the angular momentum of the field and the angular momentum of the source. Such a relation was established for each stable star reached by the numerical simulation once the code is fed with an equation of state, the central energy density and the ratio between polar and equatorial radii. We also find a regime where linear relation between gravitational angular momentum and moment of inertia (as well as angular velocity of the fluid) is valid. We give the spatial distribution of the gravitational energy and show that it has a linear dependence with the squared angular velocity of the source.Comment: 19 pages, 14 figures. arXiv admin note: text overlap with arXiv:1206.331

On Special Re-quantization of a Black Hole

Quantized expressions for the gravitational energy and momentum are derived from a linearized theory of teleparallel gravity. The derivation relies on a second-quantization procedure that constructs annihilation and creation operators for the graviton. The resulting gravitational field is a collection of gravitons, each of which has precise energy and momentum. On the basis of the weak-field approximation of Schwarzschild's solution, a new form for the quantization of the mass of a black hole is derived.Comment: 4 page

On reference frames in spacetime and gravitational energy in freely falling frames

We consider the interpretation of tetrad fields as reference frames in spacetime. Reference frames may be characterized by an antisymmetric acceleration tensor, whose components are identified as the inertial accelerations of the frame (the translational acceleration and the frequency of rotation of the frame). This tensor is closely related to gravitoelectromagnetic field quantities. We construct the set of tetrad fields adapted to observers that are in free fall in the Schwarzschild spacetime, and show that the gravitational energy-momentum constructed out of this set of tetrad fields, in the framework of the teleparallel equivalent of general relatrivity, vanishes. This result is in agreement with the principle of equivalence, and may be taken as a condition for a viable definition of gravitational energy.Comment: 19 pages, no figures, accepted by Classical and Quantum Gravit

General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry

The Hamiltonian formulation of general relativity on a null surface is established in the teleparallel geometry. No particular gauge conditons on the tetrads are imposed, such as the time gauge condition. By means of a 3+1 decomposition the resulting Hamiltonian arises as a completely constrained system. However, it is structurally different from the the standard Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the basic field quantities are tetrads that transform under the global SO(3,1) and the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra

Three-dimensional Dirac oscillator in a thermal bath

The thermal properties of the three-dimensional Dirac oscillator are considered. The canonical partition function is determined, and the high-temperature limit is assessed. The degeneracy of energy levels and their physical implications on the main thermodynamic functions are analyzed, revealing that these functions assume values greater than the one-dimensional case. So that at high temperatures, the limit value of the specific heat is three times bigger.Comment: 9 pages, 4 figures. Text improved, references added. Revised to match accepted version in Europhysics Letters

Regular string-like braneworlds

In this work, we propose a new class of smooth thick string-like braneworld in six dimensions. The brane exhibits a varying brane-tension and an $AdS$ asymptotic behavior. The brane-core geometry is parametrized by the Bulk cosmological constant, the brane width and by a geometrical deformation parameter. The source satisfies the dominant energy condition for the undeformed solution and has an exotic asymptotic regime for the deformed solution. This scenario provides a normalized massless Kaluza-Klein mode for the scalar, gravitational and gauge sectors. The near-brane geometry allows massive resonant modes at the brane for the $s$ state and nearby the brane for $l=1$.Comment: 14 pages, 12 figures. Some modifications to match the published version in EPJ