Localization of Energy in General Relativity

In the framework of the teleparallel equivalent of general relativity the energy density of asymptoticaly flat gravitational fields can be naturally and unambiguously defined. Upon integration of the energy density over the whole three dimensional space we obtain the ADM energy. We use this energy density to calculate the energy inside a Schwarzschild black hole.Comment: 12 pages, LaTex file, no figure

Gravitational energy of rotating black holes

In the teleparallel equivalent of general relativity the energy density of asymptotically flat gravitational fields can be naturaly defined as a scalar density restricted to a three-dimensional spacelike hypersurface $\Sigma$. Integration over the whole $\Sigma$ yields the standard ADM energy. After establishing the reference space with zero gravitational energy we obtain the expression of the localized energy for a Kerr black hole. The expression of the energy inside a surface of constant radius can be explicitly calculated in the limit of small $a$, the specific angular momentum. Such expression turns out to be exactly the same as the one obtained by means of the method preposed recently by Brown and York. We also calculate the energy contained within the outer horizon of the black hole for {\it any} value of $a$. The result is practically indistinguishable from $E=2M_{ir}$, where $M_{ir}$ is the irreducible mass of the black hole.Comment: 18 pages, LaTex file, one figur

Radiative corrections in bumblebee electrodynamics

We investigate some quantum features of the bumblebee electrodynamics in flat spacetimes. The bumblebee field is a vector field that leads to a spontaneous Lorentz symmetry breaking. For a smooth quadratic potential, the massless excitation (Nambu-Goldstone boson) can be identified as the photon, transversal to the vacuum expectation value of the bumblebee field. Besides, there is a massive excitation associated with the longitudinal mode and whose presence leads to instability in the spectrum of the theory. By using the principal-value prescription, we show that no one-loop radiative corrections to the mass term is generated. Moreover, the bumblebee self-energy is not transverse, showing that the propagation of the longitudinal mode can not be excluded from the effective theory.Comment: Revised version: contains some more elaborated interpretation of the results. Conclusions improve

Effects of a CPT-even and Lorentz-violating nonminimal coupling on the electron-positron scattering

We propose a new \emph{CPT}-even and Lorentz-violating nonminimal coupling between fermions and Abelian gauge fields involving the CPT-even tensor $(K_{F})_{\mu\nu\alpha\beta}$ of the standard model extension. We thus investigate its effects on the cross section of the electron-positron scattering by analyzing the process $e^{+}+e^{-}\rightarrow\mu^{+}+\mu^{-}$. Such a study was performed for the parity-odd and parity-even nonbirefringent components of the Lorentz-violating $(K_{F})_{\mu\nu\alpha\beta}$ tensor. Finally, by using experimental data available in the literature, we have imposed upper bounds as tight as $10^{-12}(eV)^{-1}$ on the magnitude of the CPT-even and Lorentz-violating parameters while nonminimally coupled.Comment: LaTeX2e, 06 pages, 01 figure

Radiative generation of the CPT-even gauge term of the SME from a dimension-five nonminimal coupling term

In this letter we show for the first time that the usual CPT-even gauge term of the standard model extension (SME) can be radiatively generated, in a gauge invariant level, in the context of a modified QED endowed with a dimension-five nonminimal coupling term recently proposed in the literature. As a consequence, the existing upper bounds on the coefficients of the tensor $(K_{F})$ can be used improve the bounds on the magnitude of the nonminimal coupling, $\lambda(K_{F}),$ by the factors $10^{5}$ or $10^{25}.$ The nonminimal coupling also generates higher-order derivative contributions to the gauge field effective action quadratic terms.Comment: Revtex style, two columns, 6 pages, revised final version to be published in the Physics Letters B (2013

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

Random variable functions used in hydrology

In this work, expressions of the cumulative distribution function of Y X, Y/X and X/(X + Y ) for continuous dependent random variables with supported on a unbounded and bounded interval are derived. The dependence approach is based on copula functions. Additionally, the methodology is applied to real data on hydrology.En este trabajo, se derivan expresiones de la función de distribución acumulada de Y X, Y/X y X/(X + Y ) para variables aleatorias dependientes continuas con soporte en un intervalo ilimitado y limitado. El enfoque de dependencia se basa en funciones cópula. Además, la metodología se aplica a datos reales de hidrología

Space-time defects and teleparallelism

We consider the class of space-time defects investigated by Puntigam and Soleng. These defects describe space-time dislocations and disclinations (cosmic strings), and are in close correspondence to the actual defects that arise in crystals and metals. It is known that in such materials dislocations and disclinations require a small and large amount of energy, respectively, to be created. The present analysis is carried out in the context of the teleparallel equivalent of general relativity (TEGR). We evaluate the gravitational energy of these space-time defects in the framework of the TEGR and find that there is an analogy between defects in space-time and in continuum material systems: the total gravitational energy of space-time dislocations and disclinations (considered as idealized defects) is zero and infinit, respectively.Comment: 22 pages, no figures, to appear in the Class. Quantum Gravit

Energy Contents of Some Well-Known Solutions in Teleparallel Gravity

In the context of teleparallel equivalent to General Relativity, we study energy and its relevant quantities for some well-known black hole solutions. For this purpose, we use the Hamiltonian approach which gives reasonable and interesting results. We find that our results of energy exactly coincide with several prescriptions in General Relativity. This supports the claim that different energy-momentum prescriptions can give identical results for a given spacetime. We also evaluate energy-momentum flux of these solutions.Comment: 16 pages, accepted for publication in Astrophys. Space Sc