On Non-commutative Corrections of Gravitational Energy in Teleparallel Gravity

In this work we use the theory of Teleparallelism Equivalent to General Relativity based in non-commutative space-time coordinates. In this context, we write the corrections of the Schwarzschild solution. As a important result, we find the corrections of the gravitational energy in the realm of teleparallel gravity due to the non-commutativity of space-time. Then we interpret such corrections as a manifestation of quantum theory in gravitational field.Comment: 11 pages, no figure

On Teleparallel Quantum Gravity in Schwarzschild Space-Time

In this article we present the quantization process for Schwarzschild space-time in the context of Teleparallel gravity. In order to achieve such a goal we use the Weyl formalism that establishes a well defined correspondence between classical quantities which are realized by functions and quantum ones which are realized by operators. In the process of quantization we introduce a fundamental constant that is used to construct what we call the quantum of matter by the imposition of periodic conditions over the eigenfunction.Comment: Accepted in Advances in High Energy Physic

Finite volume schemes on Lorentzian manifolds

We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishes the convergence of monotone and first-order finite volume schemes for a large class of (space and time) triangulations. The proof relies on a discrete version of entropy inequalities and an entropy dissipation bound, which take into account the manifold geometry accurately and generalize techniques and estimates that were known in the (flat) Euclidian setting, only. The strong convergence of the scheme then is then a consequence of the well-posed theory recently developed by Ben-Artzi and LeFloch for conservation laws on manifolds.Comment: 24 page