arXiv subjects

Emanuel Gallo

Publications and source records attributed to Emanuel Gallo.

39 records · Page 3Linked to original sources

arXiv2004

Two-dimensional Riemannian and Lorentzian geometries from second order ODEs

In this note we give an alternative geometrical derivation of the results recently presented by Garcia-Godinez, Newman and Silva-Ortigoza in [1] on the class of all two-dimensional riemannian and lorentzian metrics from 2nd order ODEs which are in duality with the two dimensional Hamilton-Jacobi equation. We show that, as it happens in the Null Surface Formulation of General Relativity, the Wuschmann-like condition can be obtained as a requirement of a vanishing torsion tensor. Furthermore, from these second order ODEs we obtain the associated Cartan connections.

gr-qc↗

arXiv2004

Cartan Normal Conformal Connections from Pairs of 2nd Order PDE's

We explore the different geometric structures that can be constructed from the class of pairs of 2nd order PDE's that satisfy the condition of a vanishing generalized Wünschmann invariant. This condition arises naturally from the requirement of a vanishing torsion tensor. In particular, we find that from this class of PDE's we can obtain all four-dimensional conformal Lorentzian metrics as well as all Cartan normal conformal O(4,2) connections. To conclude, we briefly discuss how the conformal Einstein equations can be imposed by further restricting our class of PDE's to those satisfying additional differential conditions.

gr-qc↗

arXiv2003

Generating Static Black Holes in Higher Dimensional Space-Times

In this article we extend to higher dimensional space-times a recent theorem proved by Salgado which characterizes a three-parameter family of static and spherically symmetric solutions to the Einstein Field Equations. As it happens in four dimensions, it is shown that the Schwarzschild, Reissner-Nordstrom and global monopole solutions in higher dimensions are particular cases from this family.

gr-qc↗