Masking singularities with $k-$essence fields in an emergent gravity metric

Abstract

It is known that dynamical solutions of the $k$-essence equation of motion change the metric for the perturbations around these solutions and the perturbations propagate in an emergent spacetime with metric ${\tilde{G}}^{\mu \nu }$ different from the gravitational metric $g^{\mu \nu }$. We show that for observers travelling with the perturbations, there exist homogeneous field configurations for the lagrangian $L=[\frac{1}{2}{g}^{\mu \nu }{\nabla }_{\mu }\varphi {\nabla }_{\nu }\varphi {]}^2$ for which a singularity in the gravitational metric $g^{\mu \nu }$ can be masked or hidden for such observers. This is shown for the Schwarzschild and the Reissner-Nordstrom metrics.

arXiv comment5 pages, latex, minor typo error corrected in eq.(7)