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

TL;DR

This paper demonstrates that specific $k$-essence field configurations can hide singularities in gravitational metrics like Schwarzschild and Reissner-Nordstrom from the perspective of perturbation observers, revealing a novel way to mask singularities.

Contribution

It introduces a method using $k$-essence fields to mask gravitational singularities in emergent metrics for perturbation observers.

Findings

Singularities can be hidden for perturbation observers in Schwarzschild spacetime.

Homogeneous $k$-essence configurations mask singularities in Reissner-Nordstrom spacetime.

Emergent metrics differ from gravitational metrics in the presence of $k$-essence fields.

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 $L=[{1\over 2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi]^{2}$ 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.