Generalised Schwarzschild metric from double copy of point-like charge solution in Born-Infeld theory

TL;DR

This paper explores using the classical double copy method to derive a generalized, non-singular Schwarzschild-like metric from a Born-Infeld charge solution, highlighting potential regularization of singularities in gravity solutions.

Contribution

It presents a novel application of the double copy procedure to Born-Infeld solutions, leading to a generalized Schwarzschild metric with insights into singularity behavior.

Findings

The generalized metric appears non-singular at the origin.

Curvature invariants still diverge at r=0, indicating residual singularities.

The approach suggests potential for regularized gravitational solutions.

Abstract

We discuss possible application of classical double copy procedure to construction of a generalisation of the Schwarzschild metric starting from an $\alpha'$-corrected open string analogue of Coulomb solution. The latter is approximated by a point-like charge solution of the Born-Infeld action, which represents the open string effective action for an abelian vector field in the limit when derivatives of the field strength are small. The Born-Infeld solution has a regular electric field which is constant near the origin, suggesting that corrections from derivative terms in the open string effective action may be small there. The generalization of the Schwarschild metric obtained by the double copy construction from the Born-Infeld solution looks non-singular but the corresponding curvature invariants still blow up at $r=0$. We discuss the origin of this singularity and comment on possible generalisations.