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

Understand

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 $r=0$.