Exact, non-singular black holes from a phantom DBI Field as primordial dark matter

Abstract

We present the first exact, non-singular black hole solution in General Relativity sourced by a Dirac-Born-Infeld (DBI) scalar field. Crucially, the solution is exclusively supported by \emph{the phantom branch of the DBI action}, dynamically replacing the central singularity with a regular core. The solution is asymptotically flat, possesses non-trivial scalar hair, and replaces the central singularity with a regular 2-sphere. The mechanism for singularity resolution is a dynamical \emph{kinetic stiffness} which also explains the evasion of classical no-hair theorems. We show these black holes evaporate to a non-singular relic with mass of the order of a gram. This provides a robust mechanism to evade standard evaporation constraints, opening a vast, previously forbidden mass window for light \emph{Primordial Black Holes} to constitute dark matter. The model is testable via distinctive gravitational-wave signatures from its scalar hair.

Comments: Version accepted in Physical Review D Letters, 43 pages, 5 figures, Results generalized to DBI with potential