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

TL;DR

This paper introduces an exact, non-singular black hole solution in General Relativity supported by a phantom DBI scalar field, which could explain primordial dark matter and produce detectable gravitational-wave signatures.

Contribution

It presents the first exact non-singular black hole solution with scalar hair supported by a phantom DBI field, replacing the singularity with a regular core.

Findings

Black holes evaporate to non-singular relics of about a gram.

The solution evades classical no-hair theorems through kinetic stiffness.

Potential gravitational-wave signatures from scalar hair are identified.

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.