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

Tausif Parvez, S. Shankaranarayanan

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 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 kinetic stiffness -- analogous to shear thickening in non-Newtonian fluids -- which also explains the evasion of classical no-hair theorems. We show these black holes evaporate to a stable, non-singular, extremal Planck-scale relic. This provides a robust mechanism to evade standard evaporation constraints, opening a vast, previously forbidden mass window for light Primordial Black Holes to constitute dark matter. The model is testable via distinctive gravitational-wave signatures from its scalar hair.

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 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 kinetic stiffness -- analogous to shear thickening in non-Newtonian fluids -- which also explains the evasion of classical no-hair theorems. We show these black holes evaporate to a stable, non-singular, extremal Planck-scale relic. This provides a robust mechanism to evade standard evaporation constraints, opening a vast, previously forbidden mass window for light Primordial Black Holes to constitute dark matter. The model is testable via distinctive gravitational-wave signatures from its scalar hair.

Paper Structure

This paper contains 15 sections, 78 equations, 3 figures.

Table of Contents

  1. DIRAC-BORN-INFELD (DBI) ACTION
  2. Exact solution of the field equations
  3. Solving for $f(r)$
  4. Solving for $\phi(r)$
  5. Choice of $\epsilon$
  6. Curvature invariants
  7. Ricci scalar ($R$)
  8. Ricci tensor squared ($R^{\mu\nu}R_{\mu\nu}$)
  9. Kretschmann scalar ($K$)
  10. Energy Condition: Sign of $\mathbf{T^{t}_{t}}$
  11. Black Hole Thermodynamics
  12. Horizon Radius
  13. Hawking Temperature
  14. Evaporation rate
  15. Phantom field from Non-linear sigma model

Figures (3)

  • Figure 1: The metric function $f(r)$ for the three mass regimes (where $a = G = 1$), showing the non-extremal BH (red), the stable extremal relic (Magenta), and the horizon-less regular object (blue) .
  • Figure 2: The DBI scalar field $\phi(r)$ for three mass regimes (in units where $a=B=G=1$): the non-extremal BH (red, $M=0.80$), the stable extremal relic (magenta, $M=2/3\pi$), and the horizon-less regular object (blue, $M=0.10$).
  • Figure 3: The Kretschmann scalar $K(r)$ for the three mass regimes (in units where $a=G=1$), showing the non-extremal BH (red, $M=0.30$), the stable extremal relic (magenta, $M=2/3\pi$), and the horizon-less regular object (blue, $M=0.15$).