Regular Black Hole Interior Spacetime Supported by Three-Form Field

Abstract

In this paper, we show that a minimally coupled 3-form endowed with a proper potential can support a regular black hole interior. By choosing an appropriate form for the metric function representing the radius of the 2-sphere, we solve for the 3-form field and its potential. Using the obtained solution, we construct an interior black hole spacetime which is everywhere regular. The singularity is replaced with a Nariai-type spacetime, whose topology is ${\text{dS}}_2\times {\text{S}}^2$, in which the radius of the 2-sphere is constant. So long as the interior continues to expand indefinitely, the geometry becomes essentially compactified. The 2-dimensional de Sitter geometry appears despite the negative potential of the 3-form field. Such a dynamical compactification could shed some light on the origin of de Sitter geometry of our Universe, exacerbated by the Swampland conjecture. In addition, we show that the spacetime is geodesically complete. The geometry is singularity-free due to the violation of the null energy condition.

13 pages, 6 figures. Updated to match the published version

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• Static spherically symmetric three-form stars
• Rotating traversable wormhole geometries in the presence of three-form fields
• A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality
• Gravitational lensing by traversable wormholes supported by three-form fields
• Aspects of time evolution in $p$-form field theories
• Non-canonical 3-form dark energy
• Preliminary analyses on dynamics and thermodynamics of rotating regular black holes
• Low-Energy String Theory Predicts Black Holes Hide a New Universe
• Vector wormholes as conduits for matter interaction
• Scaling solutions in three-form cosmology