[Paper Review] Black bounces as magnetically charged phantom regular black holes in Einstein-nonlinear electrodynamics gravity coupled to a self-interacting scalar field

Pedro Cañate|arXiv (Cornell University)|Feb 4, 2022

Quantum Electrodynamics and Casimir Effect54 references40 citations

TL;DR

This paper presents novel exact black-bounce solutions in Einstein-nonlinear electrodynamics coupled to a self-interacting phantom scalar field, introducing a new class of magnetically charged, globally regular black holes that avoid curvature singularities by replacing the areal radius r with √(ρ² + a²). Unlike previous Simpson-Visser-type black bounces, these solutions do not reduce to the Ellis wormhole metric and feature a spacelike throat at ρ = 0 with finite areal radius |a|, enabling a bounce between two asymptotically flat regions without a singularity.

ABSTRACT

The "black-bounce" spacetime geometries, were recently proposed in [A. Simpson, M. Visser, JCAP 02 (2019) 042] as regular black holes that bouncing into a future incarnation of the universe. In this work we will present several black-bounce exact solutions of General Relativity. Among them is a novel type of black-bounce solutions, which in contrast of the Simpson-Visser type [A. Simpson, M. Visser, JCAP 02 (2019) 042], do not have the Ellis wormhole metric as a particular case. The source of these solutions are linear superposition of phantom scalar fields and nonlinear electromagnetic fields.

Motivation & Objective

• To construct globally regular black hole solutions that avoid curvature singularities at r = 0, which plague standard black hole geometries like Kerr-Newman.
• To extend the black-bounce framework beyond the Simpson-Visser type by introducing a new class of solutions not reducing to the Ellis wormhole metric.
• To explore the role of nonlinear electrodynamics and phantom scalar fields as sources for regular, magnetically charged black holes with a spacetime bounce at ρ = 0.
• To demonstrate that the black-bounce mechanism—replacing r with √(ρ² + a²)—can be realized in a consistent gravity theory with nonlinear electromagnetic and scalar field sources.

Proposed method

• The black-bounce spacetime is constructed by transforming the radial coordinate: replacing r with √(ρ² + a²) and dr with dρ, where ρ is a new radial coordinate and a ≠ 0 is a real constant.
• The metric takes the form ds² = −n(r)dt² + n⁻¹(r)dρ² + r²(dθ² + sin²θ dϕ²), with r = √(ρ² + a²), ensuring the areal radius has a global minimum |a| at ρ = 0.
• The field equations are solved in the context of Einstein gravity coupled to a nonlinear electromagnetic field Lagrangian and a self-interacting phantom scalar field.
• The energy conditions are analyzed to confirm the solutions satisfy physical consistency, particularly the weak energy condition (WEC), despite the presence of phantom fields.
• The event horizon is located at ρ = ±ρh, where n(rh) = 0, and the spacetime remains regular at ρ = 0 due to the finite areal radius |a|.
• The solutions are shown to be globally regular, with curvature invariants finite everywhere, and the spacetime exhibits two asymptotically flat regions connected via a spacelike throat at ρ = 0.

Experimental results

Research questions

• RQ1 Can a globally regular, magnetically charged black hole be constructed in Einstein-nonlinear electrodynamics coupled to a phantom scalar field, avoiding the central curvature singularity of standard black holes?
• RQ2 Does the black-bounce mechanism—replacing r with √(ρ² + a²)—yield new exact solutions outside the Simpson-Visser class, particularly those not reducing to the Ellis wormhole metric?
• RQ3 What are the physical and geometric properties of such black-bounce solutions, including the nature of the throat at ρ = 0 and the behavior of the metric function n(r)?
• RQ4 How do the nonlinear electromagnetic field and phantom scalar field contribute to the regularity and stability of the spacetime structure?

Key findings

• The paper constructs a new class of exact black-bounce solutions in Einstein-nonlinear electrodynamics with a self-interacting phantom scalar field, distinct from the Simpson-Visser type.
• These solutions are globally regular, with all curvature invariants finite everywhere, including at the origin, due to the replacement of r with √(ρ² + a²), which ensures a minimum areal radius |a| at ρ = 0.
• The spacetime contains two asymptotically flat regions connected by a spacelike throat at ρ = 0 with finite areal radius |a|, forming a bounce between two black hole-like geometries.
• The solutions do not reduce to the Ellis wormhole metric, distinguishing them from previous black-bounce models and introducing a new type of regular black hole with magnetic charge.
• The presence of the phantom scalar field and nonlinear electromagnetic field allows for the avoidance of singularities while maintaining a consistent energy-momentum tensor that satisfies the weak energy condition.
• The event horizons exist at ρ = ±ρh, where n(rh) = 0, and the metric function n(r) remains smooth and positive definite for r > rh, ensuring causal structure consistency.