Dyonic Simpson Visser black-bounce spacetime surrounded by an exotic Einstein cluster in general relativity

Dyonic Simpson Visser black-bounce spacetime surrounded by an exotic Einstein cluster in general relativity is presented as an exact solution of general relativity coupled to Maxwell electrodynamics and an anisotropic fluid with vanishing radial pressure.

The Core Contribution

The paper introduces the dyonic Simpson-Visser black-bounce (SV-BB) spacetime, which possesses both electric and magnetic charges, as an exact solution to the Einstein field equations sourced by a combination of an Einstein cluster and a Maxwell electromagnetic field. This construction is novel because it realizes this spacetime within the framework of general relativity coupled to Maxwell electrodynamics and an exotic Einstein cluster. The solution demonstrates that the black-bounce throat is kept open by the exotic matter provided by an Einstein cluster, which consists of particles moving in circular orbits generating only tangential pressure and zero radial pressure.

Modeling the Source Matter

The exotic matter required to maintain a regular black hole spacetime is modeled as an Einstein cluster (EC). An EC is defined as a self-gravitating system of particles moving on circular geodesics in all possible angular directions and orbital radii around the center of symmetry, resulting in an anisotropic fluid description with zero radial pressure, non-zero tangential pressure, and positive energy density. The authors show that this EC constitutes a static and spherically symmetric system of particles where the angular momentum generates an outward centrifugal force counteracting gravitational attraction.

Field Equations and Solutions

The analysis involves solving the Einstein field equations for the GR-Maxwell-FL theory, which couples general relativity to Maxwell electrodynamics and an anisotropic fluid. The resulting field equations for static and spherically symmetric spacetimes are derived from the metric ansatz, yielding a set of coupled differential equations (32)-(35). The dyonic SV-BB spacetime is found to be an exact solution of these field equations with an Einstein cluster represented by an anisotropic fluid having vanishing radial pressure P = 0 and non-zero tangential pressure P˜.

Energy Conditions and Singularity Avoidance

The behavior of the matter sources is crucial for avoiding singularities, as demonstrated by the violation of energy conditions. For the Einstein cluster source, the authors conclude that its energy-momentum tensor does not satisfy the null and weak energy conditions throughout the SV-BB spacetime. Specifically, for a regular black hole configuration, the inequalities for positive energy density and pressure are simultaneously satisfied only in a region inside the event horizon. This violation of WEC allows the gravitational collapse leading to the Simpson-Visser black-bounce to evade the singularity theorem of Penrose.

Comparison with Existing Models

The work contrasts its findings with previous constructions, noting that while some models support only magnetic charge, this dyonic solution carries both magnetic and electric charges. Furthermore, the construction uses Maxwell electrodynamics in contrast to other works that employ nonlinear electrodynamics models which do not reduce to standard classical electromagnetism in the weak-field limit. The traversable wormhole configuration requires the exotic anisotropic fluid of the Einstein cluster type as a source. The presence of this exotic EC implies that the weak energy condition is violated in the dyonic Simpson-Visser black bounce spacetime, and consequently allows the Penrose singularity theorem to be evaded. The linear electromagnetic source of the dyonic SV-BB spacetime satisfies both null and weak energy conditions. The total source of the dyonic SV-BB spacetime violates the WEC outside of the event horizon for both regular black hole and traversable wormhole configurations. For the regular black hole configuration, although effective energy density remains positive in a region extending beyond the event horizon, simultaneous conditions are satisfied only in a region within or at the event horizon. The quantities rhoeff and rhoeff + Peff are plotted in figure 1 for p q2E + q q2B/m = 1 which corresponds to an event horizon radius r/m = √3. For the traversable wormhole configuration, the EC energy-momentum tensor does not satisfy the null and weak energy conditions throughout the SV-BB spacetime. The total source becomes exotic (violating the WEC outside of the event horizon of the regular black hole) because rho(loc) eff is not positive definite in the whole spacetime. For every timelike vector field k = k µ∂µ, the local energy density rho(loc) = T µνk µkν is not positive definite in the whole spacetime. The dyonic SimpsonVisser black-bounce as an exact solution of GR-Maxwell-FL does not satisfy the WEC, with the EC being responsible for the violation of WEC, and therefore the gravitational collapse leading to the Simpson-Visser black-bounce evades the singularity theorem of Penrose. The dyonic Ellis-Bronnikov traversable wormhole is an exact solution of GR-Maxwell-FL with fluid determined by rho = −q q2E + q q2B 4π(r squared + q q2E + q q2B) 2, P = 0 and P˜ = 0.

Key Results Summary

1. The dyonic SV-BB spacetime is an exact solution of GR coupled to Maxwell electrodynamics and an exotic Einstein cluster.

2. The EC provides the exotic matter necessary to keep the black-bounce throat open, characterized by anisotropic fluid with vanishing radial pressure.

3. The solution carries both magnetic and electric charges, unlike purely magnetic solutions in some literature.

4. The EC energy-momentum tensor does not satisfy the null and weak energy conditions throughout the SV-BB spacetime.

5. For regular black hole configurations, WEC violation is confined to a region inside the event horizon, allowing singularity evasion.

6. The total source of the dyonic SV-BB spacetime violates WEC outside of the event horizon for both regular black hole and traversable wormhole configurations.

Conclusion

In this work, we have presented, for the first time, a dyonic Simpson-Visser black-bounce spacetime within the framework of general relativity coupled with Maxwell electrodynamics and an exotic Einstein cluster. In contrast to the black-bounce spacetimes constructed in [12–14], which can support only magnetic charge, our SV-BB solution has both magnetic and electric charges. Furthermore, our construction of the dyonic SV-BB is within the framework of Maxwell electrodynamics, unlike [12–14, 24] where nonlinear electrodynamics models (which are physically irrelevant, since in the weak-field limit they do not reduce to standard classical electromagnetism) are used to construct dyonic black-bounces. The traversable-wormhole configuration, however, requires an exotic anisotropic fluid of the Einstein cluster type as a source in order to support the traversable wormhole structure. The presence of this exotic EC implies that the weak energy condition is violated in the dyonic Simpson-Visser black bounce spacetime, and consequently allows the Penrose singularity theorem to be evaded.

Appendix Details

The appendix provides explicit forms for the GR-NLED-SF field equations satisfied by a purely magnetic configuration. The WEC conditions for the effective energy-momentum tensor are derived, showing that the total source becomes exotic (violating the WEC outside of the event horizon). The NEC and WEC conditions for self-interacting scalar field and nonlinear electromagnetic field are detailed in equations (70)-(82). The total source of the dyonic SV-BB spacetime violates the WEC, with the EC being responsible for the violation of WEC, and therefore the gravitational collapse leading to the Simpson-Visser black-bounce evades the singularity theorem of Penrose. The local energy density rho(loc) eff is not positive definite in the whole spacetime. The quantities rhoeff and rhoeff + Peff are plotted in figure 1 for p q2E + q q2B/m = 1 which corresponds to an event horizon radius r/m = √3. The quantity rhoeff + P˜eff is everywhere positive and therefore it wasn’t included in the plots. The total source becomes exotic (violating the WEC outside of the event horizon of the regular black hole) because rho(loc) eff is not positive definite in the whole spacetime.

1. Improved understanding of exotic matter sources: The AI can now distinguish between different theoretical frameworks for generating black bounce spacetimes, specifically differentiating between those sourced by a purely magnetic nonlinear electromagnetic field and those sourced by an Einstein cluster, as shown in Section IV.

2. Ability to verify energy condition violations: The system can calculate the effective energy density rho eff and its combinations with pressures (rho eff + Peff) to determine precisely where the weak energy condition is violated, based on equations (80), (81), and (82).

3. Synthesis of dyonic solutions: The AI can construct exact solutions for dyonic black bounces that possess both electric and magnetic charges using Maxwell electrodynamics and an Einstein cluster source, moving beyond previous purely magnetic models.

4. Distinction between physical NLED models: The system can identify which Nonlinear Electrodynamics (NLED) models are physically reasonable by checking if they reduce to standard Maxwell electrodynamics in the weak-field limit as required by Ref. [42].

5. Analysis of wormhole requirements: The AI can determine the necessary source properties for a traversable wormhole, specifically identifying that it requires an exotic anisotropic fluid of the Einstein cluster type as a source to support its structure.