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

As previously proposed in Simpson and Visser [J. Cosmol. Astropart. Phys. 02 (2019) 042], Mazza et al. [J. Cosmol. Astropart. Phys. 04 (2021) 082], Franzin et al. [J. Cosmol. Astropart. Phys. 07 (2021) 036], and Lobo et al. [Phys. Rev. D 103, 084052 (2021), the black bounce spacetimes are an interesting type of globally regular modifications of the ordinary black holes (such as the Kerr-Newman geometry and its particular cases) which generically contain a spacetime singularity (usually of the curvature type) at their center. To transforms a static, spherically symmetric and asymptotically flat black hole (SSS-AF-BH) geometry regular everywhere except its center of symmetry r 1/4 0 (where r stands for the areal radius of the two-dimensional spheres of symmetry) and with (outer) event horizon at r 1/4 rh > 0, into a black pffiffiffiffiffiffiffiffiffiffiffiffiffiffibounce spacetime, is to simply replace r with rho 2 thorn a2 and dr with d rho, being rho a new radial coordinate, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiand a is some real constant nonzero. As long as rh 1/4 rho 2 h thorn a2 > jaj, the result is a globally regular (or singularity-free) black hole spacetime (called black bounce) where the singularity that occurs in the ordinary SSS-AF-BH geometry at r 1/4 0 now in the transformed geometry turns into a regular spacetime region determined by the two-dimensional spheres of symmetry of radius jaj, while the areal radius pffiffiffiffiffiffiffiffiffiffiffiffiffiffi rho 2 thorn a2 always remains positive for all rho is an element of o-infinity; infinity thorn and has a minimum at rho 1/4 0 given by jaj. Hence, in the transformed spacetime, the areal radius has a minimum, decreasing before and increasing after this minimum (defining two SSS-AF regions that bounce). In this work we will present several black-bounces exact solutions of General Relativity. Among them is a novel type of black-bounce solution, which contrast to the Simpson-Visser type {[Simpson and Visser, J. Cosmol. Astropart. Phys. 02 (2019) 042], [Mazza et al., J. Cosmol. Astropart. Phys. 04 (2021) 082], [Franzin et al., J. Cosmol. Astropart. Phys. 07 (2021) 036], [Lobo et al., Phys. Rev. D 103, 084052 (2021)]}, does not have the Ellis wormhole metric as particular case. The source of these solutions is linear superposition of phantom scalar fields and nonlinear fields.

Automated summary

The concept of black bounce spacetimes presents a globally regular modification of ordinary black holes to avoid the singularity problem at their centers, creating a globally regular black hole spacetime.