Eur. Phys. J. C (2024) 84: 1082
https://doi.org/10.1140/epjc/s10052-024-13457-3

Regular Article

Inter-disks inversion surfaces

Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava, Bezručovo náměstí 13, 74601, Opava, Czech Republic

^a daniela.pugliese@physics.slu.cz

Received: 24 June 2024
Accepted: 3 October 2024
Published online: 18 October 2024

Abstract

We consider a counter-rotating torus orbiting a central Kerr black hole (BH) with dimensionless spin a, and its accretion flow into the BH, in an agglomerate of an outer counter-rotating torus and an inner co-rotating torus. This work focus is the analysis of the inter-disks inversion surfaces. Inversion surfaces are spacetime surfaces, defined by the condition $u^{\varphi }=0$ on the flow torodial velocity, located out of the BH ergoregion, and totally embedding the BH. They emerge as a necessary condition, related to the spacetime frame-dragging, for the counter-rotating flows into the central Kerr BH. In our analysis we study the inversion surfaces of the Kerr spacetimes for the counter-rotating flow from the outer torus, impacting on the inner co-rotating disk. Being totally or partially embedded in (internal to) the inversion surfaces, the inner co-rotating torus (or jet) could be totally or in part “shielded”, respectively, from the impact with flow with $a{u}^{\varphi }<0$. We prove that, in general, in the spacetimes with $a<0.551$ the co-rotating toroids are always external to the accretion flows inversion surfaces. For $0.551<a<0.886$, co-rotating toroids could be partially internal (with the disk inner region, including the inner edge) in the flow inversion surface. For BHs with $a>0.886$, a co-rotating torus could be entirely embedded in the inversion surface and, for larger spins, it is internal to the inversion surfaces. Tori orbiting in the BH outer ergoregion are a particular case. Further constraints on the BHs spins are discussed in the article.