**Publication date:** Jul 2021

**Abstract:**

The determination of mass and spin parameters of the black holes (BHs) is crucial in the analysis of the merger of BHs and BHs formation and evolution, including accretion. Here we constrain the BH spin with the evaluation of the dimensionless parameter ξ representing the total rotational energy extracted versus the mass of the BH, following procedure introduced by Daly (2009 Astrophys. J. 691 L72-6) that is independent from the details of the specific extraction process. The energy extraction can power an outflow which can be then observed. We relate the energy extraction to the accreting configurations and the accretion processes occurring in a cluster of agglomerate corotating and counter-rotating tori orbiting one central Kerr SMBH, associating ξ to the characteristics of the accretion processes. We relate the regions of tori parameters to features of the energy extraction processes, binding ξ to properties of light surfaces by using the bundles developed by Pugliese and Quevedo (2019 Eur. Phys. J. C 79 209), relating measures in different regions of the spacetimes. We evaluate properties of the BH accretions disks, and correlate spacetimes prior and after their transition due to the energy extraction. Light surfaces are related to the generators of Killing horizons, proving limiting frequency of the stationary observers of the geometries. We consider the photon limiting curves of the stationary observers as constraints for various processes regulated by these frequencies, to relate different BH states, prior and after the energy extraction, investigating regions close to the BH horizons and rotational axis. From methodological view-point we used a naked singularity-BH correspondence defined with metric bundles to predict observational characteristics of the BH-accretion disk system. The analysis points relevant BH spins a ≈ 0.94M, a ≈ 0.7M and a ≈ 0.3M. We show the relation between the rotational law of the tori, the characteristic frequency of the bundle and the relativistic velocity defining the von Zeipel surfaces. The inferior limit on the formation of corotating tori is ℓ/a ⩾ 2, for counter-rotating tori ℓ/a ⩽ -22/5 (ℓ is the fluids specific angular momentum).

**Authors:**

Pugliese, D.; Stuchlík, Z.;