Rotational energy extraction from Kerr black-hole mimickers: charged and off-horizon regimes, horizonless branches, and observational distinguishability

The Penrose splitting process extracts rotational energy from a Kerr black hole because fragmenting a particle inside the ergoregion can put one fragment on a negative-energy orbit that falls into the horizon, with a maximum efficiency of about 20.7% for an extremal Kerr black hole. Patel, Acharya, Bambhaniya and Joshi (Universe 8, 571, 2022) computed this efficiency for two families of Kerr mimickers: the rotating Simpson-Visser regular spacetime, where they found the efficiency is independent of the regularisation parameter $l$ and equals the Kerr value, and conformally transformed singular and regular black holes of Einstein conformal gravity, where the efficiency for $l\sim M$ can be extremely large. They explicitly deferred four issues: the value of the conformal length scale $l$ is not fixed by the theory; only neutral test particles without electromagnetic fields were treated; only splitting at the outer horizon was analysed; and only the $a<M$ horizon-bearing regime was considered. In addition, their claim that the extraction signature would be observationally useful to distinguish Kerr from these mimickers was asserted but not established. Later literature has resolved parts of this programme — magnetic Penrose efficiencies for Simpson-Visser and rotating Hayward spacetimes, general off-horizon decay theory, and magnetic-reconnection extraction from spinning wormholes — but the conformally transformed families remain untreated in every extended regime, and existing X-ray reflection data already constrain $l/M<0.12$ in that same family, in tension with the $l\sim M$ regime that produces the anomalous efficiencies. The open problem is to determine whether rotational energy extraction, treated beyond the neutral, on-horizon, $a<M$ restrictions and confronted with observational constraints, can at all distinguish Kerr black holes from these mimickers.

Background

A rotating (Kerr) black hole of mass $M$ and spin parameter $a$ has two defining structures: an event horizon, the one-way surface at $r_+=M+\sqrt{M^2-a^2}$, and an ergoregion, the band around it where spacetime is dragged so strongly that no observer can remain stationary. In 1971 Penrose and Floyd showed that rotational energy can be extracted classically: a particle splitting inside the ergoregion can leave one fragment on an orbit of negative conserved energy, which falls through the horizon, while the other escapes with more energy than the original particle carried in. The efficiency $\eta$ of this Penrose process is bounded by a function of the metric tensor components at the splitting point; for a splitting at the horizon of a Kerr black hole the bound is about 20.7% and is reached for the extremal spin $a=M$. Kerr black-hole mimickers are candidate compact-object geometries — regular (singularity-free) black holes and traversable wormholes — whose exterior is so close to Kerr that electromagnetic imaging alone may not distinguish them. One such family is the Simpson-Visser black-bounce spacetime, in which the radial coordinate is replaced by $\sqrt{r^2+l^2}$ so that a length parameter $l$ interpolates between the Schwarzschild black hole ($l=0$) and a traversable wormhole — a smooth bridge joining two asymptotic regions with no horizon — reached for $l$ above the horizon scale; its rotating version, obtained with the Janis-Newman algorithm, a prescription that generates a rotating metric from a static one by complexifying coordinates in the metric tensor, is a regular black hole for $a<M$ with $l$ below the horizon scale and a horizonless wormhole otherwise. A second family consists of the rotating singularity-free solutions of Einstein gravity with conformal invariance found by Bambi, Modesto and Rachwał: a conformal factor $S=(1+l^2/\Sigma)^\nu$ (with $\Sigma=r^2+a^2\cos^2\theta$, $\nu=3$ for the singular and $\nu=4$ for the regular member) multiplies the Kerr line element, and the theory itself does not fix the length scale $l$. In 2022 Patel, Acharya, Bambhaniya and Joshi evaluated the horizon-splitting efficiency for both families. They found that in the rotating Simpson-Visser spacetime the maximum efficiency is independent of $l$ and coincides with the Kerr value, whereas in the conformally transformed singular and regular black holes the efficiency is extremely large compared with Kerr for $l$ of order $M$, suggesting a potential observational signature. The same conformal family had already been constrained observationally: X-ray reflection spectroscopy, the modelling of fluorescence line profiles from the inner accretion disk, of the stellar-mass black hole in GS 1354-645 gives $L/M<0.12$ (99% confidence level, statistical uncertainty only; $L$ is the conformal length scale of that analysis, the same scale denoted $l$ in the source paper) for the rotating singularity-free member, so the phenomenologically adopted regime $l\sim M$ is in tension with existing data, and the role of the conformal scale in the extraction claim needs to be re-examined rather than assumed.

Problem Statement

For the rotating Simpson-Visser spacetime and the conformally transformed singular ($\nu=3$) and regular ($\nu=4$) black holes of conformal gravity — the Kerr-mimicker families considered by Patel, Acharya, Bambhaniya and Joshi — determine whether rotational energy extraction can distinguish these objects from the Kerr black hole. To that end, extend their horizon-splitting, neutral-particle, $a<M$ analysis through the following five extensions, which are conjunctive and each independently mandatory rather than alternative routes to the same verdict, so that delivering any one of them does not by itself resolve the task: (1) compute the Penrose-process efficiency when the fragments are charged and an external magnetic field is present, in particular for the conformally transformed families whose anomalously large efficiencies are the core of the distinguishing claim, since the existing magnetic-Penrose treatment covers only Simpson-Visser and rotating Hayward geometries; (2) compute the efficiency of splitting events off the horizon, at general radii inside the ergoregion, establishing how the horizon bound is approached and whether such events are dynamically realizable; (3) analyse the $a\ge M$ horizonless branches of these families — a wormhole branch in the rotating Simpson-Visser case — where no horizon exists to absorb the negative-energy fragment, determining the negative-energy orbit structure and the resulting extraction efficiencies; (4) establish whether, in view of the observational constraint $l/M<0.12$ on the same conformal family from X-ray reflection spectroscopy (and any improved constraints), the anomalous efficiencies survive at observationally allowed values of the conformal length scale; and (5) assess whether any resulting high-energy outflow or jet signature of that surviving extraction could observationally distinguish these mimickers from Kerr black holes. A complete answer states, for each of the three families — rotating Simpson-Visser, conformal $\nu=3$, and conformal $\nu=4$ — and each of the regimes (1)-(5), the extraction efficiency (or bounds on it), the conditions under which negative-energy states exist, and a justified verdict on whether energy extraction in that family-regime cell is or is not a viable discriminator between Kerr black holes and these mimickers; a cell that the cited literature already settles (such as the neutral and magnetic Simpson-Visser cases) is reported as a resolved comparison, and a cell in which a given regime does not arise for a given family is reported as such. The objective is resolved only when this family-by-regime coverage is complete.

References

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