# Is extracting energy via the Penrose Process only possible with Kerr black holes?

I have been learning about extracting energy via the Penrose Process. Everything I read mentions leveraging the ergosphere of a rotating black hole.

But the ergosphere and the mechanisms of extracting energy sound a lot like frame dragging. Is it possible to extract energy from all rotating massive bodies, or must it be a rotating black hole?

Rapidly rotating compact objects could in principle possess the ergoregions (more general term than ergosphere) without event horizon. So it would be possible to extract energy via Penrose process from such an object. However, such object would also have ergoregion instability where it would be rapidly losing energy and angular momentum by spontaneously emitting gravitational and EM waves. Moreover, equations of state for real astrophysical objects such as neutron stars would not allow the formation of ergoregion without formation of a black hole. For technical details look for example one of the original works:

• Schutz, B. F., & Comins, N. (1978). On the existence of ergoregions in rotating stars. Monthly Notices of the Royal Astronomical Society, 182(1), 69-76. doi.

and for some recent developments about ergoregion instability

• Pani, P., Cardoso, V., Cadoni, M., & Cavaglia, M. (2009). Ergoregion instability of black hole mimickers. arXiv:0901.0850.

Less rapidly rotating bodies, that do not have ergoregion would not allow the extraction of energy via Penrose process, as there would be no trajectories for massive point particles with negative energy.

Of course, rotational energy and angular momentum could be extracted from a non-black hole rotating bodies by a number of other means, possibly mediated through gravitational interaction, such as tidal friction.

Another interesting mechanism for such energy extraction is superradiance which is somewhat analogous to Penrose process only for waves rather than for particles. Rotating black holes display this phenomenon but also it could be observed in a rotating bodies without horizon (and also without ergoregion). A simple way to think about superradiance is that waves (EM or gravitational) around a rotating object can have modes with negative energies. If an infalling wave excites such a negative-energy mode and this mode is either absorbed by an event horizon (for a black hole) or dissipated by other means (for other rotating bodies) then the original wave would have a greater energy with the surplus coming from the rotational energy of a body. For a details see

• Richartz, M., & Saa, A. (2013). Superradiance without event horizons in general relativity. Physical Review D, 88(4), 044008, doi, arXiv:1306.3137.

or a book (with a free version at arXiv):

• Brito, R., Cardoso, V., & Pani, P. (2015). Superradiance. Lect. Notes Phys, 906(1), 18, link, arXiv:1501.06570.

Energy extraction from Kerr black holes is possible not only through Penrose process, but from a variety of other processes. Penrose process is also not astrophysically feasible because it has been shown by Bardeen that for Penrose process to occur, the relative velocity of the split should be around $$c/2$$, i.e., the process must be relativistic. This is possible only if the disintegration process must convert most of the rest mass energy of the initial body into kinetic energy for any extraction of energy to become possible. Such conclusion might be avoided if one is willing to accept the existence of naked singularities or wormholes, where the $$g_{tt}$$ component of the metric can in principle become very large.

Alternative processes:

• Superradiance: Superradiance is nearly same as old as the Penrose process. This is a wave-analog of the Penrose process and is a fascinating area of research at present. Applications of this process is not only limited to General Relativity, but also to other areas of research like Quantum Field Theory, String Theory, Dark Matter etc.
• Magnetic Penrose Process: This is a modified version of the original Penrose process. The papers are papers I and paper II. Here the authors had incorporated the effect of magnetic field that significantly improves the energy extraction efficiency. This is an almost unexplored area but might prove useful in the study of relativistic jets.
• Blandford-Znajek process: This is a very successful and popular process for energy extraction from Kerr black holes. This is one of the best explanations for the way quasars are powered. This process exploits the magnetic field around a rotating black hole for the purpose of energy extraction.