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:
and for some recent developments about ergoregion instability
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
or a book (with a free version at arXiv):
Theoretical Astrophysicist Dr. Reva Kay Williams was the first person to successfully work out the Penrose mechanism to extract energy from a rotating black hole in 1991 for her Ph.D. dissertation. Her successful calculation was published in the Physical Review D journal in May 1995 (51, No. 10, 5387). Williams' model overcame the problems associated with previous Penrose process calculations. Specifically, her relativistic scattering processes overcame the problem proposed by Bardeen et al. in their 1972 publication (Bardeen et al. 1972, Astrophysical Journal, 178, 347). Williams’ theoretical model is one of the best explanations for how quasars and other active galactic nuclei are powered.
The above was given FYI as an update to the problem proposed by Bardeen et al. in 1972 that the Penrose process is not astrophysically feasible. As one can see from Williams’ work that this problem has been overcome with relativistic scattering events inside the ergosphere such as inverse Compton scattering and γγ ―˃ e- e+ pair production. Also, the Bardeen reference requested by Hans Aug 2 at 0:49 is provided above.
Now the answer to the question: Since local inertial frame dragging is associated with the angular momentum of any rotating, gravitating body, the gravitomagnetic (GM) force field (the gravitational analog of a magnetic field), which is the general relativistic version of the Newtonian Coriolis force in a rotating frame, will be present. The gradient of the frame-dragging velocity produces it. The GM tensor acts on the momentum components of all moving particles, independent of their electrical charge. The GM force is expected to accelerate outwardly from the central mass in the global radial and polar directions for a particle with positive azimuthal coordinate momentum, and the acceleration in the global azimuthal direction is dependent on a combination of the particle’s polar coordinate and radial momentum components. This mean emitted particles in the dragged inertial frame will generally be accelerated outwardly by the fictitious (or pseudo) GM force. However, this process will be different from the Penrose process (which occurs inside the ergosphere) because there will be no negative energy orbits.
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:
