super-Penrose Process Research Articles

Decay of charged particles near naked singularities and super-Penrose process without fine-tuning

We consider the Penrose process near the naked singularity in the Reissner-Nordstr\"{o}m metric. Particle 0 falls from infinity and decays to two fragments at some point $r_{0}$. We show that the energy extraction due to this process can be indefinitely large in the limit $r_{0}\rightarrow 0$. In doing so, the value of the particle charge can remain bounded, in contrast to the previously known examples of the Penrose process in the electric field with unbounded energy extraction. The effect persists even in the limit of the flat pace-time.

Super-Penrose Process for Nonextremal Black Holes

We consider particle collisions in the background of nonextremal spherically symmetric static black holes. It is shown that debris of collision can have indefinitely large energy at infinity, i.e. the super-Penrose process (SPP) can occur. This property is sharply contrasted with that of rotating black holes for which it is already established that the SPP is forbidden. The Reissner-Nordstrom black hole serves as an example. If an external central force exerts on particles, even the Schwarzschild background is suitable for the SPP.

Super-Penrose process for extremal charged white holes

We consider collision of two particles 1 and 2 near the horizon of the extremal Reissner–Nordström (RN) black hole that produces two other particles 3 and 4. There exists such a scenario that both new particles fall into a black hole. One of them emerges from the white hole horizon in the asymptotically flat region, and the other one oscillates between turning points. However, the unbounded energies [Formula: see text] at infinity (super-Penrose process (SPP)) turn out to be impossible for any finite angular momenta [Formula: see text]. In this sense, the situation for such a white hole scenarios is opposite to the black hole ones, where the SPP is found earlier to be possible for the RN metric even for all [Formula: see text]. However, if [Formula: see text] themselves are unbounded, the SPP does exist for white holes.

New Scenarios of High-Energy Particle Collisions Near Wormholes

We suggest two new scenarios of high-energy particle collisions in the background of a wormhole. In scenario 1, the novelty consists of the fact that the effect does not require two particles coming from different mouths. Instead, all such scenarios of high energy collisions develop, when an experimenter sends particles towards a wormhole from the same side of the throat. For static wormholes, this approach leads to indefinitely large energy in the center of mass. For rotating wormholes, it makes possible the super-Penrose process (unbounded energies measured at infinity). In scenario 2, one of colliding particles oscillates near the wormhole throat from the very beginning. In this sense, scenario 2 is intermediate between the standard one and scenario 1 since the particle under discussion does not come from infinity at all.

Super-Penrose process for extremal rotating neutral white holes

We consider collision of two particles 1 and 2 near the horizon of the extremal rotating axially symmetric neutral generic black hole producing particles 3 and 4. We discuss the scenario in which both particles 3 and 4 fall into a black hole and move in a white hole region. If particle 1 is fine-tuned, the energy $E_{c.m.}$ in the centre of mass grows unbounded (the Ba\~{n}ados-Silk-West effect). Then, particle 3 \ can, in principle, reach a flat infinity in another universe. If not only $E_{c.m.}$ but also the corresponding Killing energy $E$ is unbounded, this gives a so-called super-Penrose process (SPP). We show that the SPP\ is indeed possible. Thus white holes turn out to be potential sources of high energy fluxes that transfers from one universe to another. This generalizes recent observaitons made by Patil and Harada for the Kerr metric. We analyze two different regimes of the process on different scales.

Super-Penrose process

If two particles collide near a rotating black hole, their energy in the centre of mass frame can become unbounded under certain conditions. In doing so, the Killing energy [Formula: see text] of debris at infinity is, in general, remain restricted. If [Formula: see text] is also unbounded, this is called the super-Penrose process. We elucidate when such a process is possible and give full classification of corresponding relativistic objects for rotating space-times. We also discuss the case of a pure electric super-Penrose process that is valid even in the flat space-time. The key role in consideration is played by the Wald inequalities.

Maximal efficiency of the collisional Penrose process with spinning particles in Kerr-Sen black hole

We study the collision of two uncharged spinning particles around an extreme Kerr-Sen black hole and calculate the maximal efficiency of the energy extraction from the Kerr-Sen black hole via super Penrose process. We consider the collision of two massive particles as well as collision of a massless particle with a massive particle. We calculate the maximum efficiency for all the cases, and found that the efficiency increases as the Kerr-Sen black hole’s parameter (b=1-a) decreases.

Center of mass energy of colliding electrically neutral particles and super-Penrose process

We consider collisions of electrically neutral particles in the background of axially symmetric rotating space-times. For reactions of the kind 1+2$% \rightarrow $3+4 we give full classification of possible scenarios based on exact expressions for dynamic characteristics of particles 3 and 4 depending on particles 1 and 2. There are five nonequivalent scenarios valid for different types of space-time (black hole, naked singularity, etc.). We are mainly interested in the situations when particle collisions can give unbounded outcome for (i) the energy $E_{c.m.}$ in the center of mass frame and (ii) Killing energy $E$ at infinity. If (i) is fulfilled, this may or may not lead to (ii). If (ii) holds, this is called the super-Penrose process (SPP). For equatorial particle motion, we establish close relation between the type of behavior of $E_{c.m.}$ depending on the lapse function $% N $ in the point of collision and the possibility of the SPP. This unites separate previous observations in literature in a unified picture as a whole. In doing so, no explicit transformations to the center of mass frame and back are needed, so all consideration is carried out in the original frame. As a result,we suggest classification of sub-classes of scenarios that are able (or unable) to give rise to the SPP particle collision, super-Penrose process, center of mass frame.

Super-Penrose process and rotating wormholes

We consider collision of particles in a wormhole near its throat. Particles come from the opposite mouths. If the lapse function is small enough there, the energy $E$ of debris at infinity grows unbounded, so we are faced with the so-called super-Penrose process. This requires the existence of the ergoregion, so a wormhole should be rotating.

Energy extraction of a spinning particle via the super Penrose process from an extremal Kerr black hole

Energy extraction of a spinning particle via the super Penrose process from an extremal Kerr black hole

Collisional super-Penrose process and Wald inequalities

We consider collision of two massive particles in the equatorial plane of an axially symmetric stationary spacetime that produces two massless particles afterwards. It is implied that the horizon is absent but there is a naked singularity or another potential barrier that makes possible the head-on collision. The relationship between the energy in the center of mass frame $E_{c.m.}$ and the Killing energy $E$ measured at infinity is analyzed. It follows immediately from the Wald inequalities that unbounded $E$ is possible for unbounded $E_{c.m.}$ only. This can be realized if the spacetime is close to the threshold of the horizon formation. Different types of spacetimes (black holes, naked singularities, wormholes) correspond to different possible relations between $E_{c.m.}$ and $E$. We develop a general approach that enables us to describe the collision process in the frames of the stationary observer and ZAMO (zero angular momentum observer). The escape cone and escape fraction are derived. A simple explanation of the existence of the bright spot is given. For the particular case of the Kerr metric, our results agree with the previous ones found in M. Patil, T. Harada, K. Nakao, P.S. Joshi, and M. Kimura, Phys. Rev. D 93, 104015 (2016).

Escape probability of the super-Penrose process

We consider a head-on collision of two massive particles that move in the equatorial plane of an extremal Kerr black hole, which results in the production of two massless particles. Focusing on a typical case, where both of the colliding particles have zero angular momenta, we show that a massless particle produced in such a collision can escape to infinity with arbitrarily large energy in the near-horizon limit of the collision point. Furthermore, if we assume that the emission of the produced massless particles is isotropic in the center-of-mass frame but confined to the equatorial plane, the escape probability of the produced massless particle approaches $5/12$ and almost all escaping massless particles have arbitrarily large energy at infinity and an impact parameter approaching $2GM/c^2$, where $M$ is the mass of the black hole.

Super-Penrose process due to collisions inside ergosphere

If two particles collide inside the ergosphere, the energy in the center of mass frame can be made unbound provided at least one of particles has a large negative angular momentum [A. A. Grib and Yu. V. Pavlov, Europhys. Lett. 101 (2013) 20004]. We show that the same condition can give rise to unbounded Killing energy of debris at infinity, i.e. super-Penrose process. Proximity of the point of collision to the black hole horizon is not required.

Rapidly rotating spacetimes and collisional super-Penrose process

We consider generic axially symmetric rotating spacetimes and examine particle collisions in the ergoregion. The results are generic and agree with those obtained in the particular case of the rotating Teo wormhole in N. Tsukamoto and C. Bambi, Phys. Rev. D 91, 104040 (2015). It is shown that for sufficiently rapid rotation, the energy of a particle escaping to infinity can become arbitrary large (so-called super-Penrose process). Moreover, this energy is typically much larger than the center-of mass energy of colliding particles. In this sense the situation differs radically from that for collisions near black holes.

Is the super-Penrose process possible near black holes?

We consider collisions of particles near generic axially symmetric extremal black holes. We examine possibility of indefinitely large extraction of energy (the so-called super-Penrose process) in the limit when the point of collision approaches the horizon. Three potential options are considered (fractional powers of the lapse function in the relations between the energies and the angular momenta of particles in the point of collision), collision between outgoing particles and ingoing ones, collision in the ergoregion far from the horizon). It turns out in all three cases that states suitable for the super-Penrose process cannot be obtained from the previous collision of particles with finite masses and angular momenta.

High energy particle collisions near black holes

If two geodesic particles collide near a rotating black hole, their energy in the centre of mass frame E c.m. can become unbound under certain conditions (the so-called BSW effect). The special role is played here by so-called critical geodesics when one of particles has fine-tuned energy and angular momentum. The nature of geodesics reveals itself also in fate of the debris after collisions. One of particles moving to a remote observer is necessarily near-critical. We discuss, when such a collision can give rise not only unboud E c.m. but also unbound Killing energy E (so-called super-Penrose process).

General limitations on trajectories suitable for super-Penrose process

Collisions of particles near a rotating black hole can lead to unbound energies Ec.m. in their centre-of-mass frame. There are indications that the Killing energy of debris at infinity can also be unbound for some scenarios of collisions near the extremal black-hole horizon (the so-called super-Penrose process). They include the participation of a particle that i) has generic (not fine-tuned) parameters and ii) moves away from a black hole before collision. We show that for any finite particle's mass, such a particle cannot be obtained as a result of the preceding collision. However, this can be done if one of the initial infalling particles has the mass of the order that generalizes previous observations made in the literature for radial infall in the Kerr background.