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.
We first study the escape probability of the spinning particle emitted from the Kerr black hole and find that the escape probability increases with the spin of the particle around the extreme Kerr black hole; in contrast, the escape probability decreases at the position near the horizon but increases at the position far away from the horizon with the increasing spin of the particle. We then probe the relation between the escape probabilities and the energy extraction efficiencies of collisional Penrose processes for the particles with varying spin. For the extreme Kerr black hole, the efficien…
In this paper, I present results from theoretical and numerical (Monte Carlo) N-particle fully relativistic 4-D analysis of Penrose scattering processes (Compton and gamma-gamma-->e-e+) in the ergosphere of a supermassive or stellar mass Kerr (rotating) black hole. Specifically, the escape conditions and the escaping orbits of the Penrose pair production (gamma-gamma-->e-e+) electrons are analyzed, revealing that these particles escape along collimated, jet geodesic trajectories encircling the polar axis. Such collimated vortical tightly wound coil-like trajectories of relativistic particles a…
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 …
The center of mass (CM) energy in a collisional Penrose process - a collision taking place within the ergosphere of a Kerr black hole - can diverge under suitable extreme conditions (maximal Kerr, near horizon collision and suitable impact parameters). We present an analytic expression for the CM energy, refining expressions given in the literature. Even though the CM energy diverges, we show that the maximal energy attained by a particle that escapes the black hole's gravitational pull and reaches infinity is modest. We obtain an analytic expression for the energy of an escaping particle resu…
Particle collisions in black hole ergoregions may result in extremely high center of mass energies that could probe new physics if escape to infinity were possible. Here we show that some geodesics at high inclinations to the equatorial plane may be unbound. Hence a finite flux of annihilation debris is able to escape, especially in the case of near-extremal Kerr black holes and if the Penrose process plays a role. For a class of Penrose processes, we show that the Wald inequalities are satisfied, allowing the Penrose process to have a key role in high energy ejection. Hence the possibility of…
In a collisional Penrose process, two particles coming from the asymptotically flat region collide in the ergosphere of a compact object. The collision produces two new particles, one with positive energy and one with negative energy. When the particle with positive energy escapes to infinity, the process extracts energy from the compact object. In this paper, we study the collisional Penrose process in a rotating wormhole spacetime. We consider the simple case of a head-on collision at the throat of a Teo wormhole. We find that the process of energy extraction from a Teo wormhole can be subst…
The Penrose process in the vicinity of an extremal Banãdos-Teitelboim-Zanelli(BTZ) black hole is studied. Due to the existence of negative cosmological constant, only massless particles could escape to infinity. Hence we analyse the Penrose process by one massless particle collides with another massive particle near the horizon of BTZ black holes. Calculations of the maximum energy extraction efficiency of this process is carried out for both spinless and spinning particles. Our results show that the spinning particle have a higher energy extraction efficiency than the spinless particle. Moreo…
Collisions of particles in black holes' ergospheres may result in an arbitrarily large center of mass energy. This led recently to the suggestion (Banados et al., 2009) that black holes can act as ultimate particle accelerators. If the energy of an outgoing particle is larger than the total energy of the infalling particles the energy excess must come from the rotational energy of the black hole and hence this must involve a Penrose process. However, while the center of mass energy diverges the position of the collision makes it impossible for energetic particles to escape to infinity. Followi…
The origin of the ultra-high-energy particles we receive on the Earth from the outer space such as EeV cosmic rays and PeV neutrinos remains an enigma. All mechanisms known to us currently make use of electromagnetic interaction to accelerate charged particles. In this paper we propose a mechanism exclusively based on gravity rather than electromagnetic interaction. We show that it is possible to generate ultra-high-energy particles starting from particles with moderate energies using the collisional Penrose process in an overspinning Kerr spacetime transcending the Kerr bound only by an infin…
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.
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 …
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.
We consider the Penrose process near the naked singularity in the Reissner-Nordström 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.
If two particles collide inside the ergosphere, the energy in the centre 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, 20004 (2013)). 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.
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 col…
In many astrophysical scenarios the charge of the black hole is often neglected due to unrealistically large values of the charge required for the Reissner-Nordström spacetime metric. However, black holes may possess small electric charge due to various selective accretion mechanisms. In this paper we investigate the effect of a small hypothetical electric charge of a Schwarzschild black hole on the ionization of a freely falling neutral particle and subsequent escape of the ionized particle from the black hole. We show that the energy of ionized particle can grow ultra-high and discuss distin…
Collisions of particles near a rotating black hole can lead to unbound energies $E_{c.m.}$ 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 (so-called super-Penrose process). They include 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 b…
We analyze the collisional Penrose process between a particle on the ISCO orbit around an extreme Kerr black hole and a particle impinging from infinity. We consider both cases with non-spinning and spinning particles. We evaluate the maximal efficiency, $η_{\text{max}}=(\text{extracted energy})/(\text{input energy})$, for the elastic collision of two massive particles and for the photoemission process, in which the ISCO particle will escape to infinity after the collision with a massless impinging particle. For non-spinning particles, the maximum efficiency is $η_{\text{max}} \approx 2.562$ f…
We consider collision of two particles 1 and 2 near the horizon of the extremal Reissner-Nordström (RN) black hole that produce two other particles 3 and 4. There exists such a scenario that both new particles fall in a black hole. One of them emerges from the white hole horizon in the asymptotically flat region, the other one oscillates between turning points. However, the unbounded energies $E$ at infinity (super-Penrose process - SPP) turn out to be impossible for any finite angular momenta $L_{3.4}$. In this sense, the situation for such a white hole scenarios is opposite to the black hole…
We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, $Λ$, always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres -- associated with the black hole and the cosmological event horizons. We prove by analysing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both black hole and cosmological event horizons' areas increase, the later beco…
Let a particle move in the flat space-time under the action of the electric potential. If it decays to two fragments, the energy of debris can be larger than the original energy and, moreover, the efficiency of such a process can be unbounded. This effect can be considered as a limit of the Denardo-Ruffini process near the Reissner-Nordström black hole when the gravitational constant and/or black hole mass tend to zero. There are scenarios in which the energy of debris at infinity is much larger than the initial one. Comparison with other close but distinct effects is discussed.
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 Bañados-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 pro…
Penrose and super-Penrose energy extraction from a Reissner-Nordström black hole spacetime with a cosmological constant through the BSW mechanism: Full story
In this Letter, we wish to point out that the distinguishing feature of Magnetic Penrose process (MPP) is its super high efficiency exceeding $100\%$ (which was established in mid 1980s for discrete particle accretion) of extraction of rotational energy of a rotating black hole electromagnetically for a magnetic field of milli Gauss order. Another similar process, which is also driven by electromagnetic field, is Blandford-Znajek mechanism (BZ), which could be envisaged as high magnetic field limit MPP as it requires threshold magnetic field of order $10^4$G. Recent simulation studies of fully…
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 …
Superradiant scattering is a radiation enhancement process that takes place in many contexts, and which has recently found exciting applications in astro and particle physics. In the framework of curved spacetime physics, it has been associated with the classical Penrose process for particles. Superradiance is usually also associated with bosonic fields around geometries with ergoregions and horizons. These notions are in clear tension however: the Penrose process occurs for horizonless geometries, and particles are composed of fermions. Here, we resolve the tension in its different aspects, b…
In a paper posted on the arXiv a few weeks ago Berti, Brito and Cardoso \cite{Berti+14} suggest that ultra-high-energy particles can emerge from collisions in a black hole's ergosphere. This can happen if the process involves a particle on an outgoing trajectory very close to the black hole. Clearly such a particle cannot emerge from the black hole. It is argued \cite{Berti+14} that this particle can arise in another collision. Thus the process involves two collisions: one in which an outgoing particle is produced extremely close to the horizon, and a second one in which energy is gained. The …
Spinning black holes create electromagnetic storms when immersed in ambient magnetic fields, illuminating the otherwise epically dark terrain. In an electromagnetic extension of the Penrose process, tremendous energy can be extracted, boosting the energy of radiating particles far more efficiently than the mechanical Penrose process. We locate the regions from which energy can be mined and demonstrate explicitly that they are no longer restricted to the ergosphere. We also show that there can be toroidal regions that trap negative energy particles in orbit around the black hole. We find that t…
We investigate the effect of superradiance shielding for the analogue rotating black holes simulated by optical vortices by calculating the radial motion of massless particles in such spacetime background. We add the conditions $E<LΩ_{r_{e}}$ and $L>0$ to judge the classically forbidden region of superradiance. It is found that the superradiance forbidden region exists near the static limit inside the ergosphere,which will limit the classical Penrose process for the particles with some specific energies and angular momenta. Once these particles satisfying the superradiance conditions aremeasur…
If a supermassive black hole has some material orbiting around it at close to its innermost stable circular orbit (ISCO), then, when it plunges into a second supermassive black hole, the orbiting material has a velocity dispersion of order of speed of light about the orbital velocity of its host black hole. It becomes plausible that some of the orbiting material will be "catapulted" to the negative-energy ergosphere orbits of the second black hole at the plunge. This may provide an astrophysically plausible way to extract energy from the black hole, originally suggested by Penrose.
Theoretical and numerical (Monte Carlo) N-particle computer model simulations show that Penrose Compton scattering (PCS) near the event horizon and Penrose pair production (PPP) at or near the photon orbit, in the ergosphere of a supermassive rotating black hole, can generate the necessary energy-momentum spectra to explain the origin of the mysterious fluxes of ultrarelativistic electrons, inferred from observations to emerge from the cores of Quasars 3C 279 and 3C 273, and other active galactic nuclei (AGNs). Particles from an accretion disk surrounding the black hole fall into the ergospher…
Recently, O.B.Zaslavskii considers the collision near the horizon of the extremal Kerr black hole that produces two particles and one of two particles has divergent conserved killing energy(the so called super Penrose process). O.B.Zaslavskii shows this particle can not move in a asymptotic region in this universe. This means super Penrose process for extremal Kerr black hole is impossible. However, recently, Mandar Patil and Tomohiro Harada show this particle can enter event horizon, turns back and emerges through white hole event horizon into asymptotic region in other universe. This means s…
We consider collision of two particles that move in the equatorial plane near a general stationary rotating axially symmetric extremal black hole. One of particles is critical (with fine-tuned parameters) and moves in the outward direction. The second particle (usual, not fine-tuned) comes from infinity. We examine the efficiency $η$ of the collisional Penrose process. There are two relevant cases here: (i) a particle falling into a black hole after collision is heavy, (ii) it has a finite mass. We show that the maximum of $η$ in case (ii) is less or equal to that in case (i). It is argued tha…
The superradiant amplification in the scattering from a rotating medium was first elucidated by Sir Roger Penrose over 50 years ago as a means by which particles could gain energy from rotating black holes. Despite this fundamental process being ubiquitous also in wave physics, it has only been observed once experimentally, in a water tank, and never in an astrophysical setting. Here, we measure this amplification for a nonlinear optics experiment in the superfluid regime. In particular, by focusing a weak optical beam carrying orbital angular momentum onto the core of a strong pump vortex bea…
We present a new upper limit on the energy that may be extracted from a Kerr black hole by means of particle collisions in the ergosphere (i.e., the "collisional Penrose process"). Earlier work on this subject has focused largely on particles with critical values of angular momentum falling into an extremal Kerr black hole from infinity and colliding just outside the horizon. While these collisions are able to reach arbitrarily high center-of-mass energies, it is very difficult for the reaction products to escape back to infinity, effectively limiting the peak efficiency of such a process to r…
For particle collision near rapidly rotating Kerr black holes, the center-of-mass energy can be arbitrarily high if the angular momentum of either of the colliding particles is fine-tuned. Recently, it has been shown that particles which are produced by such a particle collision and escape to infinity cannot be very massive nor very energetic. For electrically charged black holes there is a similar phenomenon, where the center-of-mass energy for the collision of charged particles near the horizon can be arbitrarily high. One might expect that there would exist a similar bound on the energy and…
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. For all the cases, we find that the maximum efficiency decreases as the Kerr-Sen black hole's parameter($b=1-a$) increases.
Soon after the discovery of the Kerr metric, Penrose realized that superradiance can be exploited to extract energy from black holes. The original idea (involving the breakup of a single particle) yields only modest energy gains. A variant of the Penrose process consists of particle collisions in the ergoregion. The collisional Penrose process has been explored recently in the context of dark matter searches, with the conclusion that the ratio $η$ between the energy of post-collision particles detected at infinity and the energy of the colliding particles should be modest ($η\lesssim 1.5$). Sc…
On the Classical, Penrose, and Reverse Isoperimetric Inequalities in Black Holes: Insights From AdS to Flat Riemannian Backgrounds
University of Waterloo（滑铁卢大学）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Damghan University（达姆甘大学）；Khazar University（哈萨尔大学）
I present a theoretical and numerical (Monte Carlo) N-particle analysis of Penrose scattering processes in the ergosphere of a supermassive Kerr black hole. These GR model calculations reveal that the observed high energies and luminosities of quasars and other active galactic nuclei, the collimated jets about the polar axis, and the asymmetrical jets (which can be enhanced by relativistic Doppler beaming effects) all are inherent properties of rotating black holes. The Penrose scattered escaping relativistic particles exhibit tightly wound coil-like cone distributions (highly collimated vorti…
In this paper, we study the Penrose process and the maximum energy extracted from the collision of two particles near the Kerr-Newman black hole with WGC condition. We consider the collision process when two particles collide in the ergosphere region of a black hole, scattering two new particles; one of them falls into the black hole and the other escapes to infinity. Our calculations also show an increasing in the energy. We also checked how much energy could be received from a black hole for particles with different spins. Results of this paper will help us to identify and study the black ho…
For general relativistic, inviscid, axisymmetric flow around Kerr black hole one may choose different flow thickness. The stationary flow equations can be solved using methods of dynamical system to get transonic accretion flows , i.e, flow infalling in the blackhole that turns supersonic from subsonic with decreasing radial distance, or vice versa. This transonic flows are obtained by choosing the particular flow passing through critical points of phase portrait. For certain flow thickness like the one maintaining conical shape, the sonic point coincide with the critical point. But there are …
Recent general relativistic MHD simulations have suggested that relativistic jets from active galactic nuclei (AGNs) have been powered by rotational energy of central black holes. Some mechanisms of extraction of black hole rotational energy have been proposed, like the Penrose process, Blandford-Znajek mechanism, MHD Penrose process, and superradiance. The Blandford-Znajek mechanism is the most promising mechanism for the engines of the relativistic jets from AGNs. However, an intuitive interpretation of this mechanism with causality is not clarified yet, while the Penrose process has a clear…
In this paper we continue our study of the non-linear response of a Schwarzschild black hole to an ingoing gravitational wave by computing the Newman-Penrose (NP) constants. The NP constants are five complex, supertranslation-invariant quantities defined on null infinity $\mathscr{I}^+$ and although put forward in the 60's, they have never been computed in a non-stationary setting. We accomplish this through a numerical implementation of Friedrich's generalized conformal field equations whose semi-global evolution yields direct access to $\mathscr{I}+$. Generalizations of the NP constants' int…
Results from general relativistic theoretical Monte Carlo computer simulations of Compton scattering and e-e+ pair production processes in the ergosphere of a supermassive (10^8 solar mass) rotating black hole are presented. Particles from an accretion disk fall into the ergosphere and scatter off particles that are in bound equatorially and nonequatorially confined orbits. The Penrose mechanism, in general, allows rotational energy of a Kerr black hole to be extracted by scattered particles escaping from the ergosphere to infinity (i.e., large distances from the black hole). The results of th…
