The collisional Penrose process received much attention when Banados, Silk and West (BSW) pointed out the possibility of test-particle collisions with arbitrarily high center-of-mass energy in the vicinity of the horizon of an extremally rotating black hole. However, the energy that can be extracted from the black hole in this promising, if simplified, scenario, called the BSW effect, turned out to be subject to unconditional upper bounds. And although such bounds were not found for the electrostatic variant of the process, this version is also astrophysically unfeasible, since it requires a maximally charged black hole. In order to deal with these deficiencies, we revisit the unified version of the BSW effect concerning collisions of charged particles in the equatorial plane of a rotating electrovacuum black hole spacetime. Performing a general analysis of energy extraction through this process, we explain in detail how the seemingly incompatible limiting cases arise. Furthermore, we demonstrate that the unconditional upper bounds on the extracted energy are absent for arbitrarily small values of the black hole electric charge. Therefore, our setup represents an intriguing simplified model for possible highly energetic processes happening around astrophysical black holes, which may spin fast but can have only a tiny electric charge induced via interaction with an external magnetic field.
High-energy collisions can occur for radially moving charged test particles in the extremal Reissner-Nordström spacetime if one of the particles is fine-tuned and the collision point is taken close to the horizon. This is an analogy of the Banados-Silk-West (BSW) effect, first described for extremal Kerr black holes. However, it differs significantly in terms of energy extraction: unlike for the original BSW process, no unconditional upper bounds on mass and energy of an escaping test particle produced in the collision were found for the charged version. We show that these results can be repli…
Associated to every stationary extremal black hole is a unique near-horizon geometry, itself a solution of the field equations. These latter spacetimes are more tractable to analyze and most importantly, retain properties of the original black hole which are intrinsic to the event horizon. After reviewing general features of near-horizon geometries, such as SO(2,1) symmetry enhancement, I report on recent work on stationary, charged extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions and present a classification of near-horiz…
Spherical black hole (BH) solutions in Einstein-Maxwell-scalar (EMS) models wherein the scalar field is non-minimally coupled to the Maxwell invariant by some coupling function are discussed. We suggest a classification for these models into two classes, based on the properties of the coupling function, which, in particular, allow, or not, the Reissner-Nordström (RN) BH solution of electrovacuum to solve a given model. Then, a comparative analysis of two illustrative families of solutions, one belonging to each class is performed: $dilatonic$ versus $scalarised$ BHs. By including magnetic char…
It has been shown in the literature that the event horizon of an extremal asymptotically flat Reissner-Nordstrom black hole is also a stable photon sphere. We further clarify this statement and give a general proof that this holds for a large class of static spherically symmetric black hole spacetimes with an extremal horizon. In contrast, in the Doran frame, an extremal asymptotically flat Kerr black hole has an unstable photon orbit on the equatorial plane of its horizon. In addition, we show that an extremal asymptotically flat Kerr-Newman black hole exhibits two equatorial photon orbits if…
We consider isotropic and monochromatic photon emissions from equatorial emitters moving along future-directed timelike geodesics in the near-horizon extremal Kerr (NHEK) and near-horizon near-extremal Kerr (near-NHEK) regions, to asymptotic infinity. We obtain numerical results for the photon escaping probability (PEP) and derive analytical expressions for the maximum observable blueshift (MOB) of the escaping photons, both depending on the emission radius and the emitter's proper motion. In particular, we find that for all anti-plunging or deflecting emitters that can eventually reach to asy…
We show that the emergent near-horizon conformal symmetry of extremal black holes gives rise to universal behavior in perturbing fields, both near and far from the black hole horizon. The scale-invariance of the near-horizon region entails power law time-dependence with three universal features: (1) the decay off the horizon is always precisely twice as fast as the decay on the horizon; (2) the special rates of $1/t$ off the horizon and $1/\sqrt{v}$ on the horizon commonly occur; and (3) sufficiently high-order transverse derivatives grow on the horizon (Aretakis instability). The results are …
The aim of the present article is to evaluate the motion of charged test particles in the vicinity of a near-extremal rotating black hole in the presence of magnetic fields. Euler-Lagrange motion equations and effective potential methods are used to characterize the motion out of the equatorial plane. Such approach is of peculiar significance if it is considered, e.g., accretion processes onto rotating black holes. In general investigations concerning accretion focus mostly on the simplest case of particles moving in the equatorial plane. Here it will be considered that particles initially mov…
We systematically investigate axisymmetric extremal isolated horizons (EIHs) defined by vanishing surface gravity, corresponding to zero temperature. In the first part, using the Newman-Penrose and GHP formalism we derive the most general metric function for such EIHs in the Einstein-Maxwell theory, which complements the previous result of Lewandowski and Pawlowski. We prove that it depends on 5 independent parameters, namely deficit angles on the north and south poles of a spherical-like section of the horizon, its radius (area), and total electric and magnetic charges of the black hole. The …
In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr-Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound in the form of algebraic equations. For the case that the photon trajectories are limited in the equatorial plane, the shifts in the azimuthal angle and time are obtained.
We study the collision of two particles with equal masses moving in the equatorial plane near horizon of the rotating regular Ayón-Beato-García (ABG) black hole (BH) and calculate the center-of-mass (CM) energy for the colliding particles for both extremal and non-extremal cases. It turns out that CM energy depends not only on rotation parameter $a$ but also on charge $Q$. Particularly for the extremal rotating regular ABG BH, CM energy of two colliding particles could be arbitrarily high for critical angular momentum of particles. Furthermore, we also show that, for a non-extremal BH, there e…
We consider stationary, axially and equatorially symmetric systems consisting of a central rotating and charged degenerate black hole and surrounding matter. We show that $a^2+Q^2=M^2$ always holds provided that a continuous sequence of spacetimes can be identified, leading from the Kerr-Newman solution in electrovacuum to the solution in question. The quantity $a=J/M$ is the black hole's intrinsic angular momentum per unit mass, $Q$ its electric charge and $M$ the well known black hole mass parameter introduced by Christodoulou and Ruffini.
We consider generic rotating axially symmetric "dirty" (surrounded by matter) black holes. Near-horizon circular equatorial orbits are examined in two different cases of near-extremal (small surface gravity $κ$) and exactly extremal black holes. This has a number of qualitative distinctions. In the first case, it is shown that such orbits can lie as close to the horizon as one wishes on suitably chosen slices of space-time when $κ\rightarrow 0$. This generalizes observation of T.\ Jacobson Class. Quantum Grav. 28 187001 (2011) made for the Kerr metric. If a black hole is extremal ($κ=0$), circ…
The Bañados-Silk-West (BSW) effect consists in the possibility to obtain arbitrarily large energy $E_{c.m.}$ in the centre of mass frame of two colliding particles near the black hole horizon. One of the common beliefs was that the action of force on these particles (say, due to gravitational radiation) should necessarily restrict the growth of $E_{c.m.}$. We consider extremal horizons and develop a model-independent approach and analyze the conditions for the force to preserve or kill the effect, using the frames attached both to observers orbiting the black hole and to ones crossing the hori…
The gedanken experiment by Wald to destroy a black hole using a test particle in the equatorial plane is adopted to the case of extremal magnetized black holes. We find the presence of external magnetic fields resulting from the "Ernst magnetization" permits a test particle to have strong enough energy to destroy the black hole. However, the corresponding effective potentials show that such particles would never reach the horizon.
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, th…
The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii r_{ph}(a/M;cos i) of these spherical null geodesics, where a/M is the dimensionless angular-momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known…
We have studied electromagnetic line emissions from near-horizon region in the extremal Kerr-Taub-NUT black hole spacetime and then probe the effects of NUT charge on the electromagnetic line emissions. Due to the presence of the NUT charge, the equatorial plane is no more a symmetry plane of the KTN spacetime, which leads to that the dependence of electromagnetic line emission on the NUT charge for the observer in the Southern Hemisphere differs from that in the Northern one. Our result indicate that the electromagnetic line emission in the Kerr-Taub-NUT black hole case is brighter than that …
We consider monochromatic and isotropic photon emission from circular equatorial Kerr orbiters. We derive analytic expressions for the photon escape probability and the redshift-dependent total flux collected on the celestial sphere as a function of emission radius and black hole parameters. These calculations crucially involve the critical curve delineating the region of photon escape from that of photon capture in each emitter's sky. This curve generalizes to finite orbital radius the usual Kerr critical curve and displays interesting features in the limit of high spin, which we investigate …
The causal geodesics in the equatorial plane of a static extremal charged black holes in heterotic string theory are examined with regard to their geodesic stability, and compared with similar geodesics in the non-extremal situation. Extremization of the effective potential for time-like and null circular geodesics implies that in the extremal limit, the radius of ISCO(Inner-most Stable Circular Orbit) $(r_{ISCO})$, circular photon orbit (CPO) $(r_{ph})$ and marginally bound circular orbit (MBCO) $(r_{mb})$ are coincident with the event horizon $(r_{hor})$ i.e. $r_{ISCO}=r_{ph}=r_{mb}=r_{hor}=…
The so-called BSW effect is an idealised scenario for high-energy test particle collisions in the vicinity of black holes; if the black hole is extremal and one of the particles fine-tuned, the centre-of-mass collision energy can be arbitrarily high. It has been recently shown that the energy of escaping particles produced in this process can also be arbitrarily high in the given approximation, as long as both the black hole and the escaping particles are charged, regardless of how small the black-hole charge might be. We revisit these results and show that they are also compatible with proper…
We describe a model that generates first order adiabatic EMRI waveforms for quasi-circular equatorial inspirals of compact objects into rapidly rotating (near-extremal) black holes. Using our model, we show that LISA could measure the spin parameter of near-extremal black holes (for $a \gtrsim 0.9999$) with extraordinary precision, $\sim$ 3-4 orders of magnitude better than for moderate spins, $a \sim 0.9$. Such spin measurements would be one of the tightest measurements of an astrophysical parameter within a gravitational wave context. Our results are primarily based off a Fisher matrix analy…
An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al, 2016 Q. J. Mech. Appl. Math., doi=10.1093/qjmam/hbw014). To this end, the strong deflection limit for a prograde orbit around an extremal black hole is examined, and the full no…
The spherical photon orbits around a black hole with constant radii are particular important in astrophysical observations of the black hole. In this paper, the equatorial and non-equatorial spherical photon orbits around Kerr-Newman black holes are studied. The radii of these orbits satisfy a sextic polynomial equation with three parameters, the rotation parameter $u$, charge parameter $w$ and effective inclination angle $v$. It is found that there are two polar orbits and one is inside and the other is outside the event horizon. For orbits in the equatorial plane around an extremal Kerr-Newm…
The center-of-mass energy of two particles can become arbitrarily large if they collide near the event horizon of an extremal Kerr black hole, which is called the Ba$\rm \tilde n$ados-Silk-West (BSW) effect. We consider such a high-energy collision of two particles which started from infinity and follow geodesics in the equatorial plane and investigate the energy extraction from such a high-energy particle collision and the production of particles in the equatorial plane. We analytically show that, on the one hand, if the produced particles are as massive as the colliding particles, the energy…
The transformation which adds (or removes) NUT charge when it is applied to electrovacuum, axisymmetric and stationary space-times is studied. After analysing the Ehlers and the Reina-Treves transformations we propose a new one, more precise in the presence of the Maxwell electromagnetic field. The enhanced Ehlers transformation proposed turns out to act as a gravitomagnetic duality, analogously to the electromagnetic duality, but for gravity: it rotates the mass charge into the gravomagnetic (or NUT) charge. As an example the Kerr-Newman-NUT black hole is obtained with the help of this enhanc…
One of the most important geodesics in a black-hole spacetime is the marginally bound spherical orbit. This critical geodesic represents the innermost spherical orbit which is bound to the central black hole. The radii $r_{\text{mb}}({\bar a})$ of the marginally bound {\it equatorial} circular geodesics of rotating Kerr black holes were found analytically by Bardeen {\it et. al.} more than four decades ago (here $\bar a\equiv J/M^2$ is the dimensionless angular-momentum of the black hole). On the other hand, no closed-form formula exists in the literature for the radii of generic ({\it non}-eq…
We investigate here the particle acceleration by Kerr naked singularities. We consider a collision between particles dropped in from infinity at rest, which follow geodesic motion in the equatorial plane, with their angular momenta in an appropriate finite range of values. When an event horizon is absent, an initially infalling particle turns back as an outgoing particle, when it has the angular momentum in an appropriate range of values, which then collides with infalling particles. When the collision takes place close to what would have been the event horizon in the extremal case, the center…
We study analytically the relaxation phase of perturbed, rapidly rotating black holes. In particular, we derive a simple formula for the fundamental quasinormal resonances of near-extremal Kerr black holes. The formula is expressed in terms of the black-hole physical parameters: omega=m Omega-i2 pi T(n+1/2), where T and Omega are the temperature and angular velocity of the black hole, and m is the azimuthal harmonic index of a co-rotating equatorial mode. This formula implies that the relaxation period tau sim 1/Im(omega) of the black hole becomes extremely long as the extremal limit T to 0 is…
The escape fraction at infinity is evaluated for massless particles produced in collisions of weakly interacting particles accreted into a density spike near the particle horizon of an extremal Kerr black hole, for the case of equatorial orbits. We compare with the Schwarzschild case, and argue that in the case of extremal black holes, redshifted signatures can be produced that could potentially explore the physics of particle collisions at centre of mass energies that extend beyond those of any feasible terrestrial accelerator.
We semianalytically investigate the scalar self-force experienced in the final stages of extreme mass ratio inspirals of nonspinning scalar particles into supermassive nearly extremal Kerr black holes. We exploit the near-horizon conformal symmetry to find the self-force for general corotating equatorial geodesics. The angular component of the self-force is shown to be universal at leading order in the high spin limit. We verify that the energy and angular momentum losses of the scalar particle match with the asymptotic fluxes of scalar radiation. In particular, we relate the previously descri…
We consider Einstein-Maxwell-dilaton gravity with the non-minimal exponential coupling between the dilaton and the Maxwell field emerging from low energy heterotic string theory. The dilaton is endowed with a potential that originates from an electromagnetic Fayet-Iliopoulos (FI) term in $\mathcal{N}=2$ extended supergravity in four spacetime dimensions. For the case we are interested in, this potential introduces a single parameter $α$. When $α\rightarrow 0$, the static black holes (BHs) of the model are the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) solutions. When $α\rightarrow \in…
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 $C$-metric is a boost-symmetric spacetime solution to the vacuum Einstein field equations which describes black holes that are uniformly accelerated under the tension of a cosmic string. Only recently the thermodynamics of accelerating black holes and their modal stability against neutral scalar perturbations were concisely established. The generalization of accelerating black holes to incorporate an electric charge, namely the charged $C$-metric, possess three distinct families of quasinormal mode frequencies; the complex photon surface quasinormal modes associated with unstable null part…
It is known that a near-extremal Kerr black hole can be spun up beyond its extremal limit by capturing a test particle. Here we show that overspinning is always averted once back-reaction from the particle's own gravity is properly taken into account. We focus on nonspinning, uncharged, massive particles thrown in along the equatorial plane, and work in the first-order self-force approximation (i.e., we include all relevant corrections to the particle's acceleration through linear order in the ratio, assumed small, between the particle's energy and the black hole's mass). Our calculation is a …
The linear in mass ratio correction to the periapsis advance of equatorial orbits around a spinning black hole is calculated for the first time and to very high precision, providing a key benchmark for different approaches modelling spinning binaries. The high precision of the calculation is leveraged to discriminate between two recent incompatible derivations of the 4PN equations of motion. Finally, the limit of the periapsis advance near the innermost stable orbit (ISCO) allows determination of the ISCO shift, validating previous calculations using the first law of binary mechanics. Calculat…
We study the motion of a spinning test particle in Schwarzschild spacetime, analyzing the Poincaré map and the Lyapunov exponent. We find chaotic behavior for a particle with spin higher than some critical value (e.g. $S_{cr} \sim 0.64 μM$ for the total angular momentum $J=4 μM$), where $μ$ and $M$ are the masses of a particle and of a black hole, respectively. The inverse of the Lyapunov exponent in the most chaotic case is about three orbital periods, which suggests that chaos of a spinning particle may become important in some relativistic astrophysical phenomena. The ``effective potential"…
Acceleration radiation, quasinormal modes and quasi-bound states in generic rotating regular black holes
Harbin Institute of Technology（哈尔滨工业大学）；New Uzbekistan University（新乌兹别克斯坦大学）；Eastern Mediterranean University（东地中海大学）；Mapúa University（玛布亚科技学院）；National University of Uzbekistan（乌兹别克斯坦国立大学）
We study the collision of two particles with the different rest masses moving in the equatorial plane of a Kerr-Taub-NUT spacetime and get the center-of-mass (CM) energy for the particles. We find that the CM energy depends not only on the rotation parameter, $a$, but also on the NUT charge of the Kerr-Taub-NUT spacetime, $n$. Especially, for the extremal Kerr-Taub-NUT spacetime, an unlimited CM energy can be approached if the parameter $a$ is in the range $[1,\sqrt{2}]$, which is different from that of the Kerr and Kerr-Newman black holes.
The hidden Kerr/CFT proposal implies that the massless scalar wave equation in the near-region and low-frequency limit respects a hidden SL(2,R)$\times$SL(2,R) invariance in the Kerr black hole spacetime. We may use this symmetry to determine quasinormal frequencies (QNFs) of the massless scalar wave propagating around the Kerr black hole algebraically. It is shown that QNFs obtained using the hidden conformal symmetry near the horizon correspond approximately to not only those of scalar perturbation around the near-horizon region of a nearly extremal Kerr (NEK) black hole, but also those of n…
We have performed a detailed analysis of orbital motion in the vicinity of a nearly extremal Kerr black hole. For very rapidly rotating black holes (spin a=J/M>0.9524M) we have found a class of very strong field eccentric orbits whose angular momentum L_z increases with the orbit's inclination with respect to the equatorial plane, while keeping latus rectum and eccentricity fixed. This behavior is in contrast with Newtonian intuition, and is in fact opposite to the "normal" behavior of black hole orbits. Such behavior was noted previously for circular orbits; since it only applies to orbits ve…
Quintessential dark energy with pressure $p$ and density $ρ$ is related by equation of state $p=ωρ$ with the state parameter $-1<ω<-1/3$. The cosmological dark energy influence on black hole spacetime are interesting and important. In this paper, we study the Kerr-Newman-AdS solutions of the Einstein-Maxwell equation in quintessence field around a black hole by Newman-Janis algorithm and complex computations. From the horizon structure equation, we obtain the expression between quintessence parameter $α$ and cosmological constant $Λ$ if the black hole exists two cosmological horizon $r_{q}$ an…
The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various Einstein-Maxwell-scalar models. Within these models, different classes of BH solutions are possible, depending on the non-minimal coupling function $f(ϕ)$, between the scalar field and the Maxwell invariant. Here we consider the class wherein both the (bald) electrovacuum Reissner-Nordström (RN) BH and new scalarised BHs co-exist, and the former are never unstable against scalar perturbations. In particular we examine the model, within this subclass, with a quartic coupling functi…
Energy extraction and particle acceleration around a rotating dyonic black hole in $N=2$, $U(1)^2$ gauged supergravity
H. N. B. Garhwal University（H.N.B. 加尔瓦尔大学）；Gurukul Kangri Vishwavidyalaya（古鲁库尔坎格里大学）；Center for Space Research, North-West University（西北大学空间研究中心）；Instituto de Física, Pontificia Universidad Católica de Valparaíso（天主教瓦尔帕莱索大学物理研究所）；University of York（约克大学）
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…
The rotating regular Hayward's spacetime, apart from mass ($M$) and angular momentum ($a$), has an additional deviation parameter ($g$) due to the magnetic charge, which generalizes the Kerr black hole when $g\neq0$, and for $g=0$, it goes over to the Kerr black hole. We analyze how the ergoregion is affected by the parameter $g$ to show that the area of ergoregion increases with increasing values of $g$. Further, for each $g$, there exist critical $a_E$, which corresponds to a regular extremal black hole with degenerate horizons $r=r^E_H$, and $a_E$ decrease whereas $r^E_H$ increases with an …
The rotating Ayón-Beato-García (ABG) black holes, apart from mass ($M$) and rotation parameter ($a$), has an additional charge $Q$ and encompassed the Kerr black hole as particular case when $Q=0$. We demonstrate the ergoregions of rotating ABG black holes depend on both rotation parameter $a$ and charge $Q$, and the area of the ergoregions increases with increase in the values of $Q$, when compared with the Kerr black hole and the extremal regular black hole changes with the value of $Q$. Ban{ã}dos, Silk and West (BSW) demonstrated that an extremal Kerr black hole can act as a particle accele…
We study here the precession of the spin of a test gyroscope attached to a stationary observer in the Kerr spacetime, specifically, to distinguish naked singularity (NS) from black hole (BH). It was shown recently that for gyros attached to static observers, their precession frequency became arbitrarily large in the limit of approach to the ergosurface. For gyros attached to stationary observers that move with non-zero angular velocity $Ω$, this divergence at the ergosurface can be avoided. Specifically, for such gyros, the precession frequencies diverge on the event horizon of a BH, but are f…
We evaluate the \emph{surface energy~(${\cal E}_{s}^{\pm}$), rotational energy~(${\cal E}_{r}^{\pm}$) and electromagnetic energy~(${\cal E}_{em}^{\pm}$)} for a \emph{Kerr-Sen black hole~(BH)} having the event horizon~(${\cal H}^{+}$) and the Cauchy horizon~(${\cal H}^{-}$). Interestingly, we find that the \emph{sum of these three energies is equal to the mass parameter i.e. ${\cal E}_{s}^{\pm}+{\cal E}_{r}^{\pm}+{\cal E}_{em}^{\pm}={\cal M}$}. Moreover in terms of the \emph{ scale parameter ~$(ζ_{\pm})$, the distortion parameter~($ξ_{\pm}$) and a new parameter~$(σ_{\pm})$} which corresponds to…
Non-Monotonic Enhancement of the Magnetic Penrose Process in Kerr-Bertotti-Robinson Spacetime and its Implication for Electron Acceleration
National University of Uzbekistan（乌兹别克斯坦国立大学）；Institute of Fundamental and Applied Research, National Research University TIIAME（塔什干国立研究大学基础与应用研究所）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；Department of Physics, School of Advanced Sciences, Vellore Institute of Technology（维洛尔理工学院高级科学学院物理系）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Department of Physics, Hemvati Nandan Bahuguna Garhwal Central University（赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔中央大学物理系）
Kerr-Bertotti-Robinson 空间中磁 Penrose 过程的非单调增强效应，揭示了电子加速至 $10^{15}\,\mathrm{eV}$ 的潜力，并通过辐射损失降至 TeV 级。
