arXiv subjects

Ken-ichi Nakao

Publications and source records attributed to Ken-ichi Nakao.

At least 19 recordsLinked to original sources

arXiv2026

Motion of a charged test particle around a static black hole in a monopole magnetic field

We study the motion of a charged test particle in the spacetime with a spherically symmetric black hole which is immersed in a monopole magnetic field. We show that the radial motion of the charged test particle is governed by completely the same equation as that in the case of no magnetic field. This result implies that the black hole will acquire the electric charge if it is surrounded by the collisionless plasma composed of protons and electrons which obey the Maxwell velocity distribution. The drastically different situation appears in the tangential motions of charged test particles due to the magnetic field. The trajectory of a charged test particle in the black hole with the magnetic field of the order of 10 Gauss near the black hole, is confined on a very thin cone as long as the specific angular momentum of the particle is not much larger than the gravitational radius of the black hole times the speed of light. This result leads to a possibility that a plasma lump can hover over the black hole and is very hot, in the monopole magnetic field.

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arXiv2024

Electrification of a non-rotating black hole

Zajacek et al made an interesting theoretical prediction on the electrification of a non-rotating black hole; if a non-rotating black hole is surrounded by plasma composed of protons and electrons, it will acquire electric charge due to the large difference of the inertial mass of a proton and that of an electron. Furthermore they revealed the effects of the electric charge of the black hole on the surrounding plasma. Since their results mainly rely on non-relativistic analyses, we study the same subject through relativistic analyses in this paper. By investigating a test particle in the Schwarzschild spacetime, we find that if initial velocities of protons and electrons far from a black hole follow the Maxwell distribution, the black hole can acquire electric charge whose value depends on the ratio of temperature of the proton and that of the electron. We also show that if the black hole acquires the electric charge, the radii of the innermost stable circular orbit (ISCO) and the specific energy of a charged particle on ISCO can be very different from those of a neutral particle. In contrast to the result obtained by Zajacek et al, we find that the ISCO radii of a proton and an electron are necessarily larger than that of a neutral test particle as long as the black hole acquires the charge. The large ISCO radius might lead to a larger angular diameter of a black hole shadow and a different estimate of the released energy due to the accretion of plasma from the estimate based on the assumption of electric neutrality of the central black hole.

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arXiv2022

Radiative gravastar with thermal spectrum; Sudden vacuum condensation without gravitational collapse

The gravastar is an exotic compact object proposed as a final product of gravitational collapse of a massive object in order to resolve problems associated with black holes. It is enclosed by a thin crust and the inside of it is occupied by the positive cosmological constant. Recently, the present authors studied quantum particle creation through spherically symmetric gravitational collapse to form a gravastar, and showed that the newly formed gravastar emits thermal radiation with the Gibbons-Hawking temperature of its de Sitter core. In this paper, in order to understand more about the thermal radiation associated with the gravastar formation, we investigate the quantum particle creation in another toy model of the gravastar formation; a star with the hollow inside suddenly becomes a gravastar through gravitational vacuum condensation. We find that the thermal radiation is emitted from the gravastar just formed also in the present model. The thermal radiation from the gravastar just formed comes from the change of the geometry inside the star accompanied by gravitational vacuum condensate.

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arXiv2022

Relativistic orbits of S2 star in the presence of scalar field

The general theory of relativity predicts the relativistic effect in the orbital motions of S-stars which are orbiting around our Milky-way galactic center. The post-Newtonian or higher-order approximated Schwarzschild black hole models have been used by GRAVITY and UCLA galactic center groups to carefully investigate the S2 star's periastron precession. In this paper, we investigate the scalar field effect on the orbital dynamics of S2 star. Hence, we consider a spacetime, namely Janis-Newman-Winicour (JNW) spacetime which is seeded by a minimally coupled, mass-less scalar field. The novel feature of this spacetime is that one can retain the Schwarzschild spacetime from JNW spacetime considering zero scalar charge. We constrain the scalar charge of JNW spacetime by best fitting the astrometric data of S2 star using the Monte-Carlo-Markov-Chain (MCMC) technique assuming the charge to be positive. Our best-fitted result implies that similar to the Schwarzschild black hole spacetime, the JNW naked singularity spacetime with an appropriate scalar charge also offers a satisfactory fitting to the observed data for S2 star. Therefore, the JNW naked singularity could be a contender for explaining the nature of Sgr A* through the orbital motions of the S2 star.

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arXiv2022

Radiative gravastar with Gibbons-Hawking temperature

We study the quantum particle creation in a toy model of spherically symmetric gravitational collapse whose final product is not a black hole but a gravastar. Precedent studies revealed that even in the case of the gravitational collapse to form a horizonless ultra-compact object, thermal radiation named transient Hawking radiation is generated at the late stage of the gravitational collapse, and a sudden stop of collapsing motion to form a horizonless ultra-compact object causes one or two bursts of quantum particle creation. The very different behavior of the model studied in this paper from the precedent ones is quantum radiation with a thermal spectrum from the gravastar between two bursts. The temperature of the radiation is not the same as the Hawking one determined by the gravitational mass of the system but the Gibbons-Hawking one of the de Sitter core inside the gravastar.

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arXiv2022

Robustness of particle creation in the formation of a compact object

Hawking has predicted that the formation of a black hole by gravitational collapse causes quantum particle creation and the spectrum of the particles is almost thermal. This phenomenon is called the Hawking radiation. Recently, it has been predicted that the particle creation may drastically change from the Hawking radiation to a strong double burst if the gravitational collapse suddenly stops just before the formation of the event horizon. By contrast with the Hawking radiation, the burst may be so strong that it can be of observational interest even for collapsing objects with astrophysical mass scales. However, the burst phenomenon has been predicted through the studies of idealized models in which a spherical hollow shell begins to collapse, but stops shrinking and eventually settles down to a static "star". Therefore, one might guess that it could be particular to the hollow shell model. In this paper, we study the particle creation due to the gravitational collapse of a spherical object whose interior is filled with matter. In this model, we obtain similar results to those in the case of the hollow shell model. This implies that the double burst is a robust property of particle creation by the sudden braking of gravitational collapse.

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arXiv2020

Do black hole shadows merge?

The so-called black hole shadow is not a silhouette of a black hole but an image of a collapsing object or a white hole. Hence it is non-trivial whether black hole shadows merge with each other when black holes coalesce with each other. In this paper, by analyzing the null geodesic generators of the event horizon in Kastor-Traschen spacetime which describes a coalescence of black boles, we see that observers who will never see a merger of black hole shadows exist.

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arXiv2019

How does a collapsing star look?

Time evolution of an optical image of a pressureless star under gravitational collapse is studied in the geometric optics approximation. The star surface is assumed to emit radiation obeying Lambert's cosine law but with an arbitrary spectral intensity in the comoving frame. We develop a formalism for predicting observable quantities by photon counting and by radiometry, in particular, spectral photon flux and spectral radiant flux. Then, this method is applied to the two cases: One is monochromatic radiation, and the other is blackbody radiation. The two kinds of spectral flux are calculated numerically for each case. It is reconfirmed that the redshift factor remains finite and the star becomes gradually invisible due to decay of the photon flux. We also develop an approximate method to present analytic formulas that describe the late time behavior. A possible connection of our study to observation of high-energy neutrinos is briefly discussed.

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arXiv2019

Constant-mean-curvature Slicing of the Swiss-cheese Universe

A sequence of Constant-Mean-Curvature(CMC) slices in the Swiss-Cheese(SC) Universe is investigated. We focus on the CMC slices which smoothly connect to the homogeneous time slices in the Einstein-de Sitter region in the SC universe. It is shown that the slices do not pass through the black hole region but white hole region.

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arXiv2018

On gravastar formation: What can be the evidence of a black hole?

Any observer outside black holes cannot detect any physical signal produced by the black holes themselves, since, by definition, the black holes are not located in the causal past of the outside observer. In fact, what we regard as black hole candidates in our view are not black holes but will be gravitationally contracting objects. As well known, a black hole will form by a gravitationally collapsing object in the infinite future in the views of distant observers like us. At the very late stage of the gravitational collapse, the gravitationally contracting object behaves as a black body due to its gravity. Due to this behavior, the physical signals produced around it (e.g. the quasi-normal ringings and the shadow image) will be very similar to those caused in the eternal black hole spacetime. However those physical signals do not necessarily imply the formation of a black hole in the future, since we cannot rule out the possibility that the formation of the black hole is prevented by some unexpected event in the future yet unobserved. As such an example, we propose a scenario in which the final state of the gravitationally contracting spherical thin shell is a gravastar that has been proposed as a final configuration alternative to a black hole by Mazur and Mottola. This scenario implies that time necessary to observe the moment of the gravastar formation can be much longer than the lifetime of the present civilization, although such a scenario seems to be possible only if the dominant energy condition is largely violated.

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arXiv2017

Non-linear collisional Penrose process: How large energy can a black hole release?

Energy extraction from a rotating or charged black hole is one of fascinating issues in general relativity. The collisional Penrose process is one of such extraction mechanisms and has been reconsidered intensively since Banados, Silk and West pointed out the physical importance of very high energy collisions around a maximally rotating black hole. In order to get results analytically, the test particle approximation has been adopted so far. Successive works based on this approximation scheme have not yet revealed the upper bound on the efficiency of the energy extraction because of lack of the back reaction. In the Reissner-Nordstrom spacetime, by fully taking into account the self-gravity of the shells, we find that there is an upper bound on the extracted energy, which is consistent with the area law of a black hole. We also show one particular scenario in which the almost maximum energy extraction is achieved even without the Banados-Silk-West collision.

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arXiv2017

On the stability of a superspinar

The superspinar proposed by Gimon and Horava is a rapidly rotating compact entity whose exterior is described by the over-spinning Kerr geometry. The compact entity itself is expected to be governed by superstringy effects, and in astrophysical scenarios it can give rise to interesting observable phenomena. Earlier it was suggested that the superspinar may not be stable but we point out here that this does not necessarily follow from earlier studies. We show, by analytically treating the Teukolsky equations by Detwiler's method, that in fact there are infinitely many boundary conditions that make the superspinar stable, and that the modes will decay in time. It follows that we need to know more on the physical nature of the superspinar in order to decide on its stability in physical reality.

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arXiv2017

Non-linear stability of a brane wormhole

We analytically study the non-linear stability of a spherically symmetric wormhole supported by an infinitesimally thin brane of negative tension, which has been devised by Barcelo and Visser. We consider a situation in which a thin spherical shell composed of dust falls into an initially static wormhole; The dust shell plays a role of the non-linear disturbance. The self-gravity of the falling dust shell is completely taken into account through Israel's formalism of the metric junction. When the dust shell goes through the wormhole, it necessarily collides with the brane supporting the wormhole. We assume the interaction between these shells is only gravity and show the condition under which the wormhole stably persists after the dust shell goes through it.

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arXiv2017

Can we remove the systematic error due to isotropic inhomogeneities?

Usually, we assume that there is no inhomogeneity isotropic in terms of our location in our uni- verse. This assumption has not been observationally confirmed yet in sufficient accuracy, and we need to consider the possibility that there are non-negligible large-scale isotropic inhomogeneities in our universe. The existence of large-scale isotropic inhomogeneities affects the determination of the cosmological parameters. In particular, from only the distance-redshift relation, we can not dis- tinguish the inhomogeneous isotropic universe model from the homogeneous isotropic one, because of the ambiguity in the cosmological parameters. In this paper, in order to avoid such ambiguity, we consider three observables, the distance-redshift relation, the fluctuation spectrum of the cosmic microwave background radiation(CMBR) and the scale of the baryon acoustic oscillation(BAO), and compare these observables in two universe models; One is the inhomogeneous isotropic uni- verse model with the cosmological constant and the other is the homogeneous isotropic universe model with the dark energy other than the cosmological constant. We show that these two universe models can not predict the same observational data of all three observables but the same ones of only two of three, as long as the perturbations are adiabatic. In principle, we can distinguish the inhomogeneous isotropic universe from the homogeneous isotropic one through appropriate three observables, if the perturbations are adiabatic.

astro-ph.CO↗

arXiv2016

Primordial black hole formation in the matter-dominated phase of the Universe

We investigate primordial black hole formation in the matter-dominated phase of the Universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zel'dovich approximation, Thorne's hoop conjecture, and Doroshkevich's probability distribution and subsequently derive the production probability $β_{0}$ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation $σ$ at horizon entry is of the order of unity. For $σ\ll 1$, we find a semi-analytic formula $β_{0}\simeq 0.05556 σ^{5}$, which is comparable with the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for $σ\lesssim 0.05$, while they are comparable with each other for $σ\gtrsim 0.05$. We also discuss how $σ$ can be written in terms of primordial curvature perturbations.

astro-ph.CO↗

arXiv2016

Orbital angular momentum of scalar field generated by gravitational scatterings

It has been expected that astronomical observations to detect the orbital angular momenta of electromagnetic waves may give us a new insight into astrophysics. Previous works pointed out the possibility that a rotating black hole can produce orbital angular momenta of electromagnetic waves through gravitational scattering, and the spin parameter of the black hole can be measured by observing them. However, the mechanism how the orbital angular momentum of the electromagnetic wave is generated by the gravitational scattering has not been clarified sufficiently. In this paper, in order to understand it from a point of view of gravitational lensing effects, we consider an emitter which radiates a spherical wave of the real massless scalar field and study the deformation of the scalar wave by the gravitational scattering due to a black hole by invoking the geometrical optics approximation. We show that the frame dragging caused by the rotating black hole is not a necessary condition for generating the orbital angular momentum of the scalar wave. However, its components parallel to the direction cosines of images appear only if the black hole is rotating.

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arXiv2016

Infinite efficiency of collisional Penrose process: Can over-spinning Kerr geometry be the source of ultra-high-energy cosmic rays and neutrinos ?

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 infinitesimal amount, i.e., with the Kerr parameter $a=M(1+ε)$, where we take the limit $ε\rightarrow 0^+$. We consider two massive particles starting from rest at infinity that collide at $r=M$ with divergent center-of-mass energy and produce two massless particles. We show that massless particles produced in the collision can escape to infinity with the ultra-high energies exploiting the collisional Penrose process with the divergent efficiency $η\sim {1}/{\sqrtε} \rightarrow \infty$. Assuming the isotropic emission of massless particles in the center-of-mass frame of the colliding particles, we show that half of the particles created in the collisions escape to infinity with the divergent energies. To a distant observer, ultra-high-energy particles appear to originate from a bright spot which is at the angular location $ξ\sim {2M}/{r_{obs}}$ with respect to the singularity on the side which is rotating towards the observer. We show that the anisotropy in emission in the center-of-mass frame, which is dictated by the differential cross-section of underlying particle physics process, leaves a district signature on the spectrum of ultra-high-energy massless particles. Thus, it provides a unique probe into fundamental particle physics.

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arXiv2015

Timescale for trans-Planckian collisions in Kerr spacetime

We make a critical comparison between ultra-high energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time required for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years which is much shorter than the age of the Universe. Thus from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black hole counterparts.

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