arXiv subjects

Akira Tomimatsu

Publications and source records attributed to Akira Tomimatsu.

At least 19 recordsLinked to original sources

arXiv2010

Superradiant scattering of electromagnetic waves emitted from disk around Kerr black holes

We study electromagnetic perturbations around a Kerr black hole surrounded by a thin disk on the equatorial plane. Our main purpose is to reveal the black hole superradiance of electromagnetic waves emitted from the disk surface. The outgoing Kerr-Schild field is used to describe the disk emission, and the superradiant scattering is represented by a vacuum wave field which is added to satisfy the ingoing condition on the horizon. The formula to calculate the energy flux on the disk surface is presented, and the energy transport in the disk-black hole system is investigated. Within the low-frequency approximation we find that the energy extracted from the rotating black hole is mainly transported back to the disk, and the energy spectrum of electromagnetic waves observed at infinity is also discussed.

gr-qc↗

arXiv2009

Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

Considering gravitational collapse of matter, it is important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla \textit{et al.} to spherically symmetric gravitational collapse of perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecture that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.

gr-qc↗

arXiv2009

Mechanical First Law of Black Hole Spacetimes with Cosmological Constant and Its Application to Schwarzschild-de Sitter Spacetime

The mechanical first law (MFL) of black hole spacetimes is a geometrical relation which relates variations of mass parameter and horizon area. While it is well known that the MFL of asymptotic flat black hole is equivalent to its thermodynamical first law, however we do not know the detail of MFL of black hole spacetimes with cosmological constant which possess black hole and cosmological event horizons. Then this paper aims to formulate an MFL of the two-horizon spacetimes. For this purpose, we try to include the effects of two horizons in the MFL. To do so, we make use of the Iyer-Wald formalism and extend it to regard the mass parameter and the cosmological constant as two independent variables which make it possible to treat the two horizons on the same footing. Our extended Iyer-Wald formalism preserves the existence of conserved Noether current and its associated Noether charge, and gives the abstract form of MFL of black hole spacetimes with cosmological constant. Then, as a representative application of that formalism, we derive the MFL of Schwarzschild-de Sitter (SdS) spacetime. Our MFL of SdS spacetime relates the variations of three quantities; the mass parameter, the total area of two horizons and the volume enclosed by two horizons. If our MFL is regarded as a thermodynamical first law of SdS spacetime, it offers a thermodynamically consistent description of SdS black hole evaporation process: The mass decreases while the volume and the entropy increase. In our suggestion, the generalized second law is not needed to ensure the second law of SdS thermodynamics for its evaporation process.

gr-qc↗

arXiv2008

Constraints on the Evolution of Black Hole Spin due to Magnetohydrodynamic Accretion

Stationary and axisymmetric ideal magnetohydrodynamic (MHD) accretion onto a black hole is studied analytically. The accreting plasma ejected from a plasma source with low velocity must be super-fast magnetosonic before passing through the event horizon. We work out and apply a trans-fast magnetosonic solution without the detailed analysis of the regularity conditions at the magnetosonic point, by introducing the bending angle $β$ of magnetic field line, which is the ratio of the toroidal and poloidal components of the magnetic field. To accrete onto a black hole, the trans-magnetosonic solution has some restrictions on $β$, which are related to the field-aligned parameters of the MHD flows. One of the restrictions gives the boundary condition at the event horizon for the inclination of a magnetic field line. We find that this inclination is related to the energy and angular momentum transport to the black hole. Then, we discuss the spin-up/down process of a rotating black hole by cold MHD inflows in a secular evolution timescale. There are two asymptotic states for the spin evolution. One is that the angular velocity of the black hole approaches to that of the magnetic field line, and the other is that the spin-up effect by the positive angular momentum influx and the spin-down effect by the energy influx (as the mass-energy influx) are canceled. We also show that the MHD inflows prevents the evolution to the maximally rotating black hole.

astro-ph↗

arXiv2008

Disk illumination by black hole superradiance of electromagnetic perturbations

Using the Kerr-Schild formalism to solve the Einstein-Maxwell equations, we study energy transport due to time-dependent electromagnetic perturbations around a Kerr black hole, which may work as a mechanism to illuminate a disk located on the equatorial plane. For such a disk-hole system it is found that the energy extraction from the hole can occur under the well-known superradiance condition for wave frequency, even though the energy absorption into the hole should be rather dominant near the polar region of the horizon. We estimate the efficiency of the superradiant amplification of the disk illumination. Further we calculate the time-averaged energy density distribution to show explicitly the existence of a negative energy region near the horizon and to discuss the possible generation of a hot spot on the disk.

gr-qc↗

arXiv2006

Breakdown of self-similar evolution in homogeneous perfect fluid collapse

The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the equation of state $P=αρ$, we study spherically symmetric non-self-similar perturbations in homogeneous self-similar collapse described by the flat Friedmann solution. In the low pressure approximation $α\ll 1$, we analytically derive an infinite set of the normal modes and their growth (or decay) rate. The existence of one unstable normal mode is found to conclude that the self-similar behavior in homogeneous collapse of a sufficiently low pressure perfect fluid must terminate and a certain inhomogeneous density profile can develop with the lapse of time.

gr-qc↗

arXiv2006

Stability analysis of self-similar behaviors in perfect fluid gravitational collapse

Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena and instability of a naked singularity. In this paper we study spherically symmetric non-self-similar perturbations of matter and metrics in spherically symmetric self-similar backgrounds. The collapsing matter is assumed to be a perfect fluid with the equation of state $P=αρ$. We construct a single wave equation governing the perturbations, which makes their time evolution in arbitrary self-similar backgrounds analytically tractable. Further we propose an analytical application of this master wave equation to the stability problem by means of the normal mode analysis for the perturbations having the time dependence given by $\exp{(iω\log|t|)}$, and present some sufficient conditions for the absence of non-oscillatory unstable normal modes with purely imaginary $ω$.

gr-qc↗

arXiv2005

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from "quasi-normal" modes of the self-similar system as well as "high-frequency" waves are clarified. We find a characteristic power-law time evolution of the outgoing energy flux which appears just before naked singularity formation, and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.

gr-qc↗

arXiv2004

Static black holes with a negative cosmological constant: Deformed horizon and anti-de Sitter boundaries

Using perturbative techniques, we investigate the existence and properties of a new static solution for the Einstein equation with a negative cosmological constant, which we call the deformed black hole. We derive a solution for a static and axisymmetric perturbation of the Schwarzschild-anti-de Sitter black hole that is regular in the range from the horizon to spacelike infinity. The key result is that this perturbation simultaneously deforms the two boundary surfaces--i.e., both the horizon and spacelike two-surface at infinity. Then we discuss the Abbott-Deser mass and the Ashtekar-Magnon one for the deformed black hole, and according to the Ashtekar-Magnon definition, we construct the thermodynamic first law of the deformed black hole. The first law has a correction term which can be interpreted as the work term that is necessary for the deformation of the boundary surfaces. Because the work term is negative, the horizon area of the deformed black hole becomes larger than that of the Schwarzschild-anti-de Sitter black hole, if compared under the same mass, indicating that the quasistatic deformation of the Schwarzschild-anti-de Sitter black hole may be compatible with the thermodynamic second law (i.e., the area theorem).

gr-qc↗

arXiv2003

Relativistic Acceleration of Magnetically Driven Jets

We present an analytical model for describing highly relativistic acceleration of magnetically driven jets, within the framework of ideal MHD for cold, stationary and axisymmetric outflows. Our novel procedure is to treat the wind equation as an algebraic relation between the relativistic Alfvén Mach-number and the poloidal electric to toroidal magnetic field amplitudes ratio $ξ$. This allows us to obtain easily the wind solutions for trans-fast-magnetosonic flows, together with the required range of $ξ$. Then, to determine the spatial variation of $ξ$, we solve approximately the Grad-Shafranov equation applied to a jet flow ejected with a very large total specific energy $E$ and confined within a very small opening angle. Our trans-fast-magnetosonic model provides a closed-form expression for the transition from a magnetically dominated flow to a kinetic-energy dominated one, which occurs in the sub-asymptotic region far beyond the light cylinder of the radius $R_{\rm L}$. Importantly, we find that the equipartition between magnetic and kinetic energies is realized at a cylindrical radius of order of $R_{\rm L}E/c^{2}$, and confirm that the further conversion of magnetic to kinetic energy proceeds logarithmically with distance in the asymptotic region. Finally, we discuss briefly the astrophysical implications of our model for jets originating from active galactic nuclei.

astro-ph↗

arXiv2002

Slowly decaying tails of massive scalar fields in spherically symmetric spacetimes

We study the dominant late-time behaviors of massive scalar fields in static and spherically symmetric spacetimes. Considering the field evolution in the far zone where the gravitational field is weak, we show under which conditions the massive field oscillates with an amplitude that decays slowly as $t^{-5/6}$ at very late times, as previously found in (say) the Schwarzschild case. Our conclusion is that this long-lived oscillating tail is generally observed at timelike infinity in black hole spacetimes, while it may not be able to survive if the central object is a normal star. We also discuss that such a remarkable backscattering effect is absent for the field near the null cone at larger spatial distances.

gr-qc↗

arXiv2001

Hoop conjecture for colliding black holes : non-time-symmetric initial data

The hoop conjecture is well confirmed in momentarily static spaces, but it has not been investigated systematically for the system with relativistic motion. To confirm the hoop conjecture for non-time-symmetric initial data, we consider the initial data of two colliding black holes with momentum and search an apparent horizon that encloses two black holes. In testing the hoop conjecture, we use two definitions of gravitational mass : one is the ADM mass and the other is the quasi-local mass defined by Hawking. Although both definitions of gravitational mass give fairly consistent picture of the hoop conjecture, the hoop conjecture with the Hawking mass can judge the existence of an apparent horizon for wider range of parameters of the initial data compared to the ADM mass.

gr-qc↗

arXiv2001

Screw instability in black hole magnetospheres and a stabilizing effect of field-line rotation

The screw instability of magnetic field is a mechanism for prohibiting a generation of strongly twisted field lines in large scales. If it can work in black hole magnetospheres, the global axisymmetric structure and the main process of energy release will be significantly influenced. In this paper, we study the instability condition in the framework of the variational principle, paying special attention to a stabilizing effect due to field-line rotation against the screw-unstable modes satisfying the well-known Kruskal-Shafranov criterion. The basic formulation for the stability analysis of rotating force-free fields in Kerr geometry is provided. Then, for the practical use of the analytical method, the stationary configuration is assumed to be cylindrical, and we treat the long-wave mode perturbations excited at large distances from the central black hole, where the strength of gravity becomes negligibly small. This allows us to derive clearly the new criterion dependent on the rotational angular velocity of magnetic field lines, and the implications of the results obtained for magnetic activities of jets driven by a black hole are briefly discussed.

astro-ph↗

arXiv2001

Asymptotic tails of massive scalar fields in Schwarzschild background

We investigate the asymptotic tail behavior of massive scalar fields in Schwarzschild background. It is shown that the oscillatory tail of the scalar field has the decay rate of $t^{-5/6}$ at asymptotically late times, and the oscillation with the period $2π/m$ for the field mass $m$ is modulated by the long-term phase shift. These behaviors are qualitatively similar to those found in nearly extreme Reissner-Nordström background, which are discussed in terms of a resonant backscattering due to the space-time curvature.

gr-qc↗

arXiv2001

Black Hole Magnetospheres Around Thin Disks Driving Inward and Outward Winds

We construct a simple model for stationary, axisymmetric black-hole magnetospheres, in which the poloidal magnetic field is generated by a toroidal electric current in a thin disk with the inner edge, by solving the vacuum Maxwell equations in Schwarzschild background. In this work, to obtain a concise analytical form of the magnetic stream function, we use the approximation that the inner edge is far distant from the event horizon. The global magnetospheric structure with the closed-loop and open field lines threading the inner and outer parts of the disk is explicitly shown, claiming that the model is useful as a starting point to study astrophysical problems involving inward disk-driven winds to a black hole and outward ones to infinity. The asymptotic shape of the field lines at the event horizon becomes nearly cylindrical, while at infinity it becomes conical. The magnetic spot in the disk connected with the black hole through the loop field lines occupies a very narrow region with the ring area roughly equal to the horizon area. By taking account of the existence of a uniform (external) magnetic field, we also obtain the model for collimated open field lines. Then, it is found that the magnetic connection between the black hole and the disk breaks down if the uniform field is strong enough. Considering slow rotation of the magnetosphere and angular momentum transfer by inward winds from the disk, the final discussion is devoted to gradual disruption of the closed loops due to radial accretion of disk plasma toward the black hole.

astro-ph↗

arXiv2000

Asymptotic power-law tails of massive scalar fields in Reissner-Nordström background

We investigate dominant late-time tail behaviors of massive scalar fields in nearly extreme Reissner-Nordström background. It is shown that the oscillatory tail of the scalar fields has the decay rate of $t^{-5/6}$ at asymptotically late times. The physical mechanism by which the asymptotic $t^{-5/6}$ tail yields and the relation between the field mass and the time scale when the tail begins to dominate, are discussed in terms of resonance backscattering due to spacetime curvature.

gr-qc↗

arXiv2000

Vacuum Polarization of Massive Scalar Fields on the Black Hole Horizon

Vacuum polarization of massive scalar fields in a thermal state at arbitrary temperature is studied near the horizon of a Reissner-Nordström black hole. We derived an analytic form of $<ϕ^2>$ approximately in the large mass limit near the black hole horizon. We uses the zeroth order WKB approximation and power series expansion near the horizon for the Euclideanized mode function. Our formula for the vacuum polarization shows regular behavior on the horizon if the temperature of the scalar field is equal to the Hawking temperature of the black hole. The finite part of the vacuum polarization agrees with the result of the DeWitt-Schwinger approximation up to $O(m^{-4})$ which is the next leading order of the expansion.

gr-qc↗

arXiv2000

Vacuum polarization of scalar fields near Reissner-Nordström black holes and the resonance behavior in field-mass dependence

We study vacuum polarization of quantized massive scalar fields $ϕ$ in equilibrium at black-hole temperature in Reissner-Nordström background. By means of the Euclidean space Green's function we analytically derive the renormalized expression $<ϕ^{2}>_{H}$ at the event horizon with the area $4πr_{+}^{2}$. It is confirmed that the polarization amplitude $<ϕ^{2}>_{H}$ is free from any divergence due to the infinite red-shift effect. Our main purpose is to clarify the dependence of $<ϕ^{2}>_{H}$ on field mass $m$ in relation to the excitation mechanism. It is shown for small-mass fields with $mr_{+}\ll1$ how the excitation of $<ϕ^{2}>_{H}$ caused by finite black-hole temperature is suppressed as $m$ increases, and it is verified for very massive fields with $mr_{+}\gg1$ that $<ϕ^{2}>_{H}$ decreases in proportion to $m^{-2}$ with the amplitude equal to the DeWitt-Schwinger approximation. In particular, we find a resonance behavior with a peak amplitude at $mr_{+}\simeq 0.38$ in the field-mass dependence of vacuum polarization around nearly extreme (low-temperature) black holes. The difference between Scwarzschild and nearly extreme black holes is discussed in terms of the mass spectrum of quantum fields dominant near the event horizon.

gr-qc↗