44 research outputs found
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
. 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 , and present some sufficient conditions for the
absence of non-oscillatory unstable normal modes with purely imaginary
.Comment: 17 pages, 3 figures, matched to the published versio
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 , we study spherically symmetric
non-self-similar perturbations in homogeneous self-similar collapse described
by the flat Friedmann solution. In the low pressure approximation , 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.Comment: 9 pages, 1 figure, references added, published in Physical Review
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 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 , 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.Comment: 16 pages, 12 figures, submitted to PR
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.Comment: 15 pages, 2 figures, accepted for publication in Physical Review
Relativistic Dynamos in Magnetospheres of Rotating Compact Objects
The kinematic evolution of axisymmetric magnetic fields in rotating
magnetospheres of relativistic compact objects is analytically studied, based
on relativistic Ohm's law in stationary axisymmetric geometry. By neglecting
the poloidal flows of plasma in simplified magnetospheric models, we discuss
self-excited dynamos due to the frame-dragging effect (originally pointed out
by Khanna & Camenzind), and we propose alternative processes to generate
axisymmetric magnetic fields against ohmic dissipation. The first process
(which may be called induced excitation) is caused by the help of a background
uniform magnetic field in addition to the dragging of inertial frames. It is
shown that excited multipolar components of poloidal and azimuthal fields are
sustained as stationary modes, and outgoing Poynting flux converges toward the
rotation axis. The second one is self-excited dynamo through azimuthal
convection current, which is found to be effective if plasma rotation becomes
highly relativistic with a sharp gradient in the angular velocity. In this case
no frame-dragging effect is needed, and the coupling between charge separation
and plasma rotation becomes important. We discuss briefly the results in
relation to active phenomena in the relativistic magnetospheres.Comment: 16 pages, AASLaTeX macros v4.
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.Comment: 20 pages, 7 figures, references added to match the published versio
Distortion of Schwarzschild-anti-de Sitter black holes to black strings
Motivated by the existence of black holes with various topologies in
four-dimensional spacetimes with a negative cosmological constant, we study
axisymmetric static solutions describing any large distortions of
Schwarzschild-anti-de Sitter black holes parametrized by the mass . Under
the approximation such that is much larger than the anti-de Sitter radius,
it is found that a cylindrically symmetric black string is obtained as a
special limit of distorted spherical black holes. Such a prolonged distortion
of the event horizon connecting a Schwarzschild-anti-de Sitter black hole to a
black string is allowed without violating both the usual black hole
thermodynamics and the hoop conjecture for the horizon circumference.Comment: 13 pages, accepted for publication in Physical Review
Asymptotic power-law tails of massive scalar fields in Reissner-Nordstr\"{o}m background
We investigate dominant late-time tail behaviors of massive scalar fields in
nearly extreme Reissner-Nordstr\"{o}m background. It is shown that the
oscillatory tail of the scalar fields has the decay rate of at
asymptotically late times. The physical mechanism by which the asymptotic
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.Comment: 18 pages, 1 figure, accepted for publication in Physical Review
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.Comment: 15 pages 4 figures accepted for publication in Ap