173 research outputs found
The double-Kerr equilibrium configurations involving one extreme object
We demonstrate the existence of equilibrium states in the limiting cases of
the double-Kerr solution when one of the constituents is an extreme object. In
the `extreme-subextreme' case the negative mass of one of the constituents is
required for the balance, whereas in the `extreme-superextreme' equilibrium
configurations both Kerr particles may have positive masses. We also show that
the well-known relation |J|=M^2 between the mass and angular momentum in the
extreme single Kerr solution ceases to be a characteristic property of the
extreme Kerr particle in a binary system.Comment: 12 pages, 3 figures, submitted to Class. Quantum Gra
Instability of toroidal magnetic field in jets and plerions
Jets and pulsar-fed supernova remnants (plerions) tend to develop highly
organized toroidal magnetic field. Such a field structure could explain the
polarization properties of some jets, and contribute to their lateral
confinement. A toroidal field geometry is also central to models for the Crab
Nebula - the archetypal plerion - and leads to the deduction that the Crab
pulsar's wind must have a weak magnetic field. Yet this `Z-pinch' field
configuration is well known to be locally unstable, even when the magnetic
field is weak and/or boundary conditions slow or suppress global modes. Thus,
the magnetic field structures imputed to the interiors of jets and plerions are
unlikely to persist.
To demonstrate this, I present a local analysis of Z-pinch instabilities for
relativistic fluids in the ideal MHD limit. Kink instabilities dominate,
destroying the concentric field structure and probably driving the system
toward a more chaotic state in which the mean field strength is independent of
radius (and in which resistive dissipation of the field may be enhanced). I
estimate the timescales over which the field structure is likely to be
rearranged and relate these to distances along relativistic jets and radii from
the central pulsar in a plerion.
I conclude that a concentric toroidal field is unlikely to exist well outside
the Crab pulsar's wind termination shock. There is thus no dynamical reason to
conclude that the magnetic energy flux carried by the pulsar wind is much
weaker than the kinetic energy flux. Abandoning this inference would resolve a
long-standing puzzle in pulsar wind theory.Comment: 28 pages, plain TeX. Accepted for publication in Ap
Physical interpretation of NUT solution
We show that the well-known NUT solution can be correctly interpreted as
describing the exterior field of two counter-rotating semi-infinite sources
possessing negative masses and infinite angular momenta which are attached to
the poles of a static finite rod of positive mass.Comment: 7 pages, 1 figure, submitted to Classical and Quantum Gravit
Vacuum polarization of scalar fields near Reissner-Nordstr\"{o}m black holes and the resonance behavior in field-mass dependence
We study vacuum polarization of quantized massive scalar fields in
equilibrium at black-hole temperature in Reissner-Nordstr\"{o}m background. By
means of the Euclidean space Green's function we analytically derive the
renormalized expression at the event horizon with the area
. It is confirmed that the polarization amplitude
is free from any divergence due to the infinite red-shift
effect. Our main purpose is to clarify the dependence of on
field mass in relation to the excitation mechanism. It is shown for
small-mass fields with how the excitation of
caused by finite black-hole temperature is suppressed as increases, and it
is verified for very massive fields with that
decreases in proportion to with the amplitude equal to the
DeWitt-Schwinger approximation. In particular, we find a resonance behavior
with a peak amplitude at 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.Comment: 24 pages, 1 figure Accepted in PR
The X-ray jet in the Crab Nebula: radical implications for pulsar theory?
The recent Chandra image of the Crab nebula shows a striking, axisymmetric
polar jet. It is shown that jets are formed in axisymmetric, magnetized pulsar
winds and that the jet luminosity scales relative to the total as
(\gamma_0\sigma_{eq})^{-4/3}, where \sigma_{eq} is the ratio of Poynting flux
to particle kinetic energy output at the equator at the base of the flow and
\gamma_0 the initial Lorentz factor of the flow. The results are applied to the
image of the Crab nebula, and the limit is set for the Crab pulsar of
\sigma_{eq} \leq 100. It is argued that conventional pulsar theory needs to be
reexamined in light of these limits.Comment: 13 page
Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model
We present an exact collapsing solution to 2+1 gravity with a negative
cosmological constant minimally coupled to a massless scalar field, which
exhibits physical properties making it a candidate critical solution. We
discuss its global causal structure and its symmetries in relation with those
of the corresponding continously self-similar solution derived in the
case. Linear perturbations on this background lead to approximate
black hole solutions. The critical exponent is found to be .Comment: 22 pages, 6 figures. Major changes in the discussions of Sects. 2 and
5. The value of the critical exponent has been revised to \gamma = 2/
Schwarzschild black hole levitating in the hyperextreme Kerr field
The equilibrium configurations between a Schwarzschild black hole and a
hyperextreme Kerr object are shown to be described by a three-parameter
subfamily of the extended double-Kerr solution. For this subfamily, its Ernst
potential and corresponding metric functions, we provide a physical
representation which employs as arbitrary parameters the individual Komar
masses and relative coordinate distance between the sources. The calculation of
horizon's local angular velocity induced in the Schwarzschild black hole by the
Kerr constituent yields a simple expression inversely proportional to the
square of the distance parameter.Comment: 6 pages, 1 figure; improved versio
Axisymmetric Stationary Solutions as Harmonic Maps
We present a method for generating exact solutions of Einstein equations in
vacuum using harmonic maps, when the spacetime possesses two commutating
Killing vectors. This method consists in writing the axisymmetric stationry
Einstein equations in vacuum as a harmonic map which belongs to the group
SL(2,R), and decomposing it in its harmonic "submaps". This method provides a
natural classification of the solutions in classes (Weil's class, Lewis' class
etc).Comment: 17 TeX pages, one table,( CINVESTAV- preprint 12/93
Dual geometries and spacetime singularities
The notion of geometrical duality is discussed in the context of both
Brans-Dicke theory and general relativity. It is shown that, in some particular
solutions, the spacetime singularities that arise in usual Riemannian general
relativity may be avoided in its dual representation (Weyl-type general
relativity). This dual representation provides a singularity-free picture of
the World that is physicaly equivalent to the canonical general relativistic
one.Comment: 11 pages, LaTeX, no figures, version accepted for publication in PR
Transition from Regular to Chaotic Circulation in Magnetized Coronae near Compact Objects
Accretion onto black holes and compact stars brings material in a zone of
strong gravitational and electromagnetic fields. We study dynamical properties
of motion of electrically charged particles forming a highly diluted medium (a
corona) in the regime of strong gravity and large-scale (ordered) magnetic
field. We start our work from a system that allows regular motion, then we
focus on the onset of chaos. To this end, we investigate the case of a rotating
black hole immersed in a weak, asymptotically uniform magnetic field. We also
consider a magnetic star, approximated by the Schwarzschild metric and a test
magnetic field of a rotating dipole. These are two model examples of systems
permitting energetically bound, off-equatorial motion of matter confined to the
halo lobes that encircle the central body. Our approach allows us to address
the question of whether the spin parameter of the black hole plays any major
role in determining the degree of the chaoticness. To characterize the motion,
we construct the Recurrence Plots (RP) and we compare them with Poincar\'e
surfaces of section. We describe the Recurrence Plots in terms of the
Recurrence Quantification Analysis (RQA), which allows us to identify the
transition between different dynamical regimes. We demonstrate that this new
technique is able to detect the chaos onset very efficiently, and to provide
its quantitative measure. The chaos typically occurs when the conserved energy
is raised to a sufficiently high level that allows the particles to traverse
the equatorial plane. We find that the role of the black-hole spin in setting
the chaos is more complicated than initially thought.Comment: 21 pages, 20 figures, accepted to Ap
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