471 research outputs found
A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit
We obtain a fourth order accurate numerical algorithm to integrate the
Zerilli and Regge-Wheeler wave equations, describing perturbations of
nonrotating black holes, with source terms due to an orbiting particle. Those
source terms contain the Dirac's delta and its first derivative. We also
re-derive the source of the Zerilli and Regge-Wheeler equations for more
convenient definitions of the waveforms, that allow direct metric
reconstruction (in the Regge-Wheeler gauge).Comment: 30 pages, 12 figure
Upper limits of particle emission from high-energy collision and reaction near a maximally rotating Kerr black hole
The center-of-mass energy of two particles colliding near the horizon of a
maximally rotating black hole can be arbitrarily high if the angular momentum
of either of the incident particles is fine-tuned, which we call a critical
particle. We study particle emission from such high-energy collision and
reaction in the equatorial plane fully analytically. We show that the
unconditional upper limit of the energy of the emitted particle is given by
218.6% of that of the injected critical particle, irrespective of the details
of the reaction and this upper limit can be realized for massless particle
emission. The upper limit of the energy extraction efficiency for this emission
as a collisional Penrose process is given by 146.6%, which can be realized in
the collision of two massive particles with optimized mass ratio. Moreover, we
analyze perfectly elastic collision, Compton scattering, and pair annihilation
and show that net positive energy extraction is really possible for these three
reactions. The Compton scattering is most efficient among them and the
efficiency can reach 137.2%. On the other hand, our result is qualitatively
consistent with the earlier claim that the mass and energy of the emitted
particle are at most of order the total energy of the injected particles and
hence we can observe neither super-heavy nor super-energetic particles.Comment: 22 pages, 3 figures, typos corrected, reference updated, accepted for
publication in Physical Review D, typos correcte
Dirty rotating black holes: regularity conditions on stationary horizons
We consider generic, or "dirty" (surrounded by matter), stationary rotating
black holes with axial symmetry. The restrictions are found on the asymptotic
form of metric in the vicinity of non-extremal, extremal and ultra-extremal
horizons, imposed by the conditions of regularity of increasing strength:
boundedness on the horizon of the Ricci scalar, of scalar quadratic curvature
invariants, and of the components of the curvature tensor in the tetrad
attached to a falling observer. We show, in particular, that boundedness of the
Ricci scalar implies the "rigidity" of the horizon's rotation in all cases,
while the finiteness of quadratic invariants leads to the constancy of the
surface gravity. We discuss the role of quasiglobal coordinate r that is
emphasized by the conditions of regularity. Further restrictions on the metric
are formulated in terms of subsequent coefficients of expansion of metric
functions by r. The boundedness of the tetrad components of curvature tensor
for an observer crossing the horizon is shown to lead in the horizon limit to
diagonalization of Einstein tensor in the frame of zero angular momentum
observer on a circular orbit (ZAMO frame) for horizons of all degrees of
extremality.Comment: 31 pages. Misprints correcte
The French Atlantic littoral and the Massif Armoricain, part 1
The author has identified the following significant results. For interpretation of Isle of Jersey imagery, two types of taxons were defined according to their variability in time. On the whole, taxons with a similar spectral signature were opposed to those with strongly varying spectral signature. The taxon types were low diachronic variations and strong diachronic variation. Imagery interpretation was restricted to the landward part of the Fromentine area, including the sand beaches which were often difficult to spectrally separate from the barren coastal dunes in the southern part of Noirmoutier Island as well as along the Breton marsh. From 1972 to 1976, sandbanks reduced in area. Two high river discharge images showed over a two year period an identical outline for the Bilho bank to seaward, whereas upstream, the bank has receeded in the same time to a line joining Paimboeuf to Montoir. The Brillantes bank has receeded at both ends, partly due to dredging operations in the access channel to Donges harbor
Perspective on gravitational self-force analyses
A point particle of mass moving on a geodesic creates a perturbation
, of the spacetime metric , that diverges at the particle.
Simple expressions are given for the singular part of and its
distortion caused by the spacetime. This singular part h^\SS_{ab} is
described in different coordinate systems and in different gauges. Subtracting
h^\SS_{ab} from leaves a regular remainder . The
self-force on the particle from its own gravitational field adjusts the world
line at \Or(\mu) to be a geodesic of ; this adjustment
includes all of the effects of radiation reaction. For the case that the
particle is a small non-rotating black hole, we give a uniformly valid
approximation to a solution of the Einstein equations, with a remainder of
\Or(\mu^2) as .
An example presents the actual steps involved in a self-force calculation.
Gauge freedom introduces ambiguity in perturbation analysis. However,
physically interesting problems avoid this ambiguity.Comment: 40 pages, to appear in a special issue of CQG on radiation reaction,
contains additional references, improved notation for tensor harmonic
Naked Singularities as Particle Accelerators II
We generalize here our earlier results on particle acceleration by naked
singularities. We showed recently[1] that the naked singularities that form due
to gravitational collapse of massive stars provide a suitable environment where
particles could get accelerated and collide at arbitrarily high center of mass
energies. However, we focussed there only on the spherically symmetric
gravitational collapse models, which were also assumed to be self-similar. In
this paper, we broaden and generalize the result to all gravitational collapse
models leading to the formation of a naked singularity as final state of
collapse, evolving from a regular initial data, without making any prior
restrictive assumptions about the spacetime symmetries such as above. We show
that when the particles interact and collide near the Cauchy horizon, the
energy of collision in the center of mass frame will be arbitrarily high, thus
offering a window to the Planck scale physics. We also consider the issue of
various possible physical mechanisms of generation of such very high energy
particles from the vicinity of naked singularity. We then construct a model of
gravitational collapse to a timelike naked singularity to demonstrate the
working of these ideas, where the pressure is allowed to be negative but the
energy conditions are respected. We show that a finite amount of mass-energy
density has to be necessarily radiated away from the vicinity of the naked
singularity as the collapse evolves. Therefore the nature of naked
singularities, both at classical and quantum level could play an important role
in the process of particle acceleration, explaining the occurrence of highly
energetic outgoing particles in the vicinity of Cauchy horizon that participate
in extreme high energy collisions.Comment: 13 pages, 5 figures, Accepted for publication in Phys. Rev. D,
Reference and Acknowledgments adde
Quadrupole moments of rotating neutron stars
Numerical models of rotating neutron stars are constructed for four equations
of state using the computer code RNS written by Stergioulas. For five selected
values of the star's gravitational mass (in the interval between 1.0 and 1.8
solar masses) and for each equation of state, the star's angular momentum is
varied from J=0 to the Keplerian limit J=J_{max}. For each neutron-star
configuration we compute Q, the quadrupole moment of the mass distribution. We
show that for given values of M and J, |Q| increases with the stiffness of the
equation of state. For fixed mass and equation of state, the dependence on J is
well reproduced with a simple quadratic fit, Q \simeq - aJ^2/M c^2, where c is
the speed of light, and a is a parameter of order unity depending on the mass
and the equation of state.Comment: ReVTeX, 7 pages, 5 figures, additional material, and references adde
Perturbative evolution of particle orbits around Kerr black holes: time domain calculation
Treating the Teukolsky perturbation equation numerically as a 2+1 PDE and
smearing the singularities in the particle source term by the use of narrow
Gaussian distributions, we have been able to reproduce earlier results for
equatorial circular orbits that were computed using the frequency domain
formalism. A time domain prescription for a more general evolution of nearly
geodesic orbits under the effects of radiation reaction is presented. This
approach can be useful when tackling the more realistic problem of a
stellar-mass black hole moving on a generic orbit around a supermassive black
hole under the influence of radiation reaction forces.Comment: 8 pages, 5 figures, problems with references and double-printing
fixe
Regular second order perturbations of binary black holes: The extreme mass ratio regime
In order to derive the precise gravitational waveforms for extreme mass ratio
inspirals (EMRI), we develop a formulation for the second order metric
perturbations produced by a point particle moving in the Schwarzschild
spacetime. The second order waveforms satisfy a wave equation with an effective
source build up from products of the first order perturbations and its
derivatives. We have explicitly regularized this source at the horizon and at
spatial infinity. We show that the effective source does not contain squares of
the Dirac's delta and that perturbations are regular at the particle location.
We introduce an asymptotically flat gauge for the radiation fields and the
mode to compute explicitly the (leading) second order
waveforms in the headon collision case. This case represents the first
completion of the radiation reaction program self-consistently.Comment: 28 pages, no figur
Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions
An infinite family of new exact solutions of the Einstein vacuum equations
for static and axially symmetric spacetimes is presented. All the metric
functions of the solutions are explicitly computed and the obtained expressions
are simply written in terms of oblate spheroidal coordinates. Furthermore, the
solutions are asymptotically flat and regular everywhere, as it is shown by
computing all the curvature scalars. These solutions describe an infinite
family of thin dust disks with a central inner edge, whose energy densities are
everywhere positive and well behaved, in such a way that their energy-momentum
tensor are in fully agreement with all the energy conditions. Now, although the
disks are of infinite extension, all of them have finite mass. The
superposition of the first member of this family with a Schwarzschild black
hole was presented previously [G. A. Gonz\'alez and A. C.
Guti\'errez-Pi\~neres, arXiv: 0811.3002v1 (2008)], whereas that in a subsequent
paper a detailed analysis of the corresponding superposition for the full
family will be presented.Comment: 9 pages, 3 figure
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