251 research outputs found
Neutral and charged matter in equilibrium with black holes
We study the conditions of a possible static equilibrium between spherically
symmetric, electrically charged or neutral black holes and ambient matter. The
following kinds of matter are considered: (1) neutral and charged matter with a
linear equation of state p_r = w\rho (for neutral matter the results of our
previous work are reproduced), (2) neutral and charged matter with p_r \sim
\rho^m, m > 1, and (3) the possible presence of a "vacuum fluid" (the
cosmological constant or, more generally, anything that satisfies the equality
T^0_0 = T^1_1 at least at the horizon). We find a number of new cases of such
an equilibrium, including those generalizing the well-known Majumdar-Papapetrou
conditions for charged dust. It turns out, in particular, that ultraextremal
black holes cannot be in equilibrium with any matter in the absence of a vacuum
fluid; meanwhile, matter with w > 0, if it is properly charged, can surround an
extremal charged black hole.Comment: 12 pages, no figures, final version published in PR
Stationary perturbations and infinitesimal rotations of static Einstein-Yang-Mills configurations with bosonic matter
Using the Kaluza-Klein structure of stationary spacetimes, a framework for
analyzing stationary perturbations of static Einstein-Yang-Mills configurations
with bosonic matter fields is presented. It is shown that the perturbations
giving rise to non-vanishing ADM angular momentum are governed by a
self-adjoint system of equations for a set of gauge invariant scalar
amplitudes. The method is illustrated for SU(2) gauge fields, coupled to a
Higgs doublet or a Higgs triplet. It is argued that slowly rotating black holes
arise generically in self-gravitating non-Abelian gauge theories with bosonic
matter, whereas, in general, soliton solutions do not have rotating
counterparts.Comment: 8 pages, revtex, no figure
Self-accelerated Universe
It is widely believed that the large redshifts for distant supernovae are
explained by the vacuum energy dominance, or, in other words, by the
cosmological constant in Einstein's equations, which is responsible for the
anti-gravitation effect. A tacit assumption is that particles move along a
geodesic for the background metric. This is in the same spirit as the consensus
regarding the uniform Galilean motion of a free electron. However, there is a
runaway solution to the Lorentz--Dirac equation governing the behavior of a
radiating electron, in addition to the Galilean solution. Likewise, a runaway
solution to the entire system of equations, both gravitation and matter
equations of motion including, may provide an alternative explanation for the
accelerated expansion of the Universe, without recourse to the hypothetic
cosmological constant.Comment: 11 pages; Talk at the 9th Adriatic Meeting, Dubrovnic, Croatia, 4-14
September, 2003, Minor improvement, references added; to appear in ``Progress
in General Relativity and Quantum Cosmology Research'', Nova Science
Publisher
Gravitational Acceleration of Spinning Bodies From Lunar Laser Ranging Measurements
The Sun's relativistic gravitational gradient accelerations of Earth and
Moon, dependent on the motions of the latter bodies, act upon the system's
internal angular momentum. This spin-orbit force (which plays a part in
determining the gravity wave signal templates for astrophysical sources)
slightly accelerates the Earth-Moon system as a whole, but it more robustly
perturbs that system's internal dynamics with a 5 cm, synodically oscillating
range contribution which is presently measured to 4 mm precision by more than
three decades of lunar laser ranging.Comment: 10 pages, PCTex32.v3.
Study of multi black hole and ring singularity apparent horizons
We study critical black hole separations for the formation of a common
apparent horizon in systems of - black holes in a time symmetric
configuration. We study in detail the aligned equal mass cases for ,
and relate them to the unequal mass binary black hole case. We then study the
apparent horizon of the time symmetric initial geometry of a ring singularity
of different radii. The apparent horizon is used as indicative of the location
of the event horizon in an effort to predict a critical ring radius that would
generate an event horizon of toroidal topology. We found that a good estimate
for this ring critical radius is . We briefly discuss the
connection of this two cases through a discrete black hole 'necklace'
configuration.Comment: 31 pages, 21 figure
Charged Annular Disks and Reissner-Nordstr\"{o}m Type Black Holes from Extremal Dust
We present the first analytical superposition of a charged black hole with an
annular disk of extremal dust. In order to obtain the solutions, we first solve
the Einstein-Maxwell field equations for sources that represent disk-like
configurations of matter in confomastatic spacetimes by assuming a functional
dependence among the metric function, the electric potential and an auxiliary
function,which is taken as a solution of the Laplace equation. We then employ
the Lord Kelvin Inversion Method applied to models of finite extension in order
to obtain annular disks. The structures obtained extend to infinity, but their
total masses are finite and all the energy conditions are satisfied. Finally,
we observe that the extremal Reissner-Nordstr\"{o}m black hole can be embedded
into the center of the disks by adding a boundary term in the inversion.Comment: 17 revtex pages, 8 eps figure
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
Self-Interaction and Gauge Invariance
A simple unified closed form derivation of the non-linearities of the
Einstein, Yang-Mills and spinless (e.g., chiral) meson systems is given. For
the first two, the non-linearities are required by locality and consistency; in
all cases, they are determined by the conserved currents associated with the
initial (linear) gauge invariance of the first kind. Use of first-order
formalism leads uniformly to a simple cubic self-interaction.Comment: Missing last reference added. 9 pages, This article, the first paper
in Gen. Rel. Grav. [1 (1970) 9], is now somewhat inaccessible; the present
posting is the original version, with a few subsequent references included.
Updates update
A survey of spinning test particle orbits in Kerr spacetime
We investigate the dynamics of the Papapetrou equations in Kerr spacetime.
These equations provide a model for the motion of a relativistic spinning test
particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter
space search for signs of chaotic dynamics by calculating the Lyapunov
exponents for a large variety of initial conditions. We find that the
Papapetrou equations admit many chaotic solutions, with the strongest chaos
occurring in the case of eccentric orbits with pericenters close to the limit
of stability against plunge into a maximally spinning Kerr black hole. Despite
the presence of these chaotic solutions, we show that physically realistic
solutions to the Papapetrou equations are not chaotic; in all cases, the
chaotic solutions either do not correspond to realistic astrophysical systems,
or involve a breakdown of the test-particle approximation leading to the
Papapetrou equations (or both). As a result, the gravitational radiation from
bodies spiraling into much more massive black holes (as detectable, for
example, by LISA, the Laser Interferometer Space Antenna) should not exhibit
any signs of chaos.Comment: Submitted to Phys. Rev. D. Follow-up to gr-qc/0210042. Figures are
low-resolution in order to satisfy archive size constraints; a
high-resolution version is available at http://www.michaelhartl.com/papers
Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order
Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by
a matter-filled interior and an asymptotically flat vacuum exterior joined at a
surface where the Darmois matching conditions are satisfied, are considered.
The initial state is assumed to be static. The perturbations of the matching
conditions are derived and used as boundary conditions for the perturbed Ernst
equations in the exterior region. The perturbations are calculated to second
order. The boundary conditions are overdetermined: necessary and sufficient
conditions for their compatibility are derived. The special case of
perturbations of spherical bodies is given in detail.Comment: RevTeX; 32 pp. Accepted by Phys. Rev. D. Added references and extra
comments in introductio
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