556 research outputs found
Estimates for the volume of a Lorentzian manifold
We prove new estimates for the volume of a Lorentzian manifold and show
especially that cosmological spacetimes with crushing singularities have finite
volume.Comment: 8 pages, a pdf version of the preprint can also be retrieved from
http://www.math.uni-heidelberg.de/studinfo/gerhardt/LM-Volume.pdf v2: A
further estimate has been added covering the case when the mean curvature is
merely non-negative resp. non-positive (Theorem 1.1
On the Nature of Singularities in Plane Symmetric Scalar Field Cosmologies
The nature of the initial singularity in spatially compact plane symmetric
scalar field cosmologies is investigated. It is shown that this singularity is
crushing and velocity dominated and that the Kretschmann scalar diverges
uniformly as it is approached. The last fact means in particular that a maximal
globally hyperbolic spacetime in this class cannot be extended towards the past
through a Cauchy horizon. A subclass of these spacetimes is identified for
which the singularity is isotropic.Comment: 7 pages, MPA-AR-94-
Black Hole Criticality in the Brans-Dicke Model
We study the collapse of a free scalar field in the Brans-Dicke model of
gravity. At the critical point of black hole formation, the model admits two
distinctive solutions dependent on the value of the coupling parameter. We find
one solution to be discretely self-similar and the other to exhibit continuous
self-similarity.Comment: 4 pages, REVTeX 3.0, 5 figures include
Head-on collision of ultrarelativistic charges
We consider the head-on collision of two opposite-charged point particles
moving at the speed of light. Starting from the field of a single charge we
derive in a first step the field generated by uniformly accelerated charge in
the limit of infinite acceleration. From this we then calculate explicitly the
burst of radiation emitted from the head-on collision of two charges and
discuss its distributional structure. The motivation for our investigation
comes from the corresponding gravitational situation where the head-on
collision of two ultrarelativistic particles (black holes) has recently aroused
renewed interest.Comment: 4 figures, uses the AMSmat
Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid
We observe critical phenomena in spherical collapse of radiation fluid. A
sequence of spacetimes is numerically computed, containing
models () that adiabatically disperse and models () that
form a black hole. Near the critical point (), evolutions develop a
self-similar region within which collapse is balanced by a strong,
inward-moving rarefaction wave that holds constant as a function of a
self-similar coordinate . The self-similar solution is known and we show
near-critical evolutions asymptotically approaching it. A critical exponent
is found for supercritical () models.Comment: 10 pages (LaTeX) (to appear in Phys. Rev. Lett.), TAR-039-UN
Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
We investigate properties of a quasi-local mass in a higher-dimensional
spacetime having symmetries corresponding to the isomertries of an
-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity
in the presence of a cosmological constant. We assume that the Gauss-Bonnet
coupling constant is non-negative. The quasi-local mass was recently defined by
one of the authors as a counterpart of the Misner-Sharp quasi-local mass in
general relativity. The quasi-local mass is found to be a quasi-local conserved
charge associated with a locally conserved current constructed from the
generalized Kodama vector and exhibits the unified first law corresponding to
the energy-balance law. In the asymptotically flat case, it converges to the
Arnowitt-Deser-Misner mass at spacelike infinity, while it does to the
Deser-Tekin and Padilla mass at infinity in the case of asymptotically AdS.
Under the dominant energy condition, we show the monotonicity of the
quasi-local mass for any , while the positivity on an untrapped hypersurface
with a regular center is shown for and for with an additional
condition, where is the constant sectional curvature of each spatial
section of equipotential surfaces. Under a special relation between coupling
constants, positivity of the quasi-local mass is shown for any without
assumptions above. We also classify all the vacuum solutions by utilizing the
generalized Kodama vector. Lastly, several conjectures on further
generalization of the quasi-local mass in Lovelock gravity are proposed.Comment: 13 pages, no figures, 1 table; v4, new results added in the
asymptotically AdS case, accepted for publication in Physical Review
Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field
This paper continues a study on Choptuik scaling in gravitational collapse of
a complex scalar field at the threshold for black hole formation. We perform a
linear perturbation analysis of the previously derived complex critical
solution, and calculate the critical exponent for black hole mass, . We also show that this critical solution is unstable via a
growing oscillatory mode.Comment: 15 pages of latex/revtex; added details of numerics, in press in Phys
Rev D; 1 figure included, or available by anonymous ftp to
ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-58.ep
Null Geodesic Expansion in Spherical Gravitational Collapse
We derive an expression for the expansion of outgoing null geodesics in
spherical dust collapse and compute the limiting value of the expansion in the
approach to singularity formation. An analogous expression is derived for the
spherical collapse of a general form of matter. We argue on the basis of these
results that the covered as well as the naked singularity solutions arising in
spherical dust collapse are stable under small changes in the equation of
state.Comment: 10 pages, Latex File, No figure
On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust
We consider here the gravitational collapse of a spherically symmetric
inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a
general class of these models, we find that the end state of the collapse is
either a black hole or a naked singularity, depending on the parameters of the
initial density distribution, which are , the initial central density
of the massive body, and , the initial boundary. The collapse ends in a
black hole if the dimensionless quantity constructed out of this
initial data is greater than 0.0113, and it ends in a naked singularity if
is less than this number. A simple interpretation of this result can be
given in terms of the strength of the gravitational potential at the starting
epoch of the collapse.Comment: Original title changed, numerical range of naked singularity
corrected. Plain Tex File. 14 pages. To appear in Physical Review
Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field
We examine the gravitational collapse of a non-linear sigma model in
spherical symmetry. There exists a family of continuously self-similar
solutions parameterized by the coupling constant of the theory. These solutions
are calculated together with the critical exponents for black hole formation of
these collapse models. We also find that the sequence of solutions exhibits a
Hopf-type bifurcation as the continuously self-similar solutions become
unstable to perturbations away from self-similarity.Comment: 18 pages; one figure, uuencoded postscript; figure is also available
at http://www.physics.ucsb.edu/people/eric_hirschman
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