1,337 research outputs found
A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes I - Basic Formulation and a Conjecture
Einstein's equations are known to lead to the formation of black holes and
spacetime singularities. This appears to be a manifestation of the mathematical
phenomenon of finite-time blowup: a formation of singularities from regular
initial data. We present a simple hyperbolic system of two semi-linear
equations inspired by the Einstein equations. We explore a class of solutions
to this system which are analogous to static black-hole models. These solutions
exhibit a black-hole structure with a finite-time blowup on a characteristic
line mimicking the null inner horizon of spinning or charged black holes. We
conjecture that this behavior - namely black-hole formation with blow-up on a
characteristic line - is a generic feature of our semi-linear system. Our
simple system may provide insight into the formation of null singularities
inside spinning or charged black holes in the full system of Einstein
equations.Comment: 39 pages, 3 figures, extended versio
Electromagnetic and Axial Current Form Factors and Spectroscopy of Three-Flavor Holographic Baryons
We present an analysis of the three-flavor holographic model of QCD
associated to a brane configuration, with symmetry breaking induced by
a worldsheet instanton associated to a closed loop connecting
. We calculate the electromagnetic and axial couplings
of all octet and decuplet baryons, as well as several negative parity
excitations, with and without symmetry breaking effects, and demonstrate
qualitative and quantitative agreement with many available experimental
measurements, with marked improvement over the analogous two-flavor models.Comment: 23 page
Radiation-reaction-induced evolution of circular orbits of particles around Kerr Black Holes
It is demonstrated that, in the adiabatic approximation, non-Equatorial
circular orbits of particles in the Kerr metric (i.e. orbits of constant
Boyer-Lindquist radius) remain circular under the influence of gravitational
radiation reaction. A brief discussion is given of conditions for breakdown of
adiabaticity and of whether slightly non-circular orbits are stable against the
growth of eccentricity.Comment: 23 pages. Revtex 3.0. Inquiries to [email protected]
A new time-machine model with compact vacuum core
We present a class of curved-spacetime vacuum solutions which develope closed
timelike curves at some particular moment. We then use these vacuum solutions
to construct a time-machine model. The causality violation occurs inside an
empty torus, which constitutes the time-machine core. The matter field
surrounding this empty torus satisfies the weak, dominant, and strong energy
conditions. The model is regular, asymptotically-flat, and
topologically-trivial. Stability remains the main open question.Comment: 7 page
Are physical objects necessarily burnt up by the blue sheet inside a black hole?
The electromagnetic radiation that falls into a Reissner-Nordstrom black hole
develops a ``blue sheet'' of infinite energy density at the Cauchy horizon. We
consider classical electromagnetic fields (that were produced during the
collapse and then backscattered into the black hole), and investigate the
blue-sheet effects of these fields on infalling objects within a simplified
model. These effects are found to be finite and even negligible for typical
parameters.Comment: 13 pages, ordinary LaTex. Accepted for Physical Review Letters
The late-time singularity inside non-spherical black holes
It was long believed that the singularity inside a realistic, rotating black
hole must be spacelike. However, studies of the internal geometry of black
holes indicate a more complicated structure is typical. While it seems likely
that an observer falling into a black hole with the collapsing star encounters
a crushing spacelike singularity, an observer falling in at late times
generally reaches a null singularity which is vastly different in character to
the standard Belinsky, Khalatnikov and Lifschitz (BKL) spacelike singularity.
In the spirit of the classic work of BKL we present an asymptotic analysis of
the null singularity inside a realistic black hole. Motivated by current
understanding of spherical models, we argue that the Einstein equations reduce
to a simple form in the neighborhood of the null singularity. The main results
arising from this approach are demonstrated using an almost plane symmetric
model. The analysis shows that the null singularity results from the blueshift
of the late-time gravitational wave tail; the amplitude of these gravitational
waves is taken to decay as an inverse power of advanced time as suggested by
perturbation theory. The divergence of the Weyl curvature at the null
singularity is dominated by the propagating modes of the gravitational field.
The null singularity is weak in the sense that tidal distortion remains bounded
along timelike geodesics crossing the Cauchy horizon. These results are in
agreement with previous analyses of black hole interiors. We briefly discuss
some outstanding problems which must be resolved before the picture of the
generic black hole interior is complete.Comment: 16 pages, RevTeX, 3 figures included using psfi
Criticality and convergence in Newtonian collapse
We study through numerical simulation the spherical collapse of isothermal
gas in Newtonian gravity. We observe a critical behavior which occurs at the
threshold of gravitational instability leading to core formation. For a given
initial density profile, we find a critical temperature, which is of the same
order as the virial temperature of the initial configuration. For the exact
critical temperature, the collapse converges to a self-similar form, the first
member in Hunter's family of self-similar solutions. For a temperature close to
the critical value, the collapse first approaches this critical solution. Later
on, in the supercritical case, the collapse converges to another self-similar
solution, which is called the Larson-Penston solution. In the subcritical case,
the gas bounces and disperses to infinity. We find two scaling laws: one for
the collapsed mass in the supercritical case and the other for the maximum
density reached before dispersal in the subcritical case. The value of the
critical exponent is measured to be in the supercritical case,
which agrees well with the predicted value . These critical
properties are quite similar to those observed in the collapse of a radiation
fluid in general relativity. We study the response of the system to temperature
fluctuation and discuss astrophysical implications for the insterstellar medium
structure and for the star formation process. Newtonian critical behavior is
important not only because it provides a simple model for general relativity
but also because it is relevant for astrophysical systems such as molecular
clouds.Comment: 15 pages, 8 figures, accepted for publication in PRD, figures 1 and 3
at lower resolution than in journal version, typos correcte
Undersampled Phase Retrieval with Outliers
We propose a general framework for reconstructing transform-sparse images
from undersampled (squared)-magnitude data corrupted with outliers. This
framework is implemented using a multi-layered approach, combining multiple
initializations (to address the nonconvexity of the phase retrieval problem),
repeated minimization of a convex majorizer (surrogate for a nonconvex
objective function), and iterative optimization using the alternating
directions method of multipliers. Exploiting the generality of this framework,
we investigate using a Laplace measurement noise model better adapted to
outliers present in the data than the conventional Gaussian noise model. Using
simulations, we explore the sensitivity of the method to both the
regularization and penalty parameters. We include 1D Monte Carlo and 2D image
reconstruction comparisons with alternative phase retrieval algorithms. The
results suggest the proposed method, with the Laplace noise model, both
increases the likelihood of correct support recovery and reduces the mean
squared error from measurements containing outliers. We also describe exciting
extensions made possible by the generality of the proposed framework, including
regularization using analysis-form sparsity priors that are incompatible with
many existing approaches.Comment: 11 pages, 9 figure
Formation of closed timelike curves in a composite vacuum/dust asymptotically-flat spacetime
We present a new asymptotically-flat time-machine model made solely of vacuum
and dust. The spacetime evolves from a regular spacelike initial hypersurface S
and subsequently develops closed timelike curves. The initial hypersurface S is
asymptotically flat and topologically trivial. The chronology violation occurs
in a compact manner; namely the first closed causal curves form at the boundary
of the future domain of dependence of a compact region in S (the core). This
central core is empty, and so is the external asymptotically flat region. The
intermediate region surrounding the core (the envelope) is made of dust with
positive energy density. This model trivially satisfies the weak, dominant, and
strong energy conditions. Furthermore it is governed by a well-defined system
of field equations which possesses a well-posed initial-value problem.Comment: 15 pages; accepted to Phys. Rev. D (no modifications
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