37 research outputs found

### Simple Analytic Models of Gravitational Collapse

Most general relativity textbooks devote considerable space to the simplest
example of a black hole containing a singularity, the Schwarzschild geometry.
However only a few discuss the dynamical process of gravitational collapse, by
which black holes and singularities form. We present here two types of analytic
models for this process, which we believe are the simplest available; the first
involves collapsing spherical shells of light, analyzed mainly in
Eddington-Finkelstein coordinates; the second involves collapsing spheres
filled with a perfect fluid, analyzed mainly in Painleve-Gullstrand
coordinates. Our main goal is pedagogical simplicity and algebraic
completeness, but we also present some results that we believe are new, such as
the collapse of a light shell in Kruskal-Szekeres coordinates.Comment: Submitted to American Journal of Physic

### Noncommutative Black Hole Thermodynamics

We give a general derivation, for any static spherically symmetric metric, of
the relation $T_h=\frac{\cal K}{2\pi}$ connecting the black hole temperature
($T_h$) with the surface gravity ($\cal K$), following the tunneling
interpretation of Hawking radiation. This derivation is valid even beyond the
semi classical regime i. e. when quantum effects are not negligible. The
formalism is then applied to a spherically symmetric, stationary noncommutative
Schwarzschild space time. The effects of back reaction are also included. For
such a black hole the Hawking temperature is computed in a closed form. A
graphical analysis reveals interesting features regarding the variation of the
Hawking temperature (including corrections due to noncommutativity and back
reaction) with the small radius of the black hole. The entropy and tunneling
rate valid for the leading order in the noncommutative parameter are
calculated. We also show that the noncommutative Bekenstein-Hawking area law
has the same functional form as the usual one.Comment: LaTex, 17 pages, 2 figures, minor changes, references added, to
appear in Phys. Rev.

### Massive particles' Hawking radiation via tunneling from the G.H Dilaton black hole

In the past, Hawking radiation was viewed as a tunneling process and the
barrier was just created by the outgoing particle itself. In this paper,
Parikh's recent work is extended to the case of massive particles' tunneling.
We investigate the behavior of the tunneling massive particles from a
particular black hole solution-G.H Dilaton black hole which is obtained from
the string theory, and calculate the emission rate at which massive particles
tunnel across the event horizon. We obtain that the result is also consistent
with an underlying unitary theory. Furthermore, the result takes the same
functional form as that of massless particles.Comment: 6 pages, no figure, revtex

### Massive uncharged and charged particles' tunneling from the Horowitz-Strominger Dilaton black hole

Originally, Parikh and Wilczek's work is only suitable for the massless
particles' tunneling. But their work has been further extended to the cases of
massive uncharged and charged particles' tunneling recently. In this paper, as
a particular black hole solution, we apply this extended method to reconsider
the tunneling effect of the H.S Dilaton black hole. We investigate the behavior
of both massive uncharged and charged particles, and respectively calculate the
emission rate at the event horizon. Our result shows that their emission rates
are also consistent with the unitary theory. Moreover, comparing with the case
of massless particles' tunneling, we find that this conclusion is independent
of the kind of particles. And it is probably caused by the underlying
relationship between this method and the laws of black hole thermodynamics.Comment: 6 pages, no figure, revtex 4, accepted by Int. J. Mod. Phys

### Gravitational collapse of spherically symmetric plasmas in Einstein-Maxwell spacetimes

We utilize a recent formulation of a spherically symmetric spacetime endowed
with a general decomposition of the energy momentum tensor [Phys. Rev. D, 75,
024031 (2007)] to derive equations governing spherically symmetric
distributions of electromagnetic matter. We show the system reduces to the
Reissner-Nordstrom spacetime in general, spherically symmetric coordinates in
the vacuum limit. Furthermore, we show reduction to the charged Vaidya
spacetime in non-null coordinates when certain equations of states are chosen.
A model of gravitational collapse is discussed whereby a charged fluid resides
within a boundary of finite radial extent on the initial hypersurface, and is
allowed to radiate charged particles. Our formalism allows for the discussion
of all regions in this model without the need for complicated matching schemes
at the interfaces between successive regions. As further examples we consider
the collapse of a thin shell of charged matter onto a Reissner-Nordstrom black
hole. Finally, we reduce the entire system of equations to the static case such
that we have the equations for hydrostatic equilibrium of a charged fluid.Comment: Accepted for publication in Phys. Rev.

### A river model of space

Within the theory of general relativity gravitational phenomena are usually
attributed to the curvature of four-dimensional spacetime. In this context we
are often confronted with the question of how the concept of ordinary physical
three-dimensional space fits into this picture. In this work we present a
simple and intuitive model of space for both the Schwarzschild spacetime and
the de Sitter spacetime in which physical space is defined as a specified set
of freely moving reference particles. Using a combination of orthonormal basis
fields and the usual formalism in a coordinate basis we calculate the physical
velocity field of these reference particles. Thus we obtain a vivid description
of space in which space behaves like a river flowing radially toward the
singularity in the Schwarzschild spacetime and radially toward infinity in the
de Sitter spacetime. We also consider the effect of the river of space upon
light rays and material particles and show that the river model of space
provides an intuitive explanation for the behavior of light and particles at
and beyond the event horizons associated with these spacetimes.Comment: 22 pages, 5 figure

### Generalized Painleve-Gullstrand descriptions of Kerr-Newman black holes

Generalized Painleve-Gullstrand metrics are explicitly constructed for the
Kerr-Newman family of charged rotating black holes. These descriptions are free
of all coordinate singularities; moreover, unlike the Doran and other proposed
metrics, an extra tunable function is introduced to ensure all variables in the
metrics remain real for all values of the mass M, charge Q, angular momentum
aM, and cosmological constant \Lambda > - 3/(a^2). To describe fermions in
Kerr-Newman spacetimes, the stronger requirement of non-singular vierbein
one-forms at the horizon(s) is imposed and coordinate singularities are
eliminated by local Lorentz boosts. Other known vierbein fields of Kerr-Newman
black holes are analysed and discussed; and it is revealed that some of these
descriptions are actually not related by physical Lorentz transformations to
the original Kerr-Newman expression in Boyer-Lindquist coordinates - which is
the reason complex components appear (for certain ranges of the radial
coordinate) in these metrics. As an application of our constructions the
correct effective Hawking temperature for Kerr black holes is derived with the
method of Parikh and Wilczek.Comment: 5 pages; extended to include application to derivation of Hawking
radiation for Kerr black holes with Parikh-Wilczek metho

### Black holes and global structures of spherical spacetimes in Horava-Lifshitz theory

We systematically study black holes in the Horava-Lifshitz (HL) theory by
following the kinematic approach, in which a horizon is defined as the surface
at which massless test particles are infinitely redshifted. Because of the
nonrelativistic dispersion relations, the speed of light is unlimited, and test
particles do not follow geodesics. As a result, there are significant
differences in causal structures and black holes between general relativity
(GR) and the HL theory. In particular, the horizon radii generically depend on
the energies of test particles. Applying them to the spherical static vacuum
solutions found recently in the nonrelativistic general covariant theory of
gravity, we find that, for test particles with sufficiently high energy, the
radius of the horizon can be made as small as desired, although the
singularities can be seen in principle only by observers with infinitely high
energy. In these studies, we pay particular attention to the global structure
of the solutions, and find that, because of the
foliation-preserving-diffeomorphism symmetry, ${Diff}(M,{\cal{F}})$, they are
quite different from the corresponding ones given in GR, even though the
solutions are the same. In particular, the ${Diff}(M,{\cal{F}})$ does not allow
Penrose diagrams. Among the vacuum solutions, some give rise to the structure
of the Einstein-Rosen bridge, in which two asymptotically flat regions are
connected by a throat with a finite non-zero radius. We also study slowly
rotating solutions in such a setup, and obtain all the solutions characterized
by an arbitrary function $A_{0}(r)$. The case $A_{0} = 0$ reduces to the slowly
rotating Kerr solution obtained in GR.Comment: latex4, 15 figures. Some typos were correcte

### Initial data for gravity coupled to scalar, electromagnetic and Yang-Mills fields

We give ansatze for solving classically the initial value constraints of
general relativity minimally coupled to a scalar field, electromagnetism or
Yang-Mills theory. The results include both time-symmetric and asymmetric data.
The time-asymmetric examples are used to test Penrose's cosmic censorship
inequality. We find that the inequality can be violated if only the weak energy
condition holds.Comment: 16 pages, RevTeX, references added, presentational changes, version
to appear in Phys Rev.

### On elliptic solutions of the cubic complex one-dimensional Ginzburg-Landau equation

The cubic complex one-dimensional Ginzburg-Landau equation is considered.
Using the Hone's method, based on the use of the Laurent-series solutions and
the residue theorem, we have proved that this equation has neither elliptic
standing wave nor elliptic travelling wave solutions. This result amplifies the
Hone's result, that this equation has no elliptic travelling wave solutions.Comment: LaTeX, 12 page