69 research outputs found
Radial fall of a test particle onto an evaporating black hole
A test particle falling into a classical black hole crosses the event horizon
and ends up in the singularity within finite eigentime. In the `more realistic'
case of a `classical' evaporating black hole, an observer falling onto a black
hole observes a sudden evaporation of the hole. This illustrates the fact that
the discussion of the classical process commonly found in the literature may
become obsolete when the black hole has a finite lifetime. The situation is
basically the same for more complex cases, e.g. where a particle collides with
two merging black holes. It should be pointed out that the model used in this
paper is mainly of academic interest, since the description of the physics near
a black hole horizon still presents a difficult problem which is not yet fully
understood, but our model provides a valuable possibility for students to enter
the interesting field of black hole physics and to perform numerical
calculations of their own which are not very involved from the computational
point of view.Comment: 6 pages, 3 figures, LATE
A Smooth Lattice construction of the Oppenheimer-Snyder spacetime
We present test results for the smooth lattice method using an
Oppenheimer-Snyder spacetime. The results are in excellent agreement with
theory and numerical results from other authors.Comment: 60 pages, 28 figure
Hamiltonian formalism for the Oppenheimer-Snyder model
A family of effective actions in Hamiltonian form is derived for a
self-gravitating sphere of isotropic homogeneous dust. Starting from the
Einstein-Hilbert action for barotropic perfect fluids and making use of the
symmetry and equation of state of the matter distribution we obtain reduced
actions for two canonical variables, namely the radius of the sphere and its
ADM energy, the latter being conserved along trajectories of the former. These
actions differ by the value of the (conserved) geodesic energy of the radius of
the sphere which defines (disconnected) classes of solutions in correspondence
to the inner geometry and proper volume of the sphere. Each class is thus
treated as one constrained dynamical system and the union of all classes covers
the full phase space of the model. Generalization to the (inhomogeneous) Tolman
model is shown to be straightforward. Quantization is also discussed.Comment: RevTeX, 10 pages, no figure
Effective Action and Thermodynamics of Radiating Shells in General Relativity
An effective action is obtained for the area and mass aspect of a thin shell
of radiating self-gravitating matter. On following a mini-superspace approach,
the geometry of the embedding space-time is not dynamical but fixed to be
either Minkowski or Schwarzschild inside the shell and Vaidya in the external
space filled with radiation. The Euler-Lagrange equations of motion are
discussed and shown to entail the expected invariance of the effective
Lagrangian under time-reparametrization. They are equivalent to the usual
junction equations and suggest a macroscopic quasi-static thermodynamic
description.Comment: LATeX, 20 pages, 2 Fig
Gravitational Collapse of a Radiating Shell
We study the collapse of a self-gravitating and radiating shell. Matter
constituting the shell is quantized and the construction is viewed as a
semiclassical model of possible black hole formation. It is shown that the
shell internal degrees of freedom are excited by the quantum non-adiabaticity
of the collapse and, consequently, on coupling them to a massless scalar field,
the collapsing matter emits a burst of coherent (thermal) radiation.Comment: LaTeX, 34 pages, 21 EPS figures include
Black Holes in Magnetic Monopoles
We study magnetically charged classical solutions of a spontaneously broken
gauge theory interacting with gravity. We show that nonsingular monopole
solutions exist only if the Higgs vacuum expectation value is less than or
equal to a critical value , which is of the order of the Planck mass.
In the limiting case the monopole becomes a black hole, with the region outside
the horizon described by the critical Reissner-Nordstrom solution. For
, we find additional solutions which are singular at , but which
have this singularity hidden within a horizon. These have nontrivial matter
fields outside the horizon, and may be interpreted as small black holes lying
within a magnetic monopole. The nature of these solutions as a function of
and of the total mass and their relation to the Reissner-Nordstrom
solutions is discussed.Comment: (28 pages
The Semi-Classical Back Reaction to Black Hole Evaporation
The semi-classical back reaction to black hole evaporation (wherein the
renormalized energy momentum tensor is taken as source of Einstein's equations)
is analyzed in detail. It is proven that the mass of a Schwarzshild black hole
decreases according to Hawking's law where is a constant
of order one and that the particles are emitted with a thermal spectrum at
temperature .Comment: 10 pages, LATE
A Kucha\v{r} Hypertime Formalism For Cylindrically Symmetric Spacetimes With Interacting Scalar Fields
The Kucha\v{r} canonical transformation for vacuum geometrodynamics in the
presence of cylindrical symmetry is applied to a general non-vacuum case. The
resulting constraints are highly non-linear and non-local in the momenta
conjugate to the Kucha\v{r} embedding variables. However, it is demonstrated
that the constraints can be solved for these momenta and thus the dynamics of
cylindrically symmetric models can be cast in a form suitable for the
construction of a hypertime functional Schr\"odinger equation.Comment: 5 pages, LaTeX, UBCTP-93-02
Surface gravity in dynamical spherically symmetric spacetimes
A definition of surface gravity at the apparent horizon of dynamical
spherically symmetric spacetimes is proposed. It is based on a unique foliation
by ingoing null hypersurfaces. The function parametrizing the hypersurfaces can
be interpreted as the phase of a light wave uniformly emitted by some far-away
static observer. The definition gives back the accepted value of surface
gravity in the static case by virtue of its nonlocal character. Although the
definition is motivated by the behavior of outgoing null rays, it turns out
that there is a simple connection between the generalized surface gravity, the
acceleration of any radially moving observer, and the observed frequency change
of the infalling light signal. In particular, this gives a practical and simple
method of how any geodesic observer can determine surface gravity by measuring
only the redshift of the infalling light wave. The surface gravity can be
expressed as an integral of matter field quantities along an ingoing null line,
which shows that it is a continuous function along the apparent horizon. A
formula for the area change of the apparent horizon is presented, and the
possibility of thermodynamical interpretation is discussed. Finally, concrete
expressions of surface gravity are given for a number of four-dimensional and
two-dimensional dynamical black hole solutions.Comment: 35 pages, revtex, 3 figures included using eps
On scattering off the extreme Reissner-Nordstr\"om black hole in N=2 supergravity
The scattering amplitudes for the perturbed fields of the N=2 supergravity
about the extreme Reissner-Nordstr\"om black hole is examined. Owing to the
fact that the extreme hole is a BPS state of the theory and preserves an
unbroken global supersymmetry(N=1), the scattering amplitudes of the component
fields should be related to each other. In this paper, we derive the formula of
the transformation of the scattering amplitudes.Comment: 9 pages, revtex, no figures, a few typing errors correcte
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