45 research outputs found
Gravitational Collapse of a Shell of Quantized Matter
The semi-classical collapse, including lowest order back-reaction, of a thin
shell of self-gravitating quantized matter is illustrated. The conditions for
which self-gravitating matter forms a thin shell are first discussed and an
effective Lagrangian for such matter is obtained. The matter-gravity system is
then quantized, the semi-classical limit for gravitation is taken and the
method of adiabatic invariants is applied to the resulting time dependent
matter Hamiltonian. The governing equations are integrated numerically, for
suitable initial conditions, in order to illustrate the effect of
back-reaction, due to the creation of matter, in slowing down the collapse near
the horizon.Comment: 20 pages, 1 eps figure. Problem with figure fixe
The Born-Oppenheimer Approach to the Matter-Gravity System and Unitarity
The Born-Oppenheimer approach to the matter-gravity system is illustrated and
the unitary evolution for matter, in the absence of phenomena such as
tunnelling or other instabilities, verified. The Born-Oppenheimer approach to
the matter-gravity system is illustrated in a simple minisuperspace model and
the corrections to quantum field theory on a semiclassical background
exhibited. Within such a context the unitary evolution for matter, in the
absence of phenomena such as tunnelling or other instabilities, is verified and
compared with the results of other approaches. Lastly the simplifications
associated with the use of adiabatic invariants to obtain the solution of the
explicitly time dependent evolution equation for matter are evidenced.Comment: Latex, 12 pages. Revised version as accepted for publication by
Class. and Quant. Grav. Some points explained and misprints correcte
Black hole and the adiabatic phase
An open system consisting of a scalar field bound to a Kerr black hole whose
mass () and specific angular momentum () are slowly (adiabatically)
perturbed is considered. The adiabatically induced phase and the conditions for
the validity of the adiabatic approximation are obtained. The effect of closed
cycles in parameter space (, plane) on the energy levels of both stable
and unstable scalar field bound states, together with other quantities of
interest, is illustrated. Lastly it is noted that the black hole wavefunction
will acquire an equal and opposite phase to that of matter thus leading to a
change of its effective action (entropy).Comment: Plain TeX, 12 page
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
Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust
The semiclassical collapse of a sphere of quantized dust is studied. A
Born-Oppenheimer decomposition is performed for the wave function of the system
and the semiclassical limit is considered for the gravitational part. The
method of adiabatic invariants for time dependent Hamiltonians is then employed
to find (approximate) solutions to the quantum dust equations of motions. This
allows us to obtain corrections to the adiabatic approximation of the dust
states associated with the time evolution of the metric. The diverse
non-adiabatic corrections are generally associated with particle (dust)
creation and related fluctuations. The back-reaction due to the dominant
contribution to particle creation is estimated and seen to slow-down the
collapse.Comment: LaTeX, 16 pages, no figures, final version to appear in Class. and
Quantum Gravit
Method of comparison equations for cosmological perturbations
We apply the method of comparison equations to study cosmological
perturbations during inflation, obtaining the full power spectra of scalar and
tensor perturbations to first and to second order in the slow-roll parameters.
We compare our results with those derived by means of other methods, in
particular the Green's function method and the improved WKB approximation, and
find agreement for the slow-roll structure. The method of comparison equations,
just as the improved WKB approximation, can however be applied to more general
situations where the slow-roll approximation fails.Comment: 20 pages, 10 figure
A radiation-like era before inflation
We show that the semiclassical approximation to the Wheeler-DeWitt equation
for the minisuperspace of a minimally coupled scalar field in the spatially
flat de Sitter Universe prompts the existence of an initial power-law evolution
driven by non-adiabatic terms from the gravitational wavefunction which act
like radiation. This simple model hence describes the onset of inflation from a
previous radiation-like expansion during which the cosmological constant is
already present but subleading.Comment: LaTeX, 8 pages, no figures; final version to be published in JCA
Semiclassical collapse of a sphere of dust
The semiclassical collapse of a homogeneous sphere of dust is studied. After
identifying the independent dynamical variables, the system is canonically
quantised and coupled equations describing matter (dust) and gravitation are
obtained. The conditions for the validity of the adiabatic (Born--Oppenheimer)
and semiclassical approximations are derived. Further on neglecting
back--reaction effects, it is shown that in the vicinity of the horizon and
inside the dust the Wightman function for a conformal scalar field coupled to a
monopole emitter is thermal at the characteristic Hawking temperature.Comment: LaTeX, 25 pages, no figures, final version accepted for publication
in Class. and Quantum Gra
The QCD Membrane
In this paper we study spatially quenched, SU(N) Yang-Mills theory in the
large-N limit. The resulting reduced action shows the same formal look as the
Banks-Fischler-Shenker-Susskind M-theory action. The Weyl-Wigner-Moyal symbol
of this matrix model is the Moyal deformation of a p(=2)-brane action. Thus,
the large-N limit of the spatially quenched SU(N) Yang-Mills is seen to
describe a dynamical membrane. By assuming spherical symmetry we compute the
mass spectrum of this object in the WKB approximation.Comment: 14 pages, LaTeX, non figures; accepted for publication in
Class.Quant. Gra
Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation
The connection between the method of comparison equations (generalized WKB
method) and the Ermakov-Pinney equation is established. A perturbative scheme
of solution of the generalized Ermakov-Pinney equation is developed and is
applied to the construction of perturbative series for second-order
differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in
Sec. 3 are correcte