635 research outputs found
Who is the Inflaton?
In the context of the two-fluid model introduced to tame the transplanckian
problem of black hole physics, the inflaton field of the chaotic inflation
scenario is identified with the fluctuation of the density of modes. Its mass
comes about from the exchange of degrees of freedom between the two fluids.Comment: extensively revised version presented at the Corfu School and
Workshop of Theoretical Physics 200
The Inflaton and Time in the Matter-Gravity System
The emergence of time in the matter-gravity system is addressed within the
context of the inflationary paradigm. A quantum minisuperspace-homogeneous
minimally coupled inflaton system is studied with suitable initial conditions
leading to inflation and the system is approximately solved in the limit for
large scale factor. Subsequently normal matter (either non homogeneous inflaton
modes or lighter matter) is introduced as a perturbation and it is seen that
its presence requires the coarse averaging of a gravitational wave function
(which oscillates at trans-Planckian frequencies) having suitable initial
conditions. Such a wave function, which is common for all types of normal
matter, is associated with a ``time density'' in the sense that its modulus is
related to the amount of time spent in a given interval (or the rate of flow of
time). One is then finally led to an effective evolution equation (Schroedinger
Schwinger-Tomonaga) for ``normal'' matter. An analogy with the emergence of a
temperature in statistical mechanics is also pointed out.Comment: 14 pages, late
Time dependent Green functions from Wheeler De Witt solutions
The aim of this article is twofold. First we examine from a new angle the
question of recovery of time in quantum cosmology. We construct Green functions
for matter fields from the solutions of the Wheeler De Witt equation. For
simplicity we work in a mini-superspace context. By evaluating these Green
functions in a first order development of the energy ``increment'' induced by
matrix elements of field operators, we show that the background geometry is the
solution of Einstein equations driven by the mean matter energy and that it is
this background which determines the time lapses separating the field
operators. Then, by studying higher order corrections, we clarify the nature of
the small dimensionless parameters which guarantee the validity of the
approximations used. In this respect, we show that the formal expansion in the
inverse Planck mass which is sometime presented as the ``standard procedure''
is illegitimate. Secondly, by the present analysis of Green functions, we
prepare the study of quantum matter transitions in quantum cosmology. In a next
article, we show that the time parametrization of transition amplitudes appears
for the same reasons that it appeared in this article. This proves that the
background is dynamically determined by the transition under examination.Comment: 25 pages, latex, no figure
Entanglement and Thermodynamics of Black Hole Entropy
Using simple conditions drawn from the stability of the cosmos in terms of
vacuum energy density, the cut-off momentum of entanglement is related to the
planckian mass. In so doing the black hole entropy is shown to be independent
of the number of field species that contribute to vacuum fluctuations. And this
is in spite of the fact that the number of field species is a linear
multiplicand of the entanglement entropy when this latter is expressed in terms
of the fundamental momentum cut-off of all fields.Comment: 5 page
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
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
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
Hawking Radiation from Feynman Diagrams
The aim of this letter is to clarify the relationships between Hawking
radiation and the scattering of light by matter falling into a black hole. To
this end we analyze the S-matrix elements of a model composed of a massive
infalling particle (described by a quantized field) and the radiation field.
These fields are coupled by current-current interactions and propagate in the
Schwarzschild geometry. As long as the photons energy is much smaller than the
mass of the infalling particle, one recovers Hawking radiation since our
S-matrix elements identically reproduce the Bogoliubov coefficients obtained by
treating the trajectory of the infalling particle classically. But after a
brief period, the energy of the `partners' of Hawking photons reaches this mass
and the production of thermal photons through these interactions stops. The
implications of this result are discussed.Comment: 12 pages, revtex, no figure
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