90 research outputs found
Classical aspects of Hawking radiation verified in analogue gravity experiment
There is an analogy between the propagation of fields on a curved spacetime
and shallow water waves in an open channel flow. By placing a streamlined
obstacle into an open channel flow we create a region of high velocity over the
obstacle that can include wave horizons. Long (shallow water) waves propagating
upstream towards this region are blocked and converted into short (deep water)
waves. This is the analogue of the stimulated Hawking emission by a white hole
(the time inverse of a black hole). The measurements of amplitudes of the
converted waves demonstrate that they appear in pairs and are classically
correlated; the spectra of the conversion process is described by a
Boltzmann-distribution; and the Boltzmann-distribution is determined by the
determined by the change in flow across the white hole horizon.Comment: 17 pages, 10 figures; draft of a chapter submitted to the proceedings
of the IX'th SIGRAV graduate school: Analogue Gravity, Lake Como, Italy, May
201
Hawking Spectrum and High Frequency Dispersion
We study the spectrum of created particles in two-dimensional black hole
geometries for a linear, hermitian scalar field satisfying a Lorentz
non-invariant field equation with higher spatial derivative terms that are
suppressed by powers of a fundamental momentum scale . The preferred frame
is the ``free-fall frame" of the black hole. This model is a variation of
Unruh's sonic black hole analogy. We find that there are two qualitatively
different types of particle production in this model: a thermal Hawking flux
generated by ``mode conversion" at the black hole horizon, and a non-thermal
spectrum generated via scattering off the background into negative free-fall
frequency modes. This second process has nothing to do with black holes and
does not occur for the ordinary wave equation because such modes do not
propagate outside the horizon with positive Killing frequency. The horizon
component of the radiation is astonishingly close to a perfect thermal
spectrum: for the smoothest metric studied, with Hawking temperature
, agreement is of order at frequency
, and agreement to order persists out to
where the thermal number flux is ). The flux
from scattering dominates at large and becomes many orders of
magnitude larger than the horizon component for metrics with a ``kink", i.e. a
region of high curvature localized on a static worldline outside the horizon.
This non-thermal flux amounts to roughly 10\% of the total luminosity for the
kinkier metrics considered. The flux exhibits oscillations as a function of
frequency which can be explained by interference between the various
contributions to the flux.Comment: 32 pages, plain latex, 16 figures included using psfi
Black Hole Lasers Revisited
Contribution to "Quantum Analogues: From Phase Transitions to Black Holes and Cosmology" edited by William G. Unruh and Ralf Schutzhold. (Lecture Notes in Physics Vol. 718)The production of Hawking radiation by a single horizon is not dependent on the high-frequency dispersion relation of the radiated field. When there are two horizons, however, Corley and Jacobson have shown that superluminal dispersion leads to an amplification of the particle production in the case of bosons. The analytic theory of this "black hole laser" process is quite complicated, so we provide some numerical results in the hope of aiding understanding of this interesting phenomenon. Specifically, we consider sonic horizons in a moving fluid. The theory of elementary excitations in a Bose-Einstein condensate provides an example of "superluminal" (Bogoliubov) dispersion, so we add Bogoliubov dispersion to Unruh's equation for sound in the fluid. A white-hole/black-hole horizon pair will then display black hole lasing. Numerical analysis of the evolution of a wave packet gives a clear picture of the amplification process. By utilizing the similarity of a radiating horizon to a parametric amplifier in quantum optics we also analyze the black hole laser as a quantum-optical network
Black holes and Hawking radiation in spacetime and its analogues
These notes introduce the fundamentals of black hole geometry, the thermality
of the vacuum, and the Hawking effect, in spacetime and its analogues.
Stimulated emission of Hawking radiation, the trans-Planckian question, short
wavelength dispersion, and white hole radiation in the setting of analogue
models are also discussed. No prior knowledge of differential geometry, general
relativity, or quantum field theory in curved spacetime is assumed.Comment: 31 pages, 9 figures; to appear in the proceedings of the IX SIGRAV
School on 'Analogue Gravity', Como (Italy), May 2011, eds. D. Faccio et. al.
(Springer
Focusing and the Holographic Hypothesis
The ``screen mapping" introduced by Susskind to implement 't Hooft's
holographic hypothesis is studied. For a single screen time, there are an
infinite number of images of a black hole event horizon, almost all of which
have smaller area on the screen than the horizon area. This is consistent with
the focusing equation because of the existence of focal points. However, the
{\it boundary} of the past (or future) of the screen obeys the area theorem,
and so always gives an expanding map to the screen, as required by the
holographic hypothesis. These considerations are illustrated with several
axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi
Ultraviolet cut off and Bosonic Dominance
We rederive the thermodynamical properties of a non interacting gas in the
presence of a minimal uncertainty in length. Apart from the phase space measure
which is modified due to a change of the Heisenberg uncertainty relations, the
presence of an ultraviolet cut-off plays a tremendous role.
The theory admits an intrinsic temperature above which the fermion
contribution to energy density, pressure and entropy is negligible.Comment: 12 pages in revtex, 2 figures. Some coefficients have been changed in
the A_2 model and two references adde
Ultraviolet cut off, black hole-radiation equilibrium and big bang
In the presence of a minimal uncertainty in length, there exists a critical
temperature above which the thermodynamics of a gas of radiation changes
drastically.
We find that the equilibrium temperature of a system composed of a
Schwarzschild black hole surrounded by radiation is unaffected by these
modifications. This is in agreement with works related to the robustness of the
Hawking evaporation. The only change the deformation introduces concerns the
critical volume at which the system ceases to be stable.
On the contrary, the evolution of the very early universe is sensitive to the
new behavior. We readdress the shortcomings of the standard big bang
model(flatness, entropy and horizon problems) in this context, assuming a
minimal coupling to general relativity. Although they are not solved, some
qualitative differences set in.Comment: 10 pages revtex, 1 figur
On Slow Light as a Black Hole Analogue
Although slow light (electromagnetically induced transparency) would seem an
ideal medium in which to institute a ``dumb hole'' (black hole analog), it
suffers from a number of problems. We show that the high phase velocity in the
slow light regime ensures that the system cannot be used as an analog
displaying Hawking radiation. Even though an appropriately designed slow-light
set-up may simulate classical features of black holes -- such as horizon, mode
mixing, Bogoliubov coefficients, etc. -- it does not reproduce the related
quantum effects. PACS: 04.70.Dy, 04.80.-y, 42.50.Gy, 04.60.-m.Comment: 14 pages RevTeX, 5 figure
Linking the trans-Planckian and the information loss problems in black hole physics
The trans-Planckian and information loss problems are usually discussed in
the literature as separate issues concerning the nature of Hawking radiation.
Here we instead argue that they are intimately linked, and can be understood as
"two sides of the same coin" once it is accepted that general relativity is an
effective field theory.Comment: 10 pages, 2 figures. Replaced with the version to be published in
General Relativity and Gravitatio
Gravity wave analogs of black holes
It is demonstrated that gravity waves of a flowing fluid in a shallow basin
can be used to simulate phenomena around black holes in the laboratory. Since
the speed of the gravity waves as well as their high-wavenumber dispersion
(subluminal vs. superluminal) can be adjusted easily by varying the height of
the fluid (and its surface tension) this scenario has certain advantages over
the sonic and dielectric black hole analogs, for example, although its use in
testing quantum effects is dubious. It can be used to investigate the various
classical instabilities associated with black (and white) holes experimentally,
including positive and negative norm mode mixing at horizons. PACS: 04.70.-s,
47.90.+a, 92.60.Dj, 04.80.-y.Comment: 14 pages RevTeX, 5 figures, section VI modifie
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