46 research outputs found
Matter and gravitons in the gravitational collapse
We consider the effects of gravitons in the collapse of baryonic matter that
forms a black hole. We first note that the effective number of (soft off-shell)
gravitons that account for the (negative) Newtonian potential energy generated
by the baryons is conserved and always in agreement with Bekenstein's area law
of black holes. Moreover, their (positive) interaction energy reproduces the
expected post-Newtonian correction and becomes of the order of the total ADM
mass of the system when the size of the collapsing object approaches its
gravitational radius. This result supports a scenario in which the
gravitational collapse of regular baryonic matter produces a corpuscular black
hole without central singularity, in which both gravitons and baryons are
marginally bound and form a Bose-Einstein condensate at the critical point. The
Hawking emission of baryons and gravitons is then described by the quantum
depletion of the condensate and we show the two energy fluxes are comparable,
albeit negligibly small on astrophysical scales.Comment: 4 pages, no figures. Minor changes and typos fixe
Horizon Quantum mechanics: spherically symmetric and rotating sources
The Horizon Quantum Mechanics is an approach that allows one to analyse the
gravitational radius of spherically symmetric systems and compute the
probability that a given quantum state is a black hole. We first review the
(global) formalism and show how it reproduces a gravitationally inspired GUP
relation. This results leads to unacceptably large fluctuations in the horizon
size of astrophysical black holes if one insists in describing them as
(smeared) central singularities. On the other hand, if they are extended
systems, like in the corpuscular models, no such issue arises and one can in
fact extend the formalism to include asymptotic mass and angular momentum with
the harmonic model of rotating corpuscular black holes. The Horizon Quantum
Mechanics then shows that, in simple configurations, the appearance of the
inner horizon is suppressed and extremal (macroscopic) geometries seem
disfavoured.Comment: 13 pages, 6 figures, based on a talk given at the International
Lemaitre Workshop "Black holes, gravitational waves and spacetime
singularities", Specola Vaticana, May 8-12, 201
Horizon Quantum Mechanics of Rotating Black Holes
The Horizon Quantum Mechanics is an approach that was previously introduced
in order to analyse the gravitational radius of spherically symmetric systems
and compute the probability that a given quantum state is a black hole. In this
work, we first extend the formalism to general space-times with asymptotic
(ADM) mass and angular momentum. We then apply the extended Horizon Quantum
Mechanics to a harmonic model of rotating corpuscular black holes. We find that
simple configurations of this model naturally suppress the appearance of the
inner horizon and seem to disfavour extremal (macroscopic) geometries.Comment: 22 pages, 6 figures. Final version to appear in EPJ
Quantum corpuscular corrections to the Newtonian potential
We study an effective quantum description of the static gravitational
potential for spherically symmetric systems up to the first post-Newtonian
order. We start by obtaining a Lagrangian for the gravitational potential
coupled to a static matter source from the weak field expansion of the
Einstein-Hilbert action. By analysing a few classical solutions of the
resulting field equation, we show that our construction leads to the expected
post-Newtonian expressions. Next, we show that one can reproduce the classical
Newtonian results very accurately by employing a coherent quantum state and
modifications to include the first post-Newtonian corrections are considered.
Our findings establish a connection between the corpuscular model of black
holes and post-Newtonian gravity, and set the stage for further investigations
of these quantum models.Comment: 26 pages, 4 figures. Typos corrected, references and clarifications
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Thermal corpuscular black holes
We study the corpuscular model of an evaporating black hole consisting of a
specific quantum state for a large number of self-confined bosons. The
single-particle spectrum contains a discrete ground state of energy
(corresponding to toy gravitons forming the black hole), and a gapless
continuous spectrum (to accommodate for the Hawking radiation with energy
). Each constituent is in a superposition of the ground state and a
Planckian distribution at the expected Hawking temperature in the continuum. We
first find that, assuming the Hawking radiation is the leading effect of the
internal scatterings, the corresponding -particle state can be collectively
described by a single-particle wave-function given by a superposition of a
total ground state with energy and a Planckian distribution for
at the same Hawking temperature. From this collective state, we compute the
partition function and obtain an entropy which reproduces the usual area law
with a logarithmic correction precisely related with the Hawking component. By
means of the horizon wave-function for the system, we finally show the
backreaction of modes with reduces the Hawking flux. Both
corrections, to the entropy and to the Hawking flux, suggest the evaporation
properly stops for vanishing mass, if the black hole is in this particular
quantum state.Comment: PDFLaTeX, 15 pages, 2 figure. Version to appear in PR
Design and optimization under uncertainty of Energy Systems
In many engineering design and optimisation problems, the presence of uncertainty in data
and parameters is a central and critical issue. The analysis and design of advanced complex
energy systems is generally performed starting from a single operating condition and
assuming a series of design and operating parameters as fixed values. However, many of
the variables on which the design is based are subject to uncertainty because they are not
determinable with an adequate precision and they can affect both performance and cost.
Uncertainties stem naturally from our limitations in measurements, predictions and
manufacturing, and we can say that any system used in engineering is subject to some
degree of uncertainty. Different fields of engineering use different ways to describe this
uncertainty and adopt a variety of techniques to approach the problem. The past decade has
seen a significant growth of research and development in uncertainty quantification
methods to analyse the propagation of uncertain inputs through the systems. One of the
main challenges in this field are identifying sources of uncertainty that potentially affect the outcomes and the efficiency in propagating these uncertainties from the sources to the
quantities of interest, especially when there are many sources of uncertainties. Hence, the
level of rigor in uncertainty analysis depends on the quality of uncertainty quantification
method. The main obstacle of this analysis is often the computational effort, because the
representative model is typically highly non-linear and complex. Therefore, it is necessary
to have a robust tool that can perform the uncertainty propagation through a non-intrusive
approach with as few evaluations as possible.
The primary goal of this work is to show a robust method for uncertainty quantification applied to energy systems. The first step in this direction was made doing a work on the analysis of uncertainties on a recuperator for micro gas turbines, making use of the Monte Carlo and Response Sensitivity Analysis methodologies to perform this study.
However, when considering more complex energy systems, one of the main weaknesses of uncertainty quantification methods arises: the extremely high computational effort needed. For this reason, the application of a so-called metamodel was found necessary and useful. This approach was applied to perform a complete analysis under uncertainty of a solid oxide fuel cell hybrid system, starting from the evaluation of the impact of several uncertainties on the system up to a robust design including a multi-objective optimization. The response surfaces have allowed the authors to consider the uncertainties in the system when performing an acceptable number of simulations. These response were then used to perform a Monte Carlo simulation to evaluate the impact of the uncertainties on the monitored outputs, giving an insight on the spread of the resulting probability density functions and so on the outputs which should be considered more carefully during the design phase.
Finally, the analysis of a complex combined cycle with a flue gas condesing heat pump subject to market uncertainties was performed. To consider the uncertainties in the electrical price, which would impact directly the revenues of the system, a statistical study on the behaviour of such price along the years was performed. From the data obtained it was possible to create a probability density function for each hour of the day which would represent its behaviour, and then those distributions were used to analyze the variability of the system in terms of revenues and emissions
Black holes as self-sustained quantum states, and Hawking radiation
We employ the recently proposed formalism of the "horizon wave-function" to
investigate the emergence of a horizon in models of black holes as
Bose-Einstein condensates of gravitons. We start from the Klein-Gordon equation
for a massless scalar (toy graviton) field coupled to a static matter current.
The (spherically symmetric) classical field reproduces the Newtonian potential
generated by the matter source, and the corresponding quantum state is given by
a coherent superposition of scalar modes with continuous occupation number.
Assuming an attractive self-interaction that allows for bound states, one finds
that (approximately) only one mode is allowed, and the system can be confined
in a region of the size of the Schwarzschild radius. This radius is then shown
to correspond to a proper horizon, by means of the horizon wave-function of the
quantum system, with an uncertainty in size naturally related to the expected
typical energy of Hawking modes. In particular, this uncertainty decreases for
larger black hole mass (with larger number of light scalar quanta), in
agreement with semiclassical expectations, a result which does not hold for a
single very massive particle. We finally speculate that a phase transition
should occur during the gravitational collapse of a star, ideally represented
by a static matter current and Newtonian potential, that leads to a black hole,
again ideally represented by the condensate of toy gravitons, and suggest an
effective order parameter that could be used to investigate this transition.Comment: 25 pages, 6 figures. Improved text and typos fixed. Final version to
appear in PR
Thermal BEC black holes
We review some features of BEC models of black holes obtained by means of the
HWF formalism. We consider the KG equation for a toy graviton field coupled to
a static matter current in spherical symmetry. The classical field reproduces
the Newtonian potential generated by the matter source, while the corresponding
quantum state is given by a coherent superposition of scalar modes with
continuous occupation number. An attractive self-interaction is needed for
bound states to form, so that (approximately) one mode is allowed, and the
system of N bosons can be self-confined in a volume of the size of the
Schwarzschild radius. The HWF is then used to show that the radius of such a
system corresponds to a proper horizon. The uncertainty in the size of the
horizon is related to the typical energy of Hawking modes: it decreases with
the increasing of the black hole mass (larger number of gravitons), in
agreement with semiclassical calculations and different from a single very
massive particle. The spectrum contains a discrete ground state of energy
(the bosons forming the black hole), and a continuous spectrum with energy
(representing the Hawking radiation and modelled with a Planckian
distribution at the expected Hawking temperature). The -particle state can
be collectively described by a single-particle wave-function given by a
superposition of a total ground state with energy and a Planckian
distribution for at the same Hawking temperature. The partition
function is then found to yield the usual area law for the entropy, with a
logarithmic correction related with the Hawking component. The backreaction of
modes with is also shown to reduce the Hawking flux and the
evaporation properly stops for vanishing mass.Comment: 30 pages, pdflatex with 6 figures. Review paper prepared for Entropy
special issue "Entropy in Quantum Gravity and Quantum Cosmology
Horizon of quantum black holes in various dimensions
We adapt the horizon wave-function formalism to describe massive static
spherically symmetric sources in a general -dimensional space-time, for
and including the case. We find that the probability
that such objects are (quantum) black holes behaves similarly to the
probability in the framework for . In fact, for , the
probability increases towards unity as the mass grows above the relevant
-dimensional Planck scale . At fixed mass, however,
decreases with increasing , so that a particle with mass has
just about probability to be a black hole in , and smaller for
larger . This result has a potentially strong impact on estimates of black
hole production in colliders. In contrast, for , we find the probability
is comparably larger for smaller masses, but , suggesting
that such lower dimensional black holes are purely quantum and not classical
objects. This result is consistent with recent observations that sub-Planckian
black holes are governed by an effective two-dimensional gravitation theory.
Lastly, we derive Generalised Uncertainty Principle relations for the black
holes under consideration, and find a minimum length corresponding to a
characteristic energy scale of the order of the fundamental gravitational mass
in . For we instead find the uncertainty due to the horizon
fluctuations has the same form as the usual Heisenberg contribution, and
therefore no fundamental scale exists.Comment: Latex, 16 pages, 8 figures. Final version to appear in PL