216 research outputs found
The role of collapsed matter in the decay of black holes
We try to shed some light on the role of matter in the final stages of black
hole evaporation from the fundamental frameworks of classicalization and the
black-to-white hole bouncing scenario. Despite being based on very different
grounds, these two approaches attempt at going beyond the background field
method and treat black holes as fully quantum systems rather than considering
quantum field theory on the corresponding classical manifolds. They also lead
to the common prediction that the semiclassical description of black hole
evaporation should break down and the system be disrupted by internal quantum
pressure, but they both arrive at this conclusion neglecting the matter that
formed the black hole. We instead estimate this pressure from the bootstrapped
description of black holes, which allows us to express the total
Arnowitt-Deser-Misner mass in terms of the baryonic mass still present inside
the black hole. We conclude that, although these two scenarios provide
qualitatively similar predictions for the final stages, the corpuscular model
does not seem to suggest any sizeable deviation from the semiclassical time
scale at which the disruption should occur, unlike the black-to-white hole
bouncing scenario. This, in turn, makes the phenomenology of corpuscular black
holes more subtle from an astrophysical perspective.Comment: 5 pages, no figur
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
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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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
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
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
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
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
Balancing work and family in Italy: New mothersĂâ employment decisions after childbirth
Compared with other European countries, the Italian labour market stands out for the low level of both female participation and fertility. In this paper we focus on the employment patterns of Italian mothers around the time of childbirth. Our hypothesis is that the difficulties involved in reconciling work and family when there are children are among the leading causes of the low female employment rate in Italy. Data from the 2002 Italian Birth Sample Survey show that about 20 per cent of mothers who were working before childbirth, stop working one and a half years after delivery and that about 14 per cent voluntarily decide to resign. The paper analyses the factors that most influence new mothersĂâ unemployment risk after childbirth.female employment, childbirth, childcare
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
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