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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, 2017

We derive the Hawking spectrum of fermions emitted by a minimally geometric deformed (MGD) black hole. The MGD naturally describes quantum effects on the geometry in the form of a length scale related, for instance, to the existence of extra dimensions. The dynamics of the emitted fermions is described in the context of the generalised uncertainty principle and likewise contains a length scale associated with the quantum nature of space-time. We then show that the emission is practically indistinguishable from the Hawking thermal spectrum for large black hole masses, but the total flux can vanish for small and finite black hole mass. This suggests the possible existence of black hole remnants with a mass determined by the two length scales., Comment: 12 pages, 5 figures

We propose an effective anisotropic fluid description for a generic infrared-modified theory of gravity. In our framework, the additional component of the acceleration, commonly attributed to dark matter, is explained as a radial pressure generated by the reaction of the dark energy fluid to the presence of baryonic matter. Using quite general assumptions, and a microscopic description of the fluid in terms of a Bose-Einstein condensate of gravitons, we find the static, spherically symmetric solution for the metric in terms of the Misner-Sharp mass function and the fluid pressure. At galactic scales, we correctly reproduce the leading MOND-like $\log(r)$ and subleading $(1/r)\,\log(r)$ terms in the weak-field expansion of the potential. Our description also predicts a tiny (of order $10^{-6}$ for a typical spiral galaxy) Machian modification of the Newtonian potential at galactic scales, which is controlled by the cosmological acceleration., Comment: 13 pages, no figures. Replaced version: major revisions in the introduction, microscopic derivation of Tully-Fisher relation using Bose-Einstein condensate of gravitons. Some typos corrected

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 added

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 C

We show that a corpuscular description of gravity can lead to an inflationary scenario similar to Starobinsky's model without requiring the introduction of the inflaton field. All relevant properties are determined by the number of gravitons in the cosmological condensate or, equivalently, by their Compton length. In particular, the relation between the Hubble parameter $H$ and its time derivative $\dot H$ required by CMB observations at the end of inflation, as well as the (minimum) initial value of the slow-roll parameter, are naturally obtained from the Compton size of the condensate., Comment: 6 pages, 1 figure, minor typos corrected

We demonstrate that in some regions of parameter space, modified dispersion relations can lead to highly populated excited states, which we dub as "super-excited" states. In order to prepare such super-excited states, we invoke dispersion relations that have negative slope in an interim sub-horizon phase at high momenta. This behaviour of quantum fluctuations can lead to large corrections relative to the Bunch-Davies power spectrum, which mimics highly excited initial conditions. We identify the Bogolyubov coefficients that can yield these power spectra. In the course of this computation, we also point out the shortcomings of the gluing method for evaluating the power spectrum and the Bogolyubov coefficients. As we discuss, there are other regions of parameter space, where the power spectrum does not get modified. Therefore, modified dispersion relations can also lead to so-called "calm excited states" as well. We conclude by commenting on the possibility of obtaining these modified dispersion relations within the Effective Field Theory of Inflation., Comment: 1+19 pages, 4 figures

We consider a solution of the effective four-dimensional Einstein equations, obtained from the general relativistic Schwarzschild metric through the principle of Minimal Geometric Deformation (MGD). Since the brane tension can, in general, introduce new singularities on a relativistic E\"otv\"os brane model in the MGD framework, we require the absence of observed singularities, in order to constrain the brane tension. We then study the corresponding Bose-Einstein condensate (BEC) gravitational system and determine the critical stability region of BEC MGD stellar configurations. Finally, the critical stellar densities are shown to be related with critical points of the information entropy., Comment: 7 pages, 4 figures

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 fixed

We consider the lower bound for the shear viscosity-to-entropy density ratio, obtained from the fluid/gravity correspondence, in order to constrain the post-Newtonian parameter of brane-world metrics. In particular, we analyse the Casadio-Fabbri-Mazzacurati (CFM) effective solutions for the gravity side of the correspondence and argue that including higher order terms in the hydrodynamic expansion can lead to a full agreement with the experimental bounds, for the Eddington-Robertson-Schiff post-Newtonian parameter in the CFM metrics. This lends further support to the physical relevance of the viscosity-to-entropy ratio lower bound and fluid/gravity correspondence. Hence we show that CFM black branes are, effectively, Schwarzschild black branes., Comment: 20 pages, 2 figures; refs. added, improved version, to appear in EPJC

If the initial quantum state of the primordial perturbations broke rotational invariance, that would be seen as a statistical anisotropy in the angular correlations of the cosmic microwave background radiation (CMBR) temperature fluctuations. This can be described by a general parameterisation of the initial conditions that takes into account the possible direction-dependence of both the amplitude and the phase of particle creation during inflation. The leading effect in the CMBR two-point function is typically a quadrupole modulation, whose coefficient is analytically constrained here to be $|B| \lesssim 0.06$. The CMBR three-point function then acquires enhanced non-gaussianity, especially for the local configurations. In the large occupation number limit, a distinctive prediction is a modulation of the non-gaussianity around a mean value depending on the angle that short and long wavelength modes make with the preferred direction. The maximal variations with respect to the mean value occur for the configurations which are coplanar with the preferred direction and the amplitude of the non-gaussianity increases (decreases) for the short wavelength modes aligned with (perpendicular to) the preferred direction. For a high scale model of inflation with maximally pumped up isotropic occupation and $\epsilon\simeq 0.01$ the difference between these two configurations is about $0.27$, which could be detectable in the future. For purely anisotropic particle creation, the non-Gaussianity can be larger and its anisotropic feature very sharp. The non-gaussianity can then reach $f_{NL} \sim 30$ in the preferred direction while disappearing from the correlations in the orthogonal plane., Comment: v1: 13 pages, 3 figures, double column, v2: some refs added; v3: Matched the JCAP version

We investigate black hole production in pp collisions at the Large Hadron Collider by employing the horizon quantum mechanics for models of gravity with extra spatial dimensions. This approach can be applied to processes around the fundamental gravitational scale and naturally yields a suppression below the fundamental gravitational scale and for increasing number of extra dimensions. The results of numerical simulations performed with the black hole event generator BLACKMAX are here reported in order to illustrate the main differences in the number of expected black hole events and mass distributions.

Quantum physics lends a view of space-time geometry as an emergent structure that shows classical features only at some observational level. The space-time manifold can be viewed as a purely theoretical arena, where quantum states and observables are defined, with the additional freedom of changing coordinates. We focus on spherically symmetric quantum sources, and determine the probability they are black holes. The gravitational radius is promoted to quantum mechanical operator acting on the ``horizon wave-function''. This formalism is applied to several sources with mass around the fundamental scale, as natural candidates of quantum black holes. This horizon quantum mechanics supports some features of BEC models of black holes. The Klein-Gordon equation for a toy graviton field coupled to a static matter current classically reproduces the Newtonian potential, while the corresponding quantum state is given by a coherent superposition of scalar modes. When N such bosons are self-confined in a volume of the size of the Schwarzschild radius, the horizon shows that their radius corresponds to a proper horizon whose related uncertainty is connected to the typical energy of Hawking modes: it is suppressed as N increases, contrarily to a single very massive particle. The spectrum of these systems is formed by a discrete ground state and a continuous Planckian distribution at the Hawking temperature representing the radiation. Assuming the internal scatterings give rise to the Hawking radiation, the N-particle state can be collectively described by a single-particle wave-function. The partition function follows together with the usual entropy law, with a logarithmic correction related to the Hawking component. The backreaction of radiating modes is also shown to reduce the Hawking flux, and eventually stop it.

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 $m$ (the bosons forming the black hole), and a continuous spectrum with energy $\omega > m$ (representing the Hawking radiation and modelled with a Planckian distribution at the expected Hawking temperature). The $N$-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy $M = N m$ and a Planckian distribution for $E > M$ 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 $\omega > m$ 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"

We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general $(1+D)$-dimensional space-time, for $D>3$ and including the $D=1$ case. We find that the probability $P_{\rm BH}$ that such objects are (quantum) black holes behaves similarly to the probability in the $(3+1)$ framework for $D> 3$. In fact, for $D\ge 3$, the probability increases towards unity as the mass grows above the relevant $D$-dimensional Planck scale $m_D$. At fixed mass, however, $P_{\rm BH}$ decreases with increasing $D$, so that a particle with mass $m\simeq m_D$ has just about $10\%$ probability to be a black hole in $D=5$, and smaller for larger $D$. This result has a potentially strong impact on estimates of black hole production in colliders. In contrast, for $D=1$, we find the probability is comparably larger for smaller masses, but $P_{\rm BH} < 0.5$, 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 $m_D$ in $D>3$. For $D=1$ 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 PLB

We study the properties of the poles of the resummed graviton propagator obtained by resumming bubble matter diagrams which correct the classical graviton propagator. These poles have been previously interpreted as black holes precursors. Here, we show using the Horizon Wave-Function formalism that these poles indeed have properties which make them compatible with being black hole precursors. In particular, when modeled with a Breit-Wigner distribution, they have a well defined gravitational radius. The probability that the resonance is inside its own gravitational radius, and thus that it is black hole, is about one half. Our results confirm the interpretation of these poles as black hole precursors., Comment: 11 pages

The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application, and a new solution potentially useful to describe stars in the brane-world is also presented., Comment: Improved version with new solutions. 11 pages, 4 figures. To be published in CQG

We consider a solution of the effective four-dimensional brane-world equations, obtained from the General Relativistic Schwarzschild metric via the principle of Minimal Geometric Deformation, and investigate the corresponding signatures stemming from the possible existence of a warped extra dimension. In particular, we derive bounds on an extra-dimensional parameter, closely related with the fundamental gravitational length, from the experimental results of the classical tests of General Relativity in the Solar system., Comment: 6 pages, slightly improved, to appear in Europhysics Letters

We study the corpuscular model of an evaporating black hole consisting of a specific quantum state for a large number $N$ of self-confined bosons. The single-particle spectrum contains a discrete ground state of energy $m$ (corresponding to toy gravitons forming the black hole), and a gapless continuous spectrum (to accommodate for the Hawking radiation with energy $\omega>m$). 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 $N$-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy $M=N\,m$ and a Planckian distribution for $E>M$ 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 $\omega>m$ 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 PRD

We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio $\alpha>1$), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for $\alpha^2<{2}$, and this configuration has a non-vanishing probability of being a black hole, thus extending the classically allowed region for a charged black hole. However, the HWF is not normalisable for $\alpha^2 > 2$, and the uncertainty in the location of the horizon blows up at $\alpha^2=2$, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorhip might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of $\sqrt{2}$) can exist., Comment: RevTeX4, 6 pages, 2 figures. Typos corrected and comments added. Version to appear in PLB

Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investigate possible modifications to the Hubble parameter and following corrections to the cosmic microwave background spectrum. In this model, scalar and tensor perturbations are generated by the quantum depletion of the background inflaton and graviton condensate respectively. We show how the inflaton mass affects the power spectra and the tensor-to-scalar ratio. Masses approaching the Planck scale would lead to strong deviations, while standard spectra are recovered for an inflaton mass much smaller than the Planck mass.