arXiv subjects

R. Casadio

Publications and source records attributed to R. Casadio.

At least 37 records · Page 2Linked to original sources

arXiv2018

Bootstrapping Newton Gravity

A non-linear equation obtained by adding gravitational self-interaction terms to the Poisson equation for Newtonian gravity is here employed in order to analyse a static spherically sym- metric homogeneous compact source of given proper mass and radius and the outer vacuum. The main feature of this picture is that, although the freedom of shifting the potential by an ar- bitrary constant is of course lost, the solutions remain qualitatively very close to the Newtonian behaviour. We also notice that the negative gravitational potential energy is smaller than the proper mass for sources with small compactness, but for sources that should form black holes according to General Relativity, the gravitational potential energy becomes of the same order of magnitude of the proper mass, or even larger. Moreover, the pressure overcomes the energy density for large values of the compactness, but it remains finite for finite compactness, hence there exists no Buchdahl limit. This classical description is meant to serve as the starting point for investigating quantum features of (near) black hole configurations within the corpuscular picture of gravity in future developments.

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arXiv2018

Horizon Quantum Mechanics for spheroidal sources

We start investigating the extension of the Horizon Quantum Mechanics to the case of spheroidal sources. We first study the location of trapping surfaces in space-times resulting from an axial deformation of static isotropic systems, and show that the Misner-Sharp mass evaluated on the corresponding undeformed spherically symmetric space provides the correct gravitational radius to locate the horizon. We finally propose a way to determine the deformation parameter in the quantum theory.

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arXiv2018

Hawking radiation and the Bloom-Gilman duality

The decay widths of the quantum black hole precursors, determined from the poles of the resummed graviton propagator, are matched to the expected lifetime given by the Hawking decay. In this way, we impose a sort of duality between a perturbative description and an essentially non-perturbative description, bearing some similarity with the Bloom-Gilman duality for the strong interactions. General relations are then obtained for the widths and masses of the poles in terms of the number of particle species and the renormalisation scale of gravity.

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arXiv2017

Graviton propagator, renormalization scale and black-hole like states

We study the analytic structure of the resummed graviton propagator, inspired by the possible existence of black hole precursors in its spectrum. We find an infinite number of poles with positive mass, but both positive and negative effective width, and studied their asymptotic behaviour in the infinite sheet Riemann surface. We find that the stability of these precursors depend crucially on the value of the normalisation point scale.

hep-th↗

arXiv2017

Global and Local Horizon Quantum Mechanics

Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determine by spatially localised modes.

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arXiv2015

Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes

It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantisation of Einstein-Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the "superspace" of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble "minisuperspace" approach and choose the gravitational observables not simply by imposing some symmetry, but motivated by their proven relevance in the (classical) description of a given system. In particular, this review focuses on compact, spherically symmetric, quantum mechanical sources, in order to determine the probability they are black holes rather than regular particles. The gravitational radius is therefore lifted to the status of a quantum mechanical operator acting on the "horizon wave-function", the latter being determined by the quantum state of the source. This formalism is then applied to several sources with a mass around the fundamental scale, which are viewed as natural candidates of quantum black holes.

hep-th↗

arXiv2014

Horizons and non-local time evolution of quantum mechanical systems

According to general relativity, trapping surfaces and horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. The latter concept can be extended to a quantum mechanical state simply by means of the spectral decomposition, which allows one to define an associated "horizon wave-function". Since this auxiliary wave-function contains crucial information about the causal structure of space-time, a new proposal is formulated for the time-evolution of quantum states in order to account for the fundamental classical property that outer observers cannot receive signals from inside a horizon. The simple case of a single massive free particle at rest is used throughout the paper as a toy model to illustrate the main ideas.

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arXiv2013

What is the Schwarzschild radius of a quantum mechanical particle?

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arXiv2013

Horizon wave-function for single localized particles: GUP and quantum black hole decay

A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. In order to combine these two pictures, we introduce a horizon wave-function determined by the particle wave-function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass be a black hole. We also show that our construction entails an effective Generalised Uncertainty Principle (GUP), simply obtained by adding the uncertainties coming from the two wave-functions associated to a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.

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arXiv2013

Localised particles and fuzzy horizons: A tool for probing Quantum Black Holes

The horizon is a classical concept that arises in general relativity, and is therefore not clearly defined when the source cannot be reliably described by classical physics. To any (sufficiently) localised quantum mechanical wave-function, one can associate a horizon wave-function which yields the probability of finding a horizon of given radius centred around the source. We can then associate to each quantum particle a probability that it is a black hole, and the existence of a minimum black hole mass follows naturally, which agrees with the one obtained from the hoop conjecture and the Heisenberg uncertainty principle.

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arXiv2013

Charged Black Hole Remnants at the LHC

We investigate possible signatures of long-lived (or stable) charged black holes at the Large Hadron Collider. In particular, we find that black hole remnants are characterised by quite low speed. Due to this fact, the charged remnants could, in some cases, be very clearly distinguished from the background events, exploiting dE/dX measurements. We also compare the estimate energy released by such remnants with that of typical Standard Model particles, using the Bethe-Bloch formula.

hep-ph↗

arXiv2013

Quantum Harmonic Black Holes

Inspired by the recent conjecture that black holes are condensates of gravitons, we investigate a simple model for the black hole degrees of freedom that is consistent both from the point of view of Quantum mechanics and of General Relativity. Since the two perspectives should "converge" into a unified picture for small, Planck size, objects, we expect our construction is a useful step for understanding the physics of microscopic, quantum black holes. In particular, we show that a harmonically trapped condensate gives rise to two horizons, whereas the extremal case (corresponding to a remnant with vanishing Hawking temperature) naturally falls out of its spectrum.

hep-th↗

arXiv2013

Charged shells and elementary particles

We review the General Relativistic model of a (quasi) point-like particle represented by a massive shell of electrically charged matter, which displays an ADM mass M equal to the electric charge |Q| in the small-volume limit. We employ the Israel-Darboux's junction equations to explicitly derive this result, and then study the modifications introduced by the existence of a minimum length scale lambda. For lambda of the order of the Planck length (or larger), we find that the ADM mass becomes equal to the bare mass m_0 of the shell, like it occurs for the neutral case.

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arXiv2012

Brane-world stars and (microscopic) black holes

We study stars in the brane-world by employing the principle of minimal geometric deformation and find that brane-world black hole metrics with a tidal charge are consistently recovered in a suitable limit. This procedure allows us to determine the tidal charge as a function of the black hole ADM mass (and brane tension). A minimum mass for semiclassical microscopic black holes can then be derived, with a relevant impact for the description of black hole events at the LHC.

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arXiv2012

Minimum black hole mass from colliding Gaussian packets

We study the formation of a black hole in the collision of two Gaussian packets. Rather than following their dynamical evolution in details, we assume a horizon forms when the mass function for the two packets becomes larger than half the flat areal radius, as it would occur in a spherically symmetric geometry. This simple approximation allows us to determine the existence of a minimum black hole mass solely related to the width of the packets. We then comment on the possible physical implications, both in classical and quantum physics, and models with extra spatial dimensions.

hep-th↗

arXiv2012

Black Hole Remnants at the LHC

We investigate possible signatures of black hole events at the LHC in the hypothesis that such objects will not evaporate completely, but leave a stable remnant. For the purpose of defining a reference scenario, we have employed the publicly available Monte Carlo generator CHARYBDIS2, in which the remnant's behavior is mostly determined by kinematic constraints and conservation of some quantum numbers, such as the baryon charge. Our findings show that electrically neutral remnants are highly favored and a significantly larger amount of missing transverse momentum is to be expected with respect to the case of complete decay.

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arXiv2011

On the Unruh effect in de Sitter space

We give an interpretation of the temperature in de Sitter universe in terms of a dynamical Unruh effect associated with the Hubble sphere. As with the quantum noise perceived by a uniformly accelerated observer in static space-times, observers endowed with a proper motion can in principle detect the effect. In particular, we study a "Kodama observer" as a two-field Unruh detector for which we show the effect is approximately thermal. We also estimate the back-reaction of the emitted radiation and find trajectories associated with the Kodama vector fields are stable.

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arXiv2011

Bubble dynamics: (nucleating) radiation inside dust

We consider two spatially flat Friedmann-Robertson-Walker spacetimes divided by a time-like thin shell in the nontrivial case in which the inner region of finite extension contains radiation and the outer region is filled with dust. We will then show that, while the evolution is determined by a large set of constraints, an analytical description for the evolution of the bubble radius can be obtained by formally expanding for short times after the shell attains its minimum size. In particular, we will find that a bubble of radiation, starting out with vanishing expansion speed, can be matched with an expanding dust exterior, but not with a collapsing dust exterior, regardless of the dust energy density. The former case can then be used to describe the nucleation of a bubble of radiation inside an expanding dust cloud, although the final configuration contains more energy than the initial dust, and the reverse process, with collapsing radiation transforming into collapsing dust, is therefore energetically favored. We however speculate a (small) decaying vacuum energy or cosmological constant inside dust could still trigger nucleation. Finally, our perturbative (yet analytical) approach can be easily adapted to different combinations of matter inside and outside the shell, as well as to more general surface density, of relevance for cosmology and studies of defect formation during phase transitions.

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