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Fabio Scardigli

Publications and source records attributed to Fabio Scardigli.

At least 19 recordsLinked to original sources
arXiv2026

Quasinormal modes of Bonanno-Reuter black holes via the Spectral Method

In this work, we explore the quasinormal modes (QNMs) of the Bonanno-Reuter black hole, one of the first regular black hole metric suggested by the Asymptotically Safe Gravity (ASG) program. The running parameter $\alpha$ is set to a positive value, the related running Newton coupling vanishes at high energies, fully achieving an ultraviolet fixed point and eliminating non-physical UV divergences. This yields a singularity-free geometry. Hence, we focus on the resulting renormalisation-group-improved Schwarzschild metric, which naturally produces an (Anti)deSitter non-singular core. On the basis of this background, we compute the QNM spectrum for scalar, electromagnetic, and gravitational perturbations by employing the Spectral Method (SM). This method, recognised for its enhanced precision compared to high-order WKB methods, allows the identification of fundamental modes, extensive collections of overtones, and purely imaginary overdamped modes that were entirely missed in previous analyses. These characteristics, resolved here for the first time in the Bonanno-Reuter black hole, underscore the crucial importance of high-precision spectral methods in investigating delicate signatures of black hole models inspired by quantum gravity.

gr-qc↗
arXiv2026

Spectral Analysis of Quasinormal Modes of Planck Stars

We investigate the quasinormal modes (QNMs) of Planck stars within the framework of scale-dependent gravity (SDG). In our setup, the running parameter $\alpha$ is fixed to a negative value by matching the effective Newtonian potential to the one-loop EFT result. As a consequence, the associated running Newton coupling does not realise the ultraviolet fixed point of asymptotically safe gravity, and the geometry should be interpreted as an SDG-inspired effective metric rather than a realisation of asymptotically safe gravity itself. We focus on the resulting renormalisation-group-improved Schwarzschild metric, which naturally yields a finite-size Planck-density core. Building on this background, we compute the QNM spectrum for scalar, electromagnetic, and gravitational perturbations using the Spectral Method (SM). This approach, known for its superior accuracy over high-order WKB schemes, enables the detection of fundamental modes, large families of overtones, and purely imaginary overdamped modes that are entirely missed in previous analysis. Our results reveal a robust Martini glass morphology of the oscillatory spectrum across perturbation sectors, nearly equally spaced overdamped modes with characteristic anomalous gaps, and the emergence, in the gravitational sector, of isolated overdamped modes separated from the main sequence by exceptionally large frequency intervals. These features, resolved here for the first time in the Planck-star context, underscore the importance of high-precision spectral techniques in probing subtle signatures of quantum-gravity-inspired black hole models.

gr-qc↗
arXiv2025

Exponential distance relation (aka Titius-Bode rule) in extra solar planetary systems

In this paper we present phenomenological evidence for the validity of an exponential distance relation (also known as generalized Titius-Bode law) in the 32 planetary systems (31 extra solar, plus our Solar System) containing at least 5 planets each (known up to July 2023). We produce the semi-log fittings of the data, and we check them against the statistical indicators of $R^2$ and $Median$. Then we compare them with the data of 4000 artificial planetary systems created at random. In this way, a possible origin by chance of the Titius-Bode rule (TBR) is reasonably excluded. We also point out that in some systems the fittings can be definitely improved by the insertion of new planets into specific positions. We discuss the Harmonic Resonances method and fittings, and compare them with the Titius-Bode fittings. Moreover, for some specific systems, we compare the Titius-Bode fitting against a polynomial fitting ($r\sim n^2$). Further comparisons with previous relevant works are reported in the last section. It emerges that TBR describes 25 out of the 32 planetary systems ($78\%$) with a $R^2\geq 0.95$. Further, it results to be the most economical (in terms of free parameters) and best fitting law for the description of spacing among planetary orbits. This analysis allows us to conclude that an exponential distance relation can reasonably be considered as ``valid'', or strongly corroborated, also in extra solar planetary systems.

astro-ph.EP↗
arXiv2025

Gravitational Collapse in Scale-Dependent Gravity

In this paper we study an Oppenheimer-Snyder (OS)-like gravitational collapse in the general framework of scale-dependent gravity. We explore the collapse in spherically symmetric solutions suggested both by asymptotically safe gravity (characterized by a positive $\om$-parameter) and by scale-dependent gravity (negative $\om$-parameter), when a singularity at a finite positive radial coordinate is developed. The inner geometry of the collapsing star is described, as usual, by a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, and matter is uniformly distributed without any assumptions about its equation of state. The outer asymptotically-safe/scale-dependent black hole metric is smoothly matched to the inner geometry, and this yields the equation of motion of the star surface, the energy density, pressure, and equation of state of the collapsing matter. We study in detail the proper-time evolution of the event and apparent horizons. Finally, the constraints of the energy conditions on the equation of state, and its properties, are considered and discussed.

gr-qc↗
arXiv2023

Planck Stars from a Scale-dependent Gravity theory

Scale dependence of fundamental physical parameters is a generic feature of ordinary quantum field theory. When applied to gravity, this idea produces effective actions generically containing a running Newtonian coupling constant, from which new (spherically symmetric) black hole spacetimes can be inferred. As a minimum useful requirement, of course, the new metrics should match with a Schwarzschild field at large radial coordinate. By further imposing to the new scale dependent metric the simple request of matching with the Donoghue quantum corrected potential, we find a not yet explored black hole spacetime, which naturally turns out to describe the so-called Planck stars.

gr-qc↗
arXiv2023

Minimum length (scale) in Quantum Field Theory, Generalized Uncertainty Principle and the non-renormalisability of gravity

The notions of minimum geometrical length and minimum length scale are discussed with reference to correlation functions obtained from in-in and in-out amplitudes in quantum field theory. Whereas the in-in propagator for metric perturbations does not admit the former, the in-out Feynman propagator shows the emergence of the latter. A connection between the Feynman propagator of quantum field theories of gravity and the deformation parameter $δ_0$ of the generalised uncertainty principle (GUP) is then exhibited, which allows to determine an exact expression for $δ_0$ in terms of the residues of the causal propagator. A correspondence between the non-renormalisability of (some) theories (of gravity) and the existence of a minimum length scale is then conjectured to support the idea that non-renormalisable theories are self-complete and finite. The role played by the sign of the deformation parameter is further discussed by considering an implementation of the GUP on the lattice.

hep-th↗
arXiv2022

Uncertainty principle and gravity

We give a pedagogical introduction to the generalized uncertainty principle (GUP), by showing how it naturally emerges when the action of gravity is taken into account in measurement processes. We review some physical predictions of the GUP. In particular we focus on the bounds that present experimental tests can put on the value of the deformation parameter $β$, and on the prediction of black hole remnants, which are a good candidate for dark matter. In passing, we also quote a theoretical value computed for $β$, and swiftly comment on the vast parameter region still unexplored, and to be probed by future experiments.

gr-qc↗
arXiv2022

Generalized uncertainty principle and Asymptotic Safe gravity

We present a procedure to link the deformation parameter $β$ of the generalized uncertainty principle (GUP) to the two free parameters $\om$ and $γ$ of the running Newtonian coupling constant of the Asymptotic Safe gravity (ASG) program. To this aim, we compute the Hawking temperature of a black hole in two different ways. The first way involves the use of the GUP in place of the Heisenberg uncertainty relations, and therefore we get a deformed Hawking temperature containing the parameter $β$. The second way involves the deformation of the Schwarzschild metric due to the Newtonian coupling constant running according to the AS gravity prescription. The comparison of the two techniques yields a relation between $β$ and $\om$, $γ$. As a particular case, we discuss also the so called $ξ$-model. The relations between $β$ and $\om$, $ξ$ allow us to transfer upper bounds from one parameter to the others.

hep-th↗
arXiv2021

Bekenstein bound and uncertainty relations

The non zero value of Planck constant $h$ underlies the emergence of several inequalities that must be satisfied in the quantum realm, the most prominent one being Heisenberg Uncertainty Principle. Among these inequalities, Bekenstein bound provides a universal limit on the entropy that can be contained in a localized quantum system of given size and total energy. In this Letter, we explore how Bekenstein bound is affected when Heisenberg uncertainty relation is deformed so as to accommodate gravitational effects close to Planck scale (Generalized Uncertainty Principle). By resorting to general thermodynamic arguments, and in regimes where the equipartition theorem still holds, we derive in this way a "generalized Bekenstein bound". Physical implications of this result are discussed for both cases of positive and negative values of the deformation parameter.

hep-th↗
arXiv2020

Generalized Uncertainty Principle in three-dimensional gravity and the BTZ black hole

We investigate the structure of the gravity-induced Generalized Uncertainty Principle in three dimensions. The subtleties of lower dimensional gravity, and its important differences with respect to four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, $R_g$, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the $M \neq 0$ Bañados-Teitelboim-Zanelli micro black hole furnishes the most consistent $R_g$. This allows us to obtain a suitable formula for the Generalized Uncertainty Principle in three dimensions, and also to estimate the corrections induced by the latter on the Hawking temperature and Bekenstein entropy. We also point to the extremal $M=0$ case, and its natural unit of length introduced by the cosmological constant, $\ell = 1 / \sqrt{-Λ}$, as a possible alternative to $R_g$, and present a condensed matter analog realization of this scenario.

hep-th↗
arXiv2019

Heuristic derivation of Casimir effect in minimal length theories

We propose a heuristic derivation of Casimir effect in the context of minimal length theories based on a Generalized Uncertainty Principle (GUP). By considering a GUP with only a quadratic term in the momentum, we compute corrections to the standard formula of Casimir energy for the parallel-plate geometry, the sphere and the cylindrical shell. For the first configuration, we show that our result is consistent with the one obtained via more rigorous calculations in Quantum Field Theory. Experimental developments are finally discussed.

hep-th↗
arXiv2019

Some considerations on Determinism and Free Will

This article has been written, in a slightly different version, as an introductory chapter for the book collecting the essays of theoretical physicist Gerard 't Hooft, philosopher Emanuele Severino, and theologian Piero Coda, and inspired by the talks the three authors made as keynote speakers at the conference "Determinism and Free Will", held at the Cariplo Foundation Congress Center in Milan on May 13, 2017.

physics.hist-ph↗
arXiv2019

The deformation parameter of the generalized uncertainty principle

After a short introduction to the generalized uncertainty principle (GUP), we review some of the physical predictions of the GUP, and we focus in particular on the bounds that present experimental tests can put on the value of the deformation parameter $β$. We also describe a theoretical value computed for $β$, and comment on the vast parameter region still unexplored, and to be probed by future experiments.

hep-th↗
arXiv2018

Spacetimes as topological spaces, and the need to take methods of general topology more seriously

Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology sufficient for the description of spacetime singularities or a topology which incorporates the causal structure? Or both? Is it more preferable to have a topology with as many physical properties as possible, whose description might be complicated and counterintuitive, or a topology which can be described via a countable basis but misses some important information? These are just a few from the questions that we ask in this Chapter, which serves as a critical review of the terrain and contains a survey with remarks, corrections and open questions.

math-ph↗
arXiv2018

Modified Unruh effect from Generalized Uncertainty Principle

We consider a generalized uncertainty principle (GUP) corresponding to a deformation of the fundamental commutator obtained by adding a term quadratic in the momentum. From this GUP, we compute corrections to the Unruh effect and related Unruh temperature, by first following a heuristic derivation, and then a more standard field theoretic calculation. In the limit of small deformations, we recover the thermal character of the Unruh radiation. Corrections to the temperature at first order in the deforming parameter are compared for the two approaches, and found to be in agreement as for the dependence on the cubic power of the acceleration of the reference frame. The dependence of the shifted temperature on the frequency is also pointed out and discussed.

hep-th↗
arXiv2017

Lorentz violation and generalized uncertainty principle

Investigations on possible violation of Lorentz invariance have been widely pursued in the last decades, both from theoretical and experimental sides. A comprehensive framework to formulate the problem is the standard model extension (SME) proposed by A.Kostelecky, where violation of Lorentz invariance is encoded into specific coefficients. Here we present a procedure to link the deformation parameter $β$ of the generalized uncertainty principle (GUP) to the SME coefficients of the gravity sector. The idea is to compute the Hawking temperature of a black hole in two different ways. The first way involves the deformation parameter $β$, and therefore we get a deformed Hawking temperature containing the parameter $β$. The second way involves a deformed Schwarzschild metric containing the Lorentz violating terms $\bar{s}^{μν}$ of the gravity sector of the SME. The comparison between the two different techniques yields a relation between $β$ and $\bar{s}^{μν}$. In this way bounds on $β$ transferred from $\bar{s}^{μν}$ are improved by many orders of magnitude when compared with those derived in other gravitational frameworks. Also the opposite possibility of bounds transferred from $β$ to $\bar{s}^{μν}$ is briefly discussed.

hep-th↗
arXiv2017

GUP parameter from quantum corrections to the Newtonian potential

We propose a technique to compute the deformation parameter of the generalized uncertainty principle by using the leading quantum corrections to the Newtonian potential. We just assume General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum. With these minimal assumptions our calculation gives, to first order, a specific numerical result. The physical meaning of this value is discussed, and compared with the previously obtained bounds on the generalized uncertainty principle deformation parameter.

hep-th↗