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 $\textit{Martini glass}$ 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.

United Arab Emirates

Davide Batic

Denys Dutykh

Italy

Canada

Fabio Scardigli

Spectral analysis of quasinormal modes of Planck stars

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 <math><msub><mrow><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msub></math> of the generalised uncertainty principle (GUP) is then exhibited, which allows to determine an exact expression for <math><msub><mrow><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msub></math> 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.

Roberto Casadio

Wenbin Feng

Brazil

Iberê Kuntz

Minimum length (scale) in quantum field theory, generalized uncertainty principle and the non-renormalisability of gravity

We present a procedure to link the deformation parameter <math><mi>β</mi></math> of the generalized uncertainty principle (GUP) to the two free parameters <math><mover><mi>ω</mi><mo>˜</mo></mover></math> and <math><mi>γ</mi></math> of the running Newtonian coupling constant of the asymptotically safe gravity 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 <math><mi>β</mi></math>. The second way involves the deformation of the Schwarzschild metric due to the Newtonian coupling constant running according to the asymptotically safe gravity prescription. The comparison of the two techniques yields a relation between <math><mi>β</mi></math> and <math><mover><mi>ω</mi><mo>˜</mo></mover></math>, <math><mi>γ</mi></math>. As a particular case, we discuss also the so-called <math><mi>ξ</mi></math>-model. The relations between <math><mi>β</mi></math> and <math><mover><mi>ω</mi><mo>˜</mo></mover></math>, <math><mi>ξ</mi></math> allow us to transfer upper bounds from one parameter to the others.

Gaetano Lambiase

Generalized uncertainty principle and asymptotically safe gravity

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.

Japan

Luca Buoninfante

Giuseppe Gaetano Luciano

Luciano Petruzziello

Netherlands

Bekenstein bound and uncertainty relations

The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out here that the two effects are mutually exclusive when compared with experimental bounds. Moreover, the former stems from modified Poisson brackets obtained from a wrong classical limit of the deformed canonical commutators.

Generalized Uncertainty Principle, Classical Mechanics, and General Relativity

We investigate the structure of the gravity-induced generalized uncertainty principle in three dimensions. The subtleties of lower-dimensional gravity, and its important differences concerning four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, <math><msub><mi>R</mi><mi>g</mi></msub></math>, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the <math><mi>M</mi><mo>≠</mo><mn>0</mn></math> Bañados-Teitelboim-Zanelli micro-black-hole furnishes the most consistent <math><msub><mi>R</mi><mi>g</mi></msub></math>. 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 <math><mi>M</mi><mo>=</mo><mn>0</mn></math> case, and its natural unit of length introduced by the cosmological constant, <math><mo>ℓ</mo><mo>=</mo><mn>1</mn><mo>/</mo><msqrt><mrow><mo>−</mo><mi>Λ</mi></mrow></msqrt></math>, as a possible alternative to <math><msub><mi>R</mi><mi>g</mi></msub></math>, and present a condensed matter analog realization of this scenario.

Czechia

Alfredo Iorio

Pablo Pais

Generalized uncertainty principle in three-dimensional gravity and the BTZ black hole

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.

Massimo Blasone

Gaetano Luciano

Modified Unruh effect from 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 <math><mrow><mi>β</mi></mrow></math> of the generalized uncertainty principle 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 <math><mi>β</mi></math>, and therefore we get a deformed Hawking temperature containing the parameter <math><mi>β</mi></math>. The second way involves a deformed Schwarzschild metric containing the Lorentz violating terms <math><msup><mover><mi>s</mi><mo>¯</mo></mover><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> of the gravity sector of the SME. The comparison between the two different techniques yields a relation between <math><mi>β</mi></math> and <math><msup><mover><mi>s</mi><mo>¯</mo></mover><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math>. In this way bounds on <math><mi>β</mi></math> transferred from <math><msup><mover><mi>s</mi><mo>¯</mo></mover><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> are improved by many orders of magnitude when compared with those derived in other gravitational frameworks. Also the opposite possibility of bounds transferred from <math><mi>β</mi></math> to <math><msup><mover><mi>s</mi><mo>¯</mo></mover><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> is briefly discussed.

Lorentz violation and generalized uncertainty principle

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.

Kuwait

Elias C. Vagenas

GUP parameter from quantum corrections to the Newtonian potential

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a generalized uncertainty principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard general relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.