We analyse how different Generalised Uncertainty Principles could place bounds on the compactness of self-gravitating systems. By considering existing experimental bounds on the relevant parameters, we conclude that the compactness of large astrophysical objects is bounded above by the inverse of the GUP parameter, which would naturally be of order one. Conversely, the existence of black holes imposes stronger bounds on those parameters.

Italy

Roberto Casadio

Poland

Ilim Irfan Çimdiker

Romania

Octavian Micu

United States

Jonas Mureika

Bounded compactness from G(E)UP

We study the role of the equilibrium equation in bootstrapped Newtonian gravity (BNG) by including terms inspired by the post-Newtonian expansion of the Tolman–Oppenheimer–Volkov (TOV) equation. We then compare (approximate) BNG solutions for homogenous stars with their Newtonian and General Relativistic exact solutions. Regardless of the additional terms from the conservation equation, BNG stars do not exhibit a Buchdahl limit. However, specific extra terms added to this equation can cause the pressure to become negative inside stars with compactness smaller than the critical values for BNG black hole formation.

Star equilibrium: from BNG to TOV

We show how to reliably calculate quantum gravitational corrections to cosmological models using the unique effective action formalism for quantum gravity. Our calculations are model independent and apply to any ultra-violet complete theory of quantum gravity that admit general relativity as a low energy theory. We show that it is important to consider the full effective action to obtain renormalization group invariant solutions. We investigate the validity range of our techniques within simple cosmological models.

United Kingdom

Xavier Calmet

Marco Sebastianutti

Quantum gravitational corrections in cosmology

We study binary mergers in bootstrapped Newtonian gravity, where higher-order couplings are added to the non-relativistic Lagrangian for the Newtonian potential. In this theory, the Arnowitt-Deser-Misner (ADM) mass differs from both the proper mass of Newtonian gravity and the proper mass of general relativity, which affects the interpretation of astrophysical and cosmological events. The aforementioned difference particularly provides important phenomenological constraints for the mass of the emitted matter and the compactness of the final object after the merger. The interpretation of the GW150914 signal in this theory also shows that LIGO's findings do not violate the mass gap, contrary to usual claims. We indeed find that typical stellar black hole masses can fit LIGO's data for a considerable range of compactness values. We calculate the black hole entropy in this context, which leads to a generalised black hole area law. Non-linear effects are found to effectively change only the gravitational strength via the renormalisation of Newton's constant in this case.

Brazil

Iberê Kuntz

Binary mergers in bootstrapped Newtonian gravity: Mass gap and black hole area law

We study the quantum hair associated with coherent states describing slowly rotating black holes and show how it can be naturally related with the Bekenstein–Hawking entropy and with 1-loop quantum corrections of the metric for the (effectively) non-rotating case. We also estimate corrections induced by such quantum hair to the temperature of the Hawking radiation through the tunnelling method.

Wenbin Feng

Roldao Rocha

Hair and entropy for slowly rotating quantum black holes

We describe the ground state for a gravitationally collapsed ball of dust as the direct product of wavefunctions for dust particles distributed over an arbitrary number of nested layers. This allows us to estimate the expectation value of the global radius as well as the effective energy density and pressures for the dust core of quantum black holes. In particular, the size of the quantum core does not depend on the number of layers and the mass function is shown to grow linearly with the areal radius up to the outermost layer.

Quantum dust cores of black holes

We consider quantum-gravitational corrections to the Oppenheimer-Snyder metric describing time-dependent dust ball collapse. The interior metric also describes Friedmann-Lemaître-Robertson-Walker cosmology and our results are interpreted in that context. The exterior corrections are an example of quantum hair and are shown to persist throughout the collapse. Our results show that the quantum hair survives throughout the horizon formation and the internal state of the resulting black hole is accessible to outside observers.

Stephen D. H. Hsu

Folkert Kuipers

Quantum hair during gravitational collapse

Static and stationary regular black holes are examined under a minimal set of requirements consisting of (i) the existence of a well defined event horizon and (ii) the weak energy condition for matter sourcing the geometry. We perform our analysis by means of the gravitational decoupling approach and find hairy solutions free of curvature singularities. We identify the matter source producing a deformation of the Minkowski vacuum such that the maximum deformation is the Schwarzschild solution for the static case, and the Kerr metric for the stationary case.

Czechia

Chile

Jorge Ovalle

Switzerland

Andrea Giusti

Regular hairy black holes through Minkowski deformation

We consider black holes generically sourced by quantum matter described by regular wavefunctions. This allows for integrable effective energy densities and the removal of Cauchy horizons in spherically symmetric configurations. Moreover, we identify the ultrarigid rotation of the Kerr spacetime as causing the existence of an inner horizon in rotating systems, and describe general properties for quantum matter cores at the centre of rotating black holes with integrable singularities and no Cauchy horizon.

Quantum rotating black holes

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.