Roberto Casadio

Anisotropic solutions by gravitational decoupling

We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.

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 determined by spatially localised modes.

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.

Effective fluid description of the dark universe

Abstract 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.

Quantum corpuscular corrections to the Newtonian potential

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 analyzing 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.

Horizon quantum mechanics of rotating black holes

The horizon quantum mechanics is an approach that was previously introduced in order to analyze 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 disfavor extremal (macroscopic) geometries.

Emergence of a dark force in corpuscular gravity

We investigate the emergent laws of gravity when dark energy and the de Sitter space-time are modeled as a critical Bose-Einstein condensate of a large number of soft gravitons NG. We argue that this scenario requires the presence of various regimes of gravity in which NG scales in different ways. Moreover, the local gravitational interaction affecting baryonic matter can be naturally described in terms of gravitons pulled out from this dark energy condensate (DEC). We then explain the additional component of the acceleration at galactic scales, commonly attributed to dark matter, as the reaction of the DEC to the presence of baryonic matter. This additional dark force is also associated to gravitons pulled out from the DEC and correctly reproduces the modified Newtonian dynamics (MOND) acceleration. It also allows for an effective description in terms of general relativity sourced by an anisotropic fluid. We finally calculate the mass ratio between the contribution of the apparent dark matter and the baryonic matter in a region of size r at galactic scales and show that it is consistent with the.CDM predictions.

Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources

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.

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.

Generalised uncertainty principle Hawking fermions from minimally geometric deformed black holes

Roberto Casadio,1, 2, ∗ Piero Nicolini,3, † and Roldão da Rocha4, ‡ Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna, Italy INFN, Sezione di Bologna, viale B. Pichat 6, 40127 Bologna, Italy Frankfurt Institute of Advanced Studies (FIAS) and Institut für Theoretische Physik, Goethe Universitat, Frankfurt am Main, Germany Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-580, Santo André, Brazil.