Daniele Malafarina

Recent developments in gravitational collapse and spacetime singularities

It is now known that when a massive star collapses under the force of its own gravity, the final fate of such a continual gravitational collapse will be either a black hole or a naked singularity under a wide variety of physically reasonable circumstances within the framework of general theory of relativity. The research of recent years has provided considerable clarity and insight on stellar collapse, black holes and the nature and structure of spacetime singularities. We discuss several of these developments here. There are also important fundamental questions that remain unanswered on the final fate of collapse of a massive matter cloud in gravitation theory, especially on naked singularities which are hypothetical astrophysical objects and on the nature of cosmic censorship hypothesis. These issues have key implications for our understanding on black hole physics today, its astrophysical applications, and for certain basic questions in cosmology and possible quantum theories of gravity. We consider these issues here and summarize recent results and current progress in these directions. The emerging astrophysical and observational perspectives and implications are discussed, with particular reference to the properties of accretion disks around black holes and naked singularities, which may provide characteristic signatures and could help distinguish these objects.

Terminating black holes in asymptotically free quantum gravity

We study the homogeneous gravitational collapse of a spherical cloud of matter in a super-renormalizable and asymptotically free theory of gravity. We find a picture that differs substantially from the classical scenario. The central singularity appearing in classical general relativity is replaced by a bounce, after which the cloud re-expands indefinitely. We argue that a black hole, strictly speaking, never forms. The collapse only generates a temporary trapped surface, which can be interpreted as a black hole when the observational timescale is much shorter than the one of the collapse. However, it may also be possible that the gravitational collapse produces a black hole and that after the bounce the original cloud of matter evolves into a new universe.

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The nature of the super-massive black hole candidates in galactic nuclei can be tested by analyzing the profile of the K

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iron line profile from accretion disks around regular and singular exotic compact objects

iron line observed in their X-ray spectrum. In this paper, we consider the possibility that the spacetime in the immediate vicinity of these objects may be described by some non vacuum exact solutions of Einsteins equations resulting as the end-state of gravitational collapse. The vacuum far away portion of the spacetime is described by the Schwarzschild metric, while the interior part may be either regular or have a naked singularity at the center. The iron line generated around this class of objects has specific features, which can be used to distinguish such objects from Kerr black holes. In particular, their iron line cannot have the characteristic low-energy tail of the line generated from accretion disks around fast-rotating Kerr black holes. We can thus conclude that the super-massive black hole candidates whose spin parameter has been estimated to be close to 1 assuming the Kerr background cannot be this kind of objects.

Distinguishing black holes from naked singularities through their accretion disc properties

We show that, in principle, a slowly evolving gravitationally collapsing perfect fluid cloud can asymptotically settle to a static spherically symmetric equilibrium configuration with a naked singularity at the center. We consider one such asymptotic final configuration with a finite outer radius, and construct a toy model in which it is matched to a Schwarzschild exterior geometry. We examine the properties of circular orbits in this model. We then investigate the observational signatures of a thermal accretion disc in this spacetime, comparing them with the signatures expected for a disc around a black hole of the same mass. Several notable differences emerge. A disc around the naked singularity is much more luminous than one around an equivalent black hole. Also, the disc around the naked singularity has a spectrum with a high frequency power law segment that carries a major fraction of the total luminosity. Thus, at least some naked singularities can, in principle, be distinguished observationally from the black holes of the same mass. We discuss the possible implications of these results.

Equilibrium configurations from gravitational collapse

We develop here a new procedure within Einstein’s theory of gravity to generate equilibrium configurations that result as the final state of gravitational collapse from regular initial conditions. As a simplification, we assume that the collapsing fluid is supported only by tangential pressure. We show that the equilibrium geometries generated by this method form a subset of static solutions to the Einstein equations, and that they can either be regular or develop a naked singularity at the center. When a singularity is present, there are key differences in the properties of stable circular orbits relative to those around a Schwarzschild black hole with the same mass. Therefore, if an accretion disk is present around such a naked singularity it could be observationally distinguished from a disk around a black hole.

Circular geodesics and accretion disks in the Janis-Newman-Winicour and gamma metric spacetimes

We study here circular timelike geodesics in the Janis-Newman-Winicour and Gamma metric spacetimes which contain a strong curvature naked singularity and reduce to the Schwarzschild metric for a specific value of one of the parameters. We show that for both the metrics the range of allowed parameters can be divided into three regimes where structure of the circular geodesics is qualitatively different. It follows that the properties of the accretion disks around such naked singularities can be significantly different from those of disks around black holes. This adds to previous studies showing that if naked singularities exist in nature, their observational signature would be significantly different from that of the black hole.

Note on the effect of a massive accretion disk in the measurements of black hole spins

The spin measurement of black holes has important implications in physics and astrophysics. Regardless of the specific technique to estimate the black hole spin, all the current approaches assume that the space-time geometry around the compact object is exactly described by the Kerr solution. This is clearly an approximation, because the Kerr metric is a stationary solution of the vacuum Einstein equations. In this paper, we estimate the effect of a massive accretion disk in the measurement of the black hole spin with a simple analytical model. For typical accretion disks, the mass of the disk is completely negligible, even for future more accurate measurements. However, for systems with very massive disks the effect may not be ignored.

Singularity avoidance in quantum-inspired inhomogeneous dust collapse

In a previous paper, some of us studied general relativistic homogeneous gravitational collapses for dust and radiation, in which the density profile was replaced by an effective density justified by some quantum gravity models. It was found that the effective density introduces an effective pressure that becomes negative and dominant in the strong-field regime. With this set-up, the central singularity is replaced by a bounce, after which the cloud starts expanding. Motivated by the fact that in the classical case homogeneous and inhomogeneous collapse models have different properties, here we extend our previous work to the inhomogeneous case. As in the quantum-inspired homogeneous collapse model, the classical central singularity is replaced by a bounce, but the inhomogeneities strongly affect the structure of the bounce curve and of the trapped region.