Dust Collapse Research Articles

Dust Evolution in Protoplanetary Discs and the Formation of Planetesimals

After 25 years of laboratory research on protoplanetary dust agglomeration, a consistent picture of the various processes that involve colliding dust aggregates has emerged. Besides sticking, bouncing and fragmentation, other effects, like, e.g., erosion or mass transfer, have now been extensively studied. Coagulation simulations consistently show that $\rm \mu$m-sized dust grains can grow to mm- to cm-sized aggregates before they encounter the bouncing barrier, whereas sub-$\rm \mu$m-sized water-ice particles can directly grow to planetesimal sizes. For siliceous materials, other processes have to be responsible for turning the dust aggregates into planetesimals. In this article, these processes are discussed, the physical properties of the emerging dusty or icy planetesimals are presented and compared to empirical evidence from within and without the Solar System. In conclusion, the formation of planetesimals by a gravitational collapse of dust "pebbles" seems the most likely.

Cylindrically symmetric inhomogeneous dust collapse with a zero expansion component

We investigate a class of cylindrically symmetric inhomogeneous Λ-dust spacetimes which have a regular axis and some zero expansion component. For , we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For , we recover the Senovilla–Vera metric and show that it can be locally matched to an Einstein–Rosen type of exterior. Finally, we explore some consequences of the matching, such as trapped surface formation and gravitational radiation in the exterior.

Non-singular Brans–Dicke collapse in deformed phase space

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.

Black Hole Paradoxes

We propose here that the well-known black hole paradoxes such as the information loss and teleological nature of the event horizon are restricted to a particular idealized case, which is the homogeneous dust collapse model. In this case, the event horizon, which defines the boundary of the black hole, forms initially, and the singularity in the interior of the black hole at a later time. We show that, in contrast, gravitational collapse from physically more realistic initial conditions typically leads to the scenario in which the event horizon and space-time singularity form simultaneously. We point out that this apparently simple modification can mitigate the causality and teleological paradoxes, and also lends support to two recently suggested solutions to the information paradox, namely, the ‘firewall’ and ‘classical chaos’ proposals.

Quantum dust collapse in2+1dimension

In this paper we will examine the consequence of a canonical theory of quantum dust collapse in 2+1 dimensions. The solution of the WDW equation describing the collapse indicates that collapsing shells outside the apparent horizon are accompanied by outgoing shells within the apparent horizon during their collapse phase and stop collapsing once they reach the apparent horizon. Taking this picture of quantum collapse seriously, we determine a static solution with energy density corresponding to a dust ball whose collapse has terminated at the apparent horizon. We show that the boundary radius of the ball is larger than the BTZ radius confirming that no event horizon is formed. The ball is sustained by radial pressure which we determine and which we attribute to the Unruh radiation within it.

Genericity aspects of black hole formation in the collapse of spherically symmetric slightly inhomogeneous perfect fluids

We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities in homogeneous collapse leading to a black hole can change the final outcome to a naked singularity. The key feature that we assume for the perturbation profile is that of a mass profile that is separable in radial and temporal coordinates. The known models of dust and homogeneous perfect fluid collapse can be obtained from this choice of the mass profile as special cases. This choice is very general and physically well motivated and we show that this class of collapse models leads to the formation of a naked singularity as the final state.

Shear-free dust solution in general covariant Hořava–Lifshitz gravity

In this paper, we have studied non stationary dust spherically symmetric spacetime, in general covariant theory ($U(1)$ extension) of the Ho\v{r}ava-Lifshitz gravity with the minimally coupling and non-minimum coupling with matter, in the post-newtonian approximation (PPN) in the infrared limit. The Newtonian prepotential $\varphi$ was assumed null. The aim of this work is to know if we can have the same spacetime, as we know in the General Relativity Theory (GRT), in Ho\v{r}ava-Lifshitz Theory (HLT) in this limit. We have shown that there is not an analogy of the dust solution in HLT with the minimally coupling, as in GRT. Using non-minimum coupling with matter, we have shown that the solution admits a process of gravitational collapse, leaving a singularity at the end. This solution has, qualitatively, the same temporal behaviour as the dust collapse in GRT. However, we have also found a second possible solution, representing a bounce behavior that is not found in GRT.

All black holes in Lemaître–Tolman–Bondi inhomogeneous dust collapse

Within the Lemaître–Tolman–Bondi formalism for the gravitational collapse of inhomogeneous dust, we analyze the parameter space that leads to the formation of a globally covered singularity (i.e. a black hole) when some physically reasonable requirements are imposed (namely, a positive, radially decreasing and quadratic profile for the energy density and the avoidance of shell crossing singularities). It turns out that a black hole can occur as the endstate of collapse only if the singularity is simultaneous, as in the standard Oppenheimer–Snyder scenario. Given a fixed density profile, there is one velocity profile for the infalling particles that will produce a black hole. All other allowed velocity profiles will terminate the collapse in a locally naked singularity.

A quantum reduction to spherical symmetry in loop quantum gravity

Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of observables corresponds to using the radial gauge for the spatial metric and allows to identify rotations around a central observer as unitary transformations in the quantum theory. Group averaging over these rotations yields our first proposal for spherical symmetry. Hamiltonians of the full theory with angle-independent lapse preserve this spherically symmetric subsector of the full Hilbert space. A second proposal consists in implementing the vanishing of a certain vector field in spherical symmetry as a constraint on the full Hilbert space, leading to a close analogue of diffeomorphisms invariant states. While this second set of spherically symmetric states does not allow for using the full Hamiltonian, it is naturally suited to implement the spherically symmetric midisuperspace Hamiltonian, as an operator in the full theory, on it. Due to the canonical structure of the reduced variables, the holonomy-flux algebra behaves effectively as a one parameter family of 2+1-dimensional algebras along the radial coordinate, leading to a diagonal non-vanishing volume operator on 3-valent vertices. The quantum dynamics thus becomes tractable, including scenarios like spherically symmetric dust collapse.

Quantum gravitational dust collapse does not result in a black hole

Quantum gravity suggests that the paradox recently put forward by Almheiri et al. (AMPS) can be resolved if matter does not undergo continuous collapse to a singularity but condenses on the apparent horizon. One can then expect a quasi-static object to form even after the gravitational field has overcome any degeneracy pressure of the matter fields. We consider dust collapse. If the collapse terminates on the apparent horizon, the Misner–Sharp mass function of the dust ball is predicted and we construct static solutions with no tangential pressure that would represent such a compact object. The collapse wave functions indicate that there will be processes by which energy extraction from the center occurs. These leave behind a negative point mass at the center which contributes to the total energy of the system but has no effect on the energy density of the dust ball. The solutions describe a compact object whose boundary lies outside its Schwarzschild radius and which is hardly distinguishable from a neutron star.

Black holes as gravitational atoms

Recently, it was argued [A. Almheiri et al., arXiv: 1207.3123, A. Almheiri et al., arXiv: 1304.6483], via a delicate thought experiment, that it is not consistent to simultaneously require that (a) Hawking radiation is pure, (b) effective field theory is valid outside a stretched horizon and (c) infalling observers encounter nothing unusual as they cross the horizon. These are the three fundamental assumptions underlying Black Hole Complementarity and the authors proposed that the most conservative resolution of the paradox is that (c) is false and the infalling observer burns up at the horizon (the horizon acts as a "firewall"). However, the firewall violates the equivalence principle and breaks the CPT invariance of quantum gravity. This led Hawking to propose recently that gravitational collapse may not end up producing event horizons, although he did not give a mechanism for how this may happen. Here we will support Hawking's conclusion in a quantum gravitational model of dust collapse. We will show that continued collapse to a singularity can only be achieved by combining two independent and entire solutions of the Wheeler–DeWitt equation. We interpret the paradox as simply forbidding such a combination. This leads naturally to a picture in which matter condenses on the apparent horizon during quantum collapse.

Gravitational Dust Collapse in f (R) Gravity

This paper is devoted to investigate gravitational collapse of dust in metric f(R) gravity. We take FRW metric for the interior region while the Schwarzchild spacetime is considered for the exterior region of a star. The junction conditions have been derived to match interior and exterior spacetimes. The assumption of constant scalar curvature is used to find a solution of field equations. Gravitational mass is found by using the junction conditions. It is concluded that the constant curvature term f(R 0) plays the role of the cosmological constant involved in the field equations of general relativity.

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 setup, 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.

Spherical gravitational collapse in 5D Einstein-Gauss-Bonnet gravity

We have considered a spherical gravitational collapse of inhomogeneous dust (and null dust) in Einstein gravity with the Gauss-Bonnet (GB) combination of quadratic curvature terms. It turns out that the presence of the coupling constant of the GB terms completely changes the causal structure of the singularities from the analogous general relativistic case. The gravitational collapse of inhomogeneous dust in the five-dimensional GB extended Einstein equations leads to formation of a massive, but weak, timelike singularity, which is forbidden in general relativity. The apparent horizons of two different collapsing solutions have shown interesting mathematical similarity.

Naked singularity explosion in higher-dimensional dust collapse

In the context of the large extra dimensions or TeV-scale gravity, it has been argued that an effective naked singularity, called the visible border of spacetime, would be generated by high-energy particle collisions. Motivated by this interesting possibility, we investigate a particle creation by a naked singularity in general dimensions, adopting a spherically symmetric self-similar dust collapse as the simple model of a naked singularity formation. The power and energy of the particle emission behave in two distinct ways depending on a parameter in the model. In a generic case, the emission power is proportional to the quadratic inverse of the remaining time to the Cauchy horizon, which has been known for the four-dimensional case in the literature. On the other hand, in a degenerate case the emission power is proportional to the quartic inverse of the remaining time to the Cauchy horizon, and depends on the total mass of a dust fluid in spite that the central region of the collapse is scale-free due to the self-similarity. In the both cases, within a test-field approximation the energy radiated before any quantum gravitational effect dominates amounts to TeV. This suggests that a backreaction is not ignorable in the TeV-scale gravity context, in contrast to the similar phenomena in stellar collapse.

New Cosmological Solutions in Massive Gravity

In this talk, we have presented new and simple cosmological solutions with flat, open, and closed spatial geometries, recently found by the present authors. The metric and the Stückelberg fields are given explicitly, showing nontrivial configurations of the Stückelberg in the usual Friedmann-Lemaître-Robertson-Walker coordinates. The solutions exhibit self-acceleration, while being free from ghost instabilities. Our solutions can be extended to include inhomogeneous dust collapse represented by the Lemaître-Tolman-Bondi metric as well. Thus, our results can be used not only to describe homogeneous and isotropic cosmology but also to study gravitational collapse in massive gravity.

Occurrence of Naked Singularities in Higher Dimensional Dust Collapse

We consider here the gravitational collapse of a inhomogeneous dust cloud described by Tolmanbondi models. We find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of initial density distribution. Collapse ends into a black hole if the dimensionless quantity ψ is greater than −22.18033 and ends into a naked singularity if ψ ≤ −22.18033. We find the occurrence of naked singularity in higher dimensional case. We proposed the concept of ‘trapped range’ of initial data in the different higher dimensional space-times. We show that ‘trapped range’ of initial data increases with the increase in dimensions of the space-times.

Bakry–Émery black holes

Scalar–tensor gravitation theories, such as the Brans–Dicke family of theories, are commonly partly described by a modified Einstein equation in which the Ricci tensor is replaced by the Bakry–Émery–Ricci tensor of a Lorentzian metric and scalar field. In physics this formulation is sometimes referred to as the ‘Jordan frame’. Just as, in General Relativity, natural energy conditions on the stress–energy tensor become conditions on the Ricci tensor, in scalar–tensor theories expressed in the Jordan frame natural energy conditions become conditions on the Bakry–Émery–Ricci tensor. We show that, if the Bakry–Émery tensor obeys the null energy condition with an upper bound on the Bakry–Émery scalar function, there is a modified notion of apparent horizon which obeys analogues of familiar theorems from General Relativity. The Bakry–Émery modified apparent horizon always lies behind an event horizon and the event horizon obeys a modified area theorem. Under more restrictive conditions, the modified apparent horizon obeys an analogue of the Hawking topology theorem in four spacetime dimensions. Since topological censorship is known to yield a horizon topology theorem independent of the Hawking theorem, in an appendix we obtain a Bakry–Émery version of the topological censorship theorem. We apply our results to the Brans–Dicke theory, and obtain an area theorem for horizons in that theory. Our theorems can be used to understand behaviour observed in numerical simulations by Scheel et al (1995 Phys. Rev. D 51 4236–49) of dust collapse in Brans–Dicke theory.

Gravitational collapse in pure Lovelock gravity in higher dimensions

We study collapse of inhomogeneous dust and null dust (Vaidya radiation) in pure Lovelock gravity in higher dimensions. Since pure Lovelock gravity is kinematic in odd d=2N+1 dimension, hence pertinent dimension for the study is even d=2N+2, where N is degree of Lovelock polynomial. It turns out that pure Lovelock collapse favors naked singularity as against black hole for the Einstein case in the same dimension while strength of singularity as measured by divergence of Kretshmann scalar is interestingly the same in the two cases; i.e. the corresponding scalars have the same fall off behavior.

Thermalization of causal holographic information

We study causal wedges associated with a given sub-region in the boundary of asymptotically AdS spacetimes. Part of our motivation is to better understand the recently proposed holographic observable, causal holographic information (CHI), which is given by the area of a bulk co-dimension two surface lying on the boundary of the causal wedge. It has been suggested that CHI captures the basic amount of information contained in the reduced density matrix about the bulk geometry. To explore its properties further we examine its behaviour in time-dependent situations. As a simple model we focus on null dust collapse in an asymptotically AdS spacetime, modeled by the Vaidya-AdS geometry. We argue that while CHI is generically quasi-telelogical in time-dependent backgrounds, for suitable choice of sub-regions in conformal field theories, the temporal evolution of CHI is entirely causal. We comment on the implications of this observation and more generally on features of causal constructions and contrast our results with the behaviour of holographic entanglement entropy. Along the way we also derive the rate of early time growth and late time saturation (to the thermal value) of both CHI and entanglement entropy in these backgrounds.