We analyze the frequency shift of photons propagating on an asymptotically flat spacetime describing a collapsing, spherical dust cloud. We focus on the case where the interaction of the photons with the matter can be neglected. Under fairly general assumptions on the initial data characterizing the collapse, we show that photons with zero angular momentum which travel from past to future null infinity, crossing the collapsing cloud through its center, are always redshifted with respect to stationary observers. We compute this redshift as a function of proper time of a distant stationary observer and discuss its dependency on the mass distribution of the cloud. Possible implications of this redshift effect for weak cosmic censorship and light propagation in cosmological spacetimes are also briefly discussed.
It is well known that static wormhole configurations in general relativity (GR) are possible only if matter threading the wormhole throat is "exotic"---i.e., violates a number of energy conditions. For this reason, it is impossible to construct {static} wormholes supported only by dust-like matter which satisfies all usual energy conditions. However, this is not the case for non-static configurations. In 1934, Tolman found a general solution describing the evolution of a spherical dust shell in GR. In this particular case, Tolman's solution describes the collapsing dust ball; the inner space--…
The present paper deals with the gravitational collapse of an inhomogeneous spherical star consisting of dust fluid in the background of dark energy components with linear equation of state. We discussed the development of apparent horizon to investigate the black-hole formation in gravitational collapsing process. The collapsing process is examined first separately for dust cloud and dark energy and then under the combined effect of dust interacting with dark energy. It is obtained that when only dust cloud or dark energy is present the collapse leads to the formation of black-hole under cert…
We investigate the fate of the classical singularity in a collapsing dust cloud. For this purpose, we quantize the marginally bound Lemaitre-Tolman-Bondi model for spherically-symmetric dust collapse by considering each dust shell in the cloud individually, taking the outermost shell as a representative. Because the dust naturally provides a preferred notion of time, we can construct a quantum mechanical model for this shell and demand unitary evolution for wave packets. It turns out that the classical singularity can generically be avoided provided the quantization ambiguities fulfill some we…
The work is devoted to the search for explicit isometric embeddings of a metric corresponding to the collapse of spherically symmetric matter with the formation of a black hole. Two approaches are considered: in the first, the embedding is constructed for the whole manifold at once; in the second, the idea of a junction of solutions, obtained separately for areas inside and outside the dust ball, is used. In the framework of the first approach, a global smooth embedding in 7D space with a signature (2 + 5) was constructed. It corresponds to the formation of the horizon as a result of matter fa…
We investigate gravitational collapse of a spherically symmetric thin shell in the Einstein-Gauss-Bonnet (EGB) gravity. Under the recently proposed 4D limit, we find that the collapsing shell will be bounced back at a small radius, without forming a singularity. This bouncing behavior is similar to those of a test particle and a homogeneous spherical dust star, in accordance with the expectation that the Gauss-Bonnet term will modify the small scale behavior of the Einstein gravity. We analyze the causal structure of the dynamic spacetime that represents the bouncing process, finding that the …
In three-dimensional low-energy string theory, we study the formation of a black string from a dust cloud. We analytically obtain two distinct classes of exact solutions with arbitrary functions responsible for mass distributions of the dust cloud. The first and second kinds of solutions may describe collapsing dusts but the first kind is only for inhomogeneous dust distribution while the second kind has a homogeneous limit. The finite collapse time and the Israel junction conditions tell us that the first kind solution describes a desired collapsing phenomenon, whereas the scale factor in the…
The fate of matter forming a black hole is still an open problem, although models of quantum gravity corrected black holes are available. In loop quantum gravity (LQG) models were presented, which resolve the classical singularity in the centre of the black hole by means of a black-to-white hole transition, but neglect the collapse process. The situation is similar in other quantum gravity approaches, where eternal non-singular models are available. In this paper, a strategy is presented to generalise these eternal models to dynamical collapse models by surface matching. Assuming 1) the validi…
The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychaudhuri equations and could be reduced to them when there is no torsion. Using the Einstein-Cartan-Sciama-Kibble field equations the effective stress-energy tensor is derived. We also consider an Oppenheimer-Snyder model for the gravitational collapse of dust. It is shown that the null energy condition (NEC) is violated before the density of the collapsing dust reaches the Planck den…
Based on the effective dynamics in the $\bar μ$ scheme of the spherical symmetry reduced model in the reduced phase space formulation of loop quantum gravity (LQG), we investigate the gravitational collapse of a homogeneous dust cloud, with Gaussian dust serving as both the reference field and the source of the gravitational collapse. The effective dynamics from the considered model for a homogeneous dust cloud reduces precisely to the effective dynamics of loop quantum cosmology (LQC) with extrinsic curvature based K-quantization, indicating that the LQC effective dynamics lives as a subsecto…
There is a viable vector-tensor gravity (VTG) theory, whose vector field produces repulsive forces leading to important effects. In the background universe, the effect of these forces is an accelerated expansion identical to that produced by vacuum energy (cosmological constant). Here, we prove that another of these effects arises for great enough collapsing masses which lead to Schwarzschild black holes and singularities in general relativity (GR). For these masses, pressure becomes negligible against gravitational attraction and the complete collapse cannot be stopped in the context of GR; h…
The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static ob…
We analyze the stability of the Cauchy horizon associated with a globally naked, shell-focussing singularity arising from the complete gravitational collapse of a spherical dust cloud. In previous work, we have studied the dynamics of spherical test scalar fields on such a background. In particular, we proved that such fields cannot develop any divergences which propagate along the Cauchy horizon. In the present work, we extend our analysis to the more general case of test fields without symmetries and to linearized gravitational perturbations with odd parity. To this purpose, we first conside…
In the quantum treatment of collapsing matter, a viable mode analysis is supposed to give information regarding emission during the collapse. Nevertheless, partly owing to operator ordering ambiguities involved in a typical quantum gravity analysis, the availability of such well-defined modes is not guaranteed. We study the mode decomposition of the unitarily evolving wave packet constructed for the quantum model of spherically symmetric dust collapsing in a marginally bound Lema\^ıtre-Tolman-Bondi (LTB) model. We identify the observable depicting mode decomposition, and using the freedom of o…
We study the quantum gravitational collapse of spherically symmetric pressureless dust. Using an effective equation derived from a polymer quantization in the connection-triad phase space variables of general relativity, we find numerically, for a variety of initial dust configurations, that (i) trapped surfaces form and disappear as an initially collapsing density profile evolves into an outgoing shockwave; (ii) black hole lifetime is proportional to the square of its mass; and (iii) there is no mass inflation at inner apparent horizons. These results provide a substantially different view of…
In the functional Schrodinger formalism, we obtain the wave function describing collapsing dust in an anti-de Sitter background, as seen by a co-moving observer, by mapping the resulting variable mass Schrodinger equation to that of the quantum isotonic oscillator. Using this wave function, we perform a causal de Broglie-Bohm analysis, and obtain the corresponding quantum potential. We construct a bouncing geometry via a disformal transformation, incorporating quantum effects. We derive the external solution that matches with this smoothly, and is also quantum corrected. Due to a pressure term…
Inhomogeneous dust collapse in five-dimensional AdS-Chern-Simons gravity
Facultad de Ciencias, Universidad Arturo Prat（阿图罗·普拉特大学理学院）；Instituto de Ciencias Exactas y Naturales (ICEN), Universidad Arturo Prat（阿图罗·普拉特大学精确与自然科学研究所）；Departamento de Ciencias Exactas, Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院精确科学系）
In three-dimensional AdS space, we consider the gravitational collapse of dust shell and then investigate the quantum radiation from the collapsing shell by employing the functional Schrödinger formalism. In the formation of the BTZ black hole, the interior geometry of the shell can be chosen as either the massless black hole or the global AdS space. In the incipient black hole limit, we obtain the wave function exactly from the time-dependent Schrödinger equation for a massless scalar field. Then, we show that the occupation number of excited states can be written by analytic expressions, and…
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is tentatively assumed (the continuity of the metric and its first derivatives on the time-…
