LeMaître-Tolman-Bondi models of spherical dust collapse have been used and continue to be used extensively to study various stellar collapse scenarios. It is by now well known that these models lead to the formation of black holes and naked singularities from regular initial data. The final outcome of the collapse, particularly in the event of naked singularity formation, depends very heavily on quantum effects during the final stages. These quantum effects cannot generally be treated semiclassically as quantum fluctuations of the gravitational field are expected to dominate before the final state is reached. We present a canonical reduction of LeMaître-Tolman-Bondi space-times describing the marginally bound collapse of inhomogeneous dust, in which the physical radius R, the proper time of the collapsing dust , and the mass function F are the canonical coordinates R(r), (r) and F(r) on the phase space. Dirac's constraint quantization leads to a simple functional ͑Wheeler-DeWitt͒ equation. The equation is solved and the solution can be employed to study some of the effects of quantum gravity during gravitational collapse with different initial conditions.
We extend the classical and quantum treatment of the Lemaı ˆtre-Tolman-Bondi (LTB) model to the nonmarginal case (defined by the fact that the shells of the dust cloud start with a nonvanishing velocity at infinity). We present the classical canonical formalism and address with particular care the boundary terms in the action. We give the general relation between dust time and Killing time. Employing a lattice regularization, we then derive and discuss for particular factor orderings exact solutions to all quantum constraints.
Following Ruffini and Bonazzola, we use a quantized boson field to describe condensates of axions forming compact objects. Without substantial modifications, the method can only be applied to axions with decay constant, f a , satisfying δ = (f a / M P ) 2 1, where M P is the Planck mass. Similarly, the applicability of the Ruffini-Bonazzola method to axion stars also requires that the relative binding energy of axions satisfies1, where E a and m a are the energy and mass of the axion. The simultaneous expansion of the equations of motion in δ and ∆ leads to a simplified set of equations, depending only on the parameter, λ = √ δ / ∆ in leading order of the expansions. Keeping leading order in ∆ is equivalent to the infrared limit, in which only relevant and marginal terms contribute to the equations of motion. The number of axions in the star is uniquely determined by λ. Numerical solutions are found in a wide range of λ. At small λ the mass and radius of the axion star rise linearly with λ. While at larger λ the radius of the star continues to rise, the mass of the star, M , attains a maximum at λ max 0.58. All stars are unstable for λ > λ max . We discuss the relationship of our results to current observational constraints on dark matter and the phenomenology of Fast Radio Bursts.
There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. We argue that the semiclassical approximation (i.e. quantum field theory on a classical curved background) used in these analyses ceases to be valid about one Planck time before the epoch of naked singularity formation, because by then the curvature in the central region of the star reaches Planck scale. It is shown that during the epoch in which the semiclassical approximation is valid, the total emitted energy is about one Planck unit, and is not divergent. We also argue that back reaction in this model does not become important so long as gravity can be treated classically. It follows that the further evolution of the star will be determined by quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time scale or settles down into a black hole state.Comment: 16 pages, paper rewritten into sections, conclusions unchanged, 4 references added, to appear in Phys. Rev. D (Rapid Communication
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.
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