Quantizing Gravitational Collapse

I summarize some results obtained from a canonical quantization of gravitational collapse. The quantization is carried out in Kuchar variables on the LeMaitre-Tolman-Bondi family of spacetimes. I show how mass quantization, the black hole entropy and Hawking radiation may be understood in these models. Hawking radiation is obtained in the WKB approximation but the first order quantum gravity correction makes the near-horizon spectrum non-thermal, suggesting that unitarity is preserved. The quantization may be used to study quantum gravity effects in collapse leading to the formation of both covered and naked singularities.Comment: 7 pages, LaTeX. Contribution to the proceedings of QTS3, held the University of Cincinnati, September 10-14, 200

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 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.Comment: 12 pages, no figures. Title changed. Discussion added. Version to appear in Nucl. Phys.

Dark Radiation and Localization of Gravity on the Brane

We discuss the dynamics of a spherically symmetric dark radiation vaccum in the Randall-Sundrum brane world scenario. Under certain natural assumptions we show that the Einstein equations on the brane form a closed system. For a de Sitter brane we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We define the conditions leading to singular or globally regular solutions. We also analyse the localization of gravity near the brane and show that a phase transition to a regime where gravity propagates away from the brane may occur at short distances during the collapse of positive dark energy density.Comment: 7 pages, latex with 2 eps figures. Talk given by Rui Neves, Fourth International Workshop on New Worlds in Astroparticle Physics, Algarve University, Faro, 5-7 September, 2002. To be published in the corresponding proceedings, World Scientifi

Inhomogeneous Dark Radiation Dynamics on a de Sitter Brane

Assuming spherical symmetry we analyse the dynamics of an inhomogeneous dark radiation vaccum on a Randall and Sundrum 3-brane world. Under certain natural conditions we show that the effective Einstein equations on the brane form a closed system. On a de Sitter brane and for negative dark energy density we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We also identify the conditions leading to the formation of a singularity or of regular bounces inside the dark radiation vaccum.Comment: 6 pages, LaTeX, 1 EPS figure. Talk given at the Workshop The Cosmology of Extra Dimensions and Varying Fundamental Constants of the Conference JENAM 2002, The Unsolved Universe: Challenges for the Future, 2-7 September 2002, Porto, Portuga