G\"odel Incompleteness and the Black Hole Information Paradox

Semiclassical reasoning suggests that the process by which an object collapses into a black hole and then evaporates by emitting Hawking radiation may destroy information, a problem often referred to as the black hole information paradox. Further, there seems to be no unique prediction of where the information about the collapsing body is localized. We propose that the latter aspect of the paradox may be a manifestation of an inconsistent self-reference in the semiclassical theory of black hole evolution. This suggests the inadequacy of the semiclassical approach or, at worst, that standard quantum mechanics and general relavity are fundamentally incompatible. One option for the resolution for the paradox in the localization is to identify the G\"odel-like incompleteness that corresponds to an imposition of consistency, and introduce possibly new physics that supplies this incompleteness. Another option is to modify the theory in such a way as to prohibit self-reference. We discuss various possible scenarios to implement these options, including eternally collapsing objects, black hole remnants, black hole final states, and simple variants of semiclassical quantum gravity.Comment: 14 pages, 2 figures; revised according to journal requirement

Gravitational collapse of spherically symmetric stars in noncommutative general relativity

Gravitational collapse of a class of spherically symmetric stars is investigated. We quantise the geometries describing the gravitational collapse by a deformation quantisation procedure. This gives rise to oncommutative spacetimes with gravitational collapse

Methodology to evaluate alternative coastal zone management policies: Application in the Texas coastal zone: Example Application III: Environmental and Economic Impacts of Recreational Community Development, Mustang Island and North Padre Island. Volum I - Final Report

National Science Foundation, Grant No. AEN74-13590-A01Division of Planning Coordination Office of the Governor of TexasCenter for Water and the Environmen