99,915 research outputs found
Noncommutative gravity, a `no strings attached' quantum-classical duality, and the cosmological constant puzzle
There ought to exist a reformulation of quantum mechanics which does not
refer to an external classical spacetime manifold. Such a reformulation can be
achieved using the language of noncommutative differential geometry. A
consequence which follows is that the `weakly quantum, strongly gravitational'
dynamics of a relativistic particle whose mass is much greater than Planck mass
is dual to the `strongly quantum, weakly gravitational' dynamics of another
particle whose mass is much less than Planck mass. The masses of the two
particles are inversely related to each other, and the product of their masses
is equal to the square of Planck mass. This duality explains the observed value
of the cosmological constant, and also why this value is nonzero but extremely
small in Planck units.Comment: 7 pages. Second Prize in Gravity Research Foundation Essay
Competition, 2008. Two paragraphs added to original essay to enhance clarity.
To appear in Gen. Rel. Gra
A characterization of the central shell-focusing singularity in spherical gravitational collapse
We give a characterization of the central shell-focusing curvature
singularity that can form in the spherical gravitational collapse of a bounded
matter distribution obeying the dominant energy condition. This
characterization is based on the limiting behaviour of the mass function in the
neighbourhood of the singularity. Depending on the rate of growth of the mass
as a function of the area radius R, the singularity may be either covered or
naked. The singularity is naked if this growth rate is slower than R, covered
if it is faster than R, and either naked or covered if the growth rate is same
as R.Comment: 12 pages, Latex, significantly revised version, including change of
title. Revised version to appear in Classical and Quantum Gravit
A note on the thermodynamics of gravitational radiation
It is shown that linearized gravitational radiation confined in a cavity can
achieve thermal equilibrium if the mean density of the radiation and the size
of the cavity satisfy certain constraints.Comment: 8 pages; discussion expanded and some issues clarified; revised
version accepted for publication in Classical and Quantum Gravit
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