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