Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light

We study the dynamical consequences of Maggiore's unique generalised uncertainty principle (GUP). We find that it leads naturally, and generically, to novel consequences. In the high temperature limit, there is a drastic reduction in the degrees of freedom, of the type found, for example, in strings far above the Hagedorn temperature. In view of this, the present GUP may perhaps be taken as the new version of the Heisenberg uncertainty principle, conjectured by Atick and Witten to be responsible for such reduction. Also, the present GUP leads naturally to varying speed of light and modified dispersion relations. They are likely to have novel implications for cosmology and black hole physics, a few of which we discuss qualitatively.Comment: Latex file. 15 pages. Version 2: Typo corrected. Version 3: References added. To appear in Physics Letters

Size of Black Holes through Polymer Scaling

We imagine the strings on the stretched horizon of any $d$ space-time dimensional black hole to be bits of polymer. Then, proposing an interaction between these bits we obtain the size of the configuration, and thus of the black hole, using the scaling laws. The transition from a typical black hole state to a typical string state has a simple explanation, which also holds for the extremal black holes.Comment: Latex file, 8 page