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Full-Text Articles in Physical Sciences and Mathematics
Sub-Planckian Black Holes And The Generalized Uncertainty Principle, Bernard Carr, Jonas R. Mureika, Piero Nicolini
Sub-Planckian Black Holes And The Generalized Uncertainty Principle, Bernard Carr, Jonas R. Mureika, Piero Nicolini
Physics Faculty Works
The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under M ↔ M−1 naturally implies a Generalized Uncertainty Principle with the linear form Δx∼1/Δp+Δp. We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble …
How Spherical Is A Cube (Gravitationally)?, Jeff Sanny, David M. Smith
How Spherical Is A Cube (Gravitationally)?, Jeff Sanny, David M. Smith
Physics Faculty Works
An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center.1,2 By integrating over ring elements of a spherical shell, we show that the gravitational force on a point mass outside the shell is the same as that of a particle with the same mass as the shell at its center. This derivation works for objects with spherical symmetry while depending on the fact that the gravitational …