Quantum Raychaudhuri equation

We compute quantum corrections to the Raychaudhuri equation, by replacing classical geodesics with quantal (Bohmian) trajectories, and show that they prevent focusing of geodesics, and the formation of conjugate points. We discuss implications for the Hawking-Penrose singularity theorems, and for curvature singularities.Comment: Section on singularity theorems revised. To appear in Phys. Rev. D. 4 pages, revte

Cosmic coincidence or graviton mass?

Using the quantum corrected Friedmann equation, obtained from the quantum Raychudhuri equation, and assuming a small mass of the graviton (but consistent with observations and theory), we propose a resolution of the smallness problem(why is observed vacuum energy so small?) and the coincidence problem(why does it constitute most of the universe, about 70%, in the current epoch?).Comment: This essay received an Honorable Mention in the 2014 Gravity Research Foundation Essay Competition. 2 pages, revtex4. arXiv admin note: text overlap with arXiv:1404.309

How classical are TeV-scale black holes?

We show that the Hawking temperature and the entropy of black holes are subject to corrections from two sources: the generalized uncertainty principle and thermal fluctuations. Both effects increase the temperature and decrease the entropy, resulting in faster decay and ``less classical'' black holes. We discuss the implications of these results for TeV-scale black holes that are expected to be produced at future colliders.Comment: 10 pages, no figures, REVTeX style. Extra comments and references to match version accepted to Classical and Quantum Gravit

Lorentz invariant mass and length scales

We show that the standard Lorentz transformations admit an invariant mass (length) scale, such as the Planck scale. In other words, the frame independence of such scale is built-in within those transformations, and one does not need to invoke the principle of relativity for their invariance. This automatically ensures the frame-independence of the spectrum of geometrical operators in quantum gravity. Furthermore, we show that the above predicts a small but measurable difference between the inertial and gravitational mass of any object, regardless of its size or whether it is elementary or composite.Comment: 10 page

Comments on "Schwinger's Model of Angular Momentum with GUP" by H. Verma et al, arXiv:1808.00766

In this note, we show that the methodology and conclusions of "Schwinger's Model of Angular Momentum with GUP" [arxiv:1808.00766] are flawed and that the conclusions of "Generalized Uncertainty Principle and angular momentum" (P. Bosso and S. Das) [arxiv:1607.01083] remain valid.Comment: 3 page