2024/03/11 by Miltiadis Paschalis, Paschalis, Miltiadis
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2403.06562
In this paper we establish Hardy and Heisenberg uncertainty-type inequalities for the exterior of a Schwarzschild black hole. The weights that appear in both inequalities are tailored to fit the geometry, and can both be compared to the related Riemannian distance from the event horizon to yield inequalities for that distance. Moreover, in both cases the classic Euclidean inequalities with a point singularity can be recovered in the limit where one stands "far enough" from the black hole, as expected from the asymptotic flatness of the metric.