Book Review: The Experience of God: Icons of the Mystery

A review of The Experience of God: Icons of the Mystery by Raimon Panikkar

Density of solutions to quadratic congruences

A classical result in number theory is Dirichlet's theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k>1. Building upon a proof by E.M. Wright in 1954, we compute the natural density of such numbers where each prime satisfies a congruence condition. As an application, we obtain the density of squarefree n not greater than x with k prime factors such that a fixed quadratic equation has exactly 2^k solutions modulo n

Book Review:\u3cem\u3ePilgrimage of Awakening: The Extraordinary Lives of Murray and Mary Rogers\u3c/em\u3e

Book Review of Pilgrimage of Awakening: The Extraordinary Lives of Murray and Mary Rogers. By Mary V. T. Cattan. Eugene, OR: Wipf & Stock, 2016, 421 pages

Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity

We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in the sense of Ashtekar and Hansen. Using a cylindrical 3-manifold of both null and spatial directions of approach towards spatial infinity, we impose appropriate regularity conditions on the Weyl tensor near spatial infinity along null directions. The asymptotic Einstein equations on this 3-manifold and the regularity conditions imply that the relevant Weyl tensor components on past null infinity are antipodally matched to those on future null infinity. The subalgebra of totally fluxless supertranslations near spatial infinity provides a natural isomorphism between the BMS-supertranslations on past and future null infinity. This proves that the flux of the supermomenta is conserved from past to future null infinity in a classical gravitational scattering process provided additional suitable conditions are satisfied at the timelike infinities.Comment: v2: corrected formula for epsilon in Eqs. A.4E and A.9 v1: (published version in JHEP) 49 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1808.0786