Tabasum Rahnuma “Recursive Construction of the Gravitational Field via Multipolar Post-Minkowskian Expansion”

by Tabasum Rahnuma (KIAS)

Thursday 11 Jun 2026, 16:00 → 18:00 Asia/Seoul

We construct the exterior metric of a stationary compact source within the multipolar post-Minkowskian (MPM) formalism, reformulated directly in momentum space. The MPM framework solves the vacuum Einstein equations outside a compact source by expanding perturbatively in Newton's constant(G), and decomposing the metric into symmetric trace-free mass and current multipole moments. Working in momentum space, where the multipolar structure emerges naturally from the recursive field equations, we solve Einstein's equations iteratively to higher PM orders. The recursive structure makes explicit the nonlinear multipole interactions — including monopole, quadrupole, and higher-order couplings — and simplifies the organization of tensor structures at each PM order.

As a consistency check, we match the generic multipolar solution to the Kerr metric, verifying that the recursive construction reproduces the full Kerr multipole tower and its defining moment relations. This confirms that the momentum-space MPM formulation correctly captures the nonlinear structure of rotating vacuum solutions. Besides, to establish the formalism, I will show how to construct the Kerr black hole metric independently via solving Einstein’s equations recursively, where the perturbation theory is a double expansion in G and spin-length a. The framework provides a technically efficient basis for higher-order multipolar calculations and for connecting classical multipolar expansions with modern amplitude-based approaches to general relativity.