The Case Against Smooth Null Infinity IV: Linearised Gravity Around Schwarzschild -- An Overview

2024/01/08 by Leonhard M. A. Kehrberger, Kehrberger, Lionor · 5 citations
Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Pulsars and Gravitational Waves Research

paper · pdf · doi:10.48550/arxiv.2401.04170

openalex publication_date 2024/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic setups. It provides an overview of the physical ideas involved in setting up the mathematical problem, the mathematical challenges that need to be overcome once the problem is posed, as well as the main new results we obtain in the companion paper [KM24]. From the physical perspective, this includes a discussion of how Post-Newtonian theory provides a prediction on the gravitational radiation emitted by N infalling masses from the infinite past in the intermediate zone, i.e. up to some finite advanced time. From the mathematical perspective, we then take this prediction, together with the condition that there be no incoming radiation from I^-, as a starting point to set up a scattering problem for the linearised Einstein vacuum equations around Schwarzschild and near spacelike infinity, and we outline how to solve this scattering problem and obtain the asymptotic properties of the scattering solution near i⁰ and I⁺. The full mathematical details are presented in the companion paper [KM24].

Citations

• Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
• Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
• Multipole expansions of gravitational radiation
• An Approach to Gravitational Radiation by a Method of Spin Coefficients
• On the relation between asymptotic charges, the failure of peeling and late-time tails
• Global stability of Minkowski spacetime with minimal decay

Cited by

• Twisting asymptotically-flat spacetimes
• Asymptotic Simplicity and Scattering in General Relativity from Quantum Field Theory
• Controlled regularity at future null infinity from past asymptotic initial data: the wave equation
• From spatial to null infinity: Connecting initial data to peeling
• Newman-Penrose-like exact and approximate conservation laws: a covariant and conformal formulation

Related

• The Case Against Smooth Null Infinity I: Heuristics and Counter-Examples
• The Case Against Smooth Null Infinity V: Early-Time Asymptotics of Linearised Gravity Around Schwarzschild for Fixed Spherical Harmonic Modes
• A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole II: The Full System
• Estimates for the Maxwell field near the spatial and null infinity of the Schwarzschild spacetime
• Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: forward asymptotics and scattering from infinity