Spacetime Encodings I- A Spacetime Reconstruction Problem

TL;DR

This paper discusses the theoretical development of an algorithmic approach to reconstruct the spacetime structure of a compact object from gravitational wave observations, aiming to understand its gravitational nature.

Contribution

It introduces a mathematical framework for a machine that can reconstruct spacetime metrics from gravitational radiation data, advancing gravitational wave data analysis.

Findings

Proposes a mathematical outline for spacetime reconstruction

Highlights the potential of gravitational wave observations for spacetime analysis

Lays groundwork for future algorithmic implementations

Abstract

This paper explores features of an idealized mathematical machine (algorithm) that would be capable of reconstructing the gravitational nature (the multipolar structure or spacetime metric) of a compact object, by observing gravitational radiation emitted by a small object that orbits and spirals into it. An outline is given of the mathematical developments that must be carried out in order to construct such a machine.