Analytical proxy to families of numerical solutions: the case study of spherical mini-boson stars

TL;DR

This paper introduces a simple analytical proxy method for entire families of numerical solutions of Einstein's equations, demonstrated on spherical mini-boson stars, to facilitate data compression and broader analysis.

Contribution

It proposes a novel approach using basis expansions to create proxies for families of solutions, aiding in data reduction and analysis across parameter spaces.

Findings

Effective in reducing data size for solution families

Demonstrated on spherical mini-boson stars as a case study

Highlights challenges in covering large parameter spaces

Abstract

The Einstein field equations, or generalizations thereof, are difficult to solve analytically. On the other hand, numerical solutions of the same equations have become increasingly common, in particular concerning compact objects. Whereas analytic approximations to each individual solution within a numerical family have been proposed, proxies for whole families are missing, which can facilitate studying properties across the parameter space, data compression and a wider usage of such solutions. In this work we tackle this need, proposing a simple strategy based on two different expansions of the unknown functions in an appropriately chosen basis, to build such proxy. We use as an exploratory case-study spherical, fundamental mini-boson stars, to illustrate the feasibility of such an approach, emphasise its advantage in reducing the data size, and the challenges, say, in covering large parameter spaces.