Finite size effects in DBI and Born-Infeld for screened spherically symmetric objects

TL;DR

This paper investigates how finite size influences the linear response of spherically symmetric objects in Born-Infeld and DBI theories, revealing a hierarchy in multipole responses that could inform about the object's size and screening scale.

Contribution

It extends previous point-like models by analyzing finite-sized objects, showing how their response coefficients differ and establishing a hierarchy between multipoles based on size and screening effects.

Findings

Finite size causes non-zero response coefficients for higher multipoles.

A hierarchy between even and odd multipoles is established.

Potential measurements can reveal the object's size and screening scale.

Abstract

We study finite size effects on the linear response of spherically symmetric objects in Born-Infeld (BI) electromagnetism and Dirac-Born-Infeld (DBI) scalar field theories. Previous works show that the linear response coefficients for a point-like source vanish for odd multipoles above the dipole, a feature that resembles the vanishing of Love numbers for black holes. This work goes beyond the point-like idealisation and considers a sphere of finite radius. We find that the vanishing of the linear response coefficients ceases as they acquire a correction due to the finite size of the object. This introduces a hierarchy between the even and odd multipoles of the response coefficients determined by the separation of scales between the radius of the sphere and the screening scale of non-linearities. From a phenomenological viewpoint, the hierarchy between the odd and even multipoles would give access to the screening scale and the object's radius by measuring the behaviour of the potentials at infinity.