Saddle stresses for generic theories with a preferred acceleration scale

TL;DR

This paper develops a scaling method to generate tidal stress templates for a broad class of MONDian theories with a preferred acceleration scale, enabling tests in the solar system via missions like LISA Pathfinder.

Contribution

It introduces a scaling prescription that simplifies the generation of tidal stress templates for alternative gravity theories, bypassing complex numerical computations.

Findings

LPF can tightly constrain the acceleration scale a_0 and parameter κ.

The scaling method applies to moon saddle predictions, aiding mission planning.

The approach separates local tests from astrophysical and cosmological constraints.

Abstract

We show how scaling arguments may be used to generate templates for the tidal stresses around saddles for a vast class of MONDian theories {\it detached from their obligations as dark matter alternatives}. Such theories are to be seen simply as alternative theories of gravity with a preferred acceleration scale, and could be tested in the solar system by extending the LISA Pathfinder (LPF) mission. The constraints thus obtained may then be combined, if one wishes, with requirements arising from astrophysical and cosmological applications, but a clear separation of the issues is achieved. The central technical content of this paper is the derivation of a scaling prescription allowing complex numerical work to be bypassed in the generation of templates. We find that LPF could constrain very tightly the acceleration $a_0$ and the free parameter $\kappa$ present in these theories. As an application of our technique we also produce predictions for the moon saddle (for which a similar scaling argument is applicable) with the result that we recommend that it should be included in orbit design.