Coincidence limit and generalized interaction term structure in multigravity

TL;DR

This paper analyzes the structure of interaction terms in multigravity theories, defining the coincidence limit, deriving compatibility conditions, and exploring invariant volumes and mass terms in weak field limits.

Contribution

It introduces a generalized interaction term structure, derives a compatibility equation, and provides formulas for invariant volume and mass terms in multigravity.

Findings

Derived a general formula for multigravity invariant volume using three means.

Obtained the Pauli-Fierz mass term for bigravity in the weak field limit.

Analyzed the properties of the scalar potential and invariant volume in multigravity.

Abstract

Generalized structure of the interaction term of multigravity is analyzed in detail. The coincidence limit of any multigravity theory is defined and the compatibility equation for the interaction potential is derived which is studied in the weak perturbation limit of metric. The most general properties of the invariant volume and the scalar potential of multigravity are investigated. The general formula for multigravity invariant volume using three means (arithmetic, geometric and harmonic) is derived. The Pauli-Fierz mass term for bigravity in the weak field limit is obtained.