Causality of Massive Spin 2 Field in External Gravity

TL;DR

This paper explores the conditions under which a massive spin 2 field interacts consistently with external gravity, identifying specific spacetime backgrounds and parameters that ensure causal propagation and correct degrees of freedom.

Contribution

It introduces a family of theories for massive spin 2 fields in external gravity, highlighting conditions for causality, gauge invariance, and the massless limit in arbitrary dimensions.

Findings

Existence of a one-parameter family of causal theories in vacuum Einstein spacetimes.

Identification of gauge invariance at a specific parameter value as the massless limit.

Discovery of a parameter value leading to non-physical gauge invariance.

Abstract

We investigate the structure of equations of motion and lagrangian constraints in a general theory of massive spin 2 field interacting with external gravity. We demonstrate how consistency with the flat limit can be achieved in a number of specific spacetimes. One such example is an arbitrary static spacetime though equations of motion in this case may lack causal properties. Another example is provided by external gravity fulfilling vacuum Einstein equations with arbitrary cosmological constant. In the latter case there exists one-parameter family of theories describing causal propagation of the correct number of degrees of freedom for the massive spin 2 field in arbitrary dimension. For a specific value of the parameter a gauge invariance with a vector parameter appears, this value is interpreted as massless limit of the theory. Another specific value of the parameter produces gauge invariance with a scalar parameter and this cannot be interpreted as a consistent massive or massless theory.