The omega-tends-to-infinity limit of Brans-Dicke theory

TL;DR

This paper clarifies the conditions under which Brans-Dicke theory approaches general relativity, showing that the limit omega-tends-to-infinity does not always lead to equivalence, especially when the matter trace vanishes.

Contribution

The paper provides a rigorous derivation of the asymptotic behavior of the Brans-Dicke scalar, clarifying misconceptions about the omega-tends-to-infinity limit.

Findings

Brans-Dicke theory does not always reduce to general relativity in the omega-tends-to-infinity limit.

The behavior of the scalar field depends on the trace of the matter energy-momentum tensor.

A new approach clarifies the conditions for the limit to hold.

Abstract

The standard tenet that Brans-Dicke theory reduces to general relativity in the omega-tends-to-infinity limit has been shown to be false when the trace of the matter energy-momentum tensor vanishes. The issue is clarified in a new approach and the asymptotic behaviour of the Brans-Dicke scalar is rigorously derived.