The discussion clarifies the concepts of background metric and reference metric within the framework of General Relativity. A background metric is utilized to analyze the motion of a small body, often modeled as a test particle moving along a geodesic. In scenarios involving gravitational wave emission, the small body introduces a metric perturbation on the background metric, serving as an approximation technique. The term 'reference metric' remains undefined in this context, indicating a lack of consensus or clarity among participants.
PREREQUISITESPhysicists, researchers in gravitational wave astronomy, and students of General Relativity seeking to deepen their understanding of metric concepts and their implications in theoretical frameworks.
thanksPAllen said:Background metric is used to consider the motion of a body considered to be 'small'. In the simplest case, the small body is treated as a 'test particle' moving as a geodesic in the background metric. On the other hand, to consider backreaction from gravitational wave emission without the full machinery of numerical relativity, the small body is considered to provide a metric perturbation on top of the background metric. These are just approximation techniques. They do not suggest there are really different types of metrics in the theory of General Relativity.
I have not heard of the term 'reference metric', so I can't answer that question.