Reparametrization invariance of the classical metric

TL;DR

This paper argues that the classical metric is invariant under reparametrization, countering recent claims that it depends on parametrization, thus reaffirming the metric's fundamental invariance.

Contribution

The paper provides a proof demonstrating the reparametrization invariance of the classical metric, challenging recent assertions of parametrization dependence.

Findings

Classical metric is reparametrization invariant.

Counterexample to recent claims of parametrization dependence.

Reaffirms the fundamental invariance of the classical metric.

Abstract

There is a statement on the parametrization dependence of the classical metric in the recent paper of N.E.J. Bjerrum-Bohr, J.F. Donoghue, B.R. Holstein, gr-qc/0610096. I completely disagree with this statement. Here I show reparametrization invariance of the classical metric.