Einsteins hole dilemma and gauge freedom

TL;DR

This paper revisits the issue of gauge freedom in Einstein's theory, emphasizing how coordinate choices affect physical measurements and the interpretation of spacetime solutions, highlighting observer dependence.

Contribution

It clarifies the role of gauge fixing in general relativity and demonstrates the observer-dependent nature of solutions and measurements.

Findings

Gauge fixing influences measurement results.

Exterior spacetime geometry depends on gauge choice.

Solutions in general relativity are observer-dependent.

Abstract

The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric generated by static spherically symmetric distribution of matter can be matched with wide family of vacuum solution and the exterior spacetime geometry could not be deduced directly from the interior perfect fluid solution, without reference to a gauge fixing or viceversa. The property of sollutions in general relativity is indeed an observer dependent concept.