The Goldberg-Sachs theorem in linearized gravity
S. Dain, O. M. Moreschi
TL;DR
This paper demonstrates that the Goldberg-Sachs theorem, crucial for constructing algebraically special solutions in Einstein's vacuum equations, does not hold in linearized gravity, impacting the understanding of linearized solutions' physical significance.
Contribution
It proves that the Goldberg-Sachs theorem is invalid in linearized gravity, revealing limitations of algebraic classification in approximate solutions.
Findings
Goldberg-Sachs theorem does not apply in linearized gravity
Most physical vacuum solutions are algebraically special
Implications for understanding linearized gravitational solutions
Abstract
The Goldberg-Sachs theorem has been very useful in constructing algebraically special exact solutions of Einstein vacuum equation. Most of the physical meaningful vacuum exact solutions are algebraically special. We show that the Goldberg-Sachs theorem is not true in linearized gravity. This is a remarkable result, which gives light on the understanding of the physical meaning of the linearized solutions.
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