Compatibility Complex for Black Hole Spacetimes
Journal article, 2021

The set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (Aksteiner and Bäckdahl in Phys Rev Lett 121:051104, 2018) is shown to be complete. In particular, any gauge invariant quantity for linearized gravity on Kerr that is local and of finite order in derivatives can be expressed in terms of these gauge invariants and derivatives thereof. The proof is carried out by constructing a complete compatibility complex for the Killing operator, and demonstrating the equivalence of the gauge invariants from Aksteiner and Bäckdahl (Phys Rev Lett 121:051104, 2018) with the first compatibility operator from that complex.


Steffen Aksteiner

Max Planck Society

Lars Andersson

Max Planck Society

Thomas Bäckdahl

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Max Planck Society

Igor Khavkine

Czech Academy of Sciences

Bernard Whiting

University of Florida

Communications in Mathematical Physics

0010-3616 (ISSN) 1432-0916 (eISSN)

Vol. 384 3 1585-1614

Subject Categories

Algebra and Logic


Mathematical Analysis



More information

Latest update