Jan 25 – 27, 2023
Lindenberg cultuurhuis
Europe/Amsterdam timezone

Linear local gauge invariant observables: construction and applications

Jan 27, 2023, 2:10 PM
Valkhofzaal (Lindenberg cultuurhuis)


Lindenberg cultuurhuis

Ridderstraat 23, 6511 TM Nijmegen


Dr Igor Khavkine (Institute of Mathematics, Czech Academy of Sciences)


The Killing operator $K_{ab}[v]=\nabla_a v_b + \nabla_b v_a$ is the generator of gauge symmetries (linearized diffeomorphisms) $h_{ab}\mapsto h_{ab} + K_{ab}[v]$ in linearized gravity. A linear local gauge-invariant observable is a differential operator $I[h]$ such that $I[K[v]] = 0$ for any gauge parameter field $v_a$. A set $\{I_i[h]\}$ of such observables is complete if the simultaneous conditions $I_i[h] = 0$ are sufficient to conclude that the argument is locally a pure gauge mode, $h_{ab} = K_{ab}[v]$. The explicit knowledge of a complete set of local gauge invariant observables has multiple applications from the points of view of both physics and geometry, whenever a precise separation of physical and gauge degrees of freedom is required. I will sketch some recent progress on constructing complete sets of such observables on spacetimes of sub-maximal symmetry (like cosmologies and black holes) and applications thereof.

Primary author

Dr Igor Khavkine (Institute of Mathematics, Czech Academy of Sciences)

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