Classification of Surface Charges for a Spin 2 Field on a Curved Background Solution

Abstract

We give an explicit proof of the result that non trivial conserved n − 2 forms for a spin 2 field on a background corresponding to a solution to Einstein's equation (with or without cosmological constant) are characterized uniquely by the Killing vector fields of the background.

Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

“…• for n ≥ 3, that all n − 2 forms that are closed for all solutions h of the linearized theory are given, on solutions h, by k ξ for some Killing vector ξ, up to d exact n − 2 forms which do not contribute to the integrals [15,17,18],…”

Three-dimensional origin of Gödel spacetimes and black holes

“…When α 2 l 2 = 1, the limit µ → 0 can be taken smoothly in the coordinatesr = γr,t = t/γ in which the solution becomes The charge differences between a given solution (g µν , A µ ) and an infinitesimally close one (g µν + δg µν , A µ + δA µ ) are controlled by the linearized theory around (g µν , A µ ). The equivalence classes of conserved n− 2-forms (here 1-forms) of the linearized theory can be shown [26,27] to be in one-to-one correspondence with gauge parameters (ξ µ , ǫ) satisfying…”

Note on the first law withp-form potentials

“…Indeed, decomposing δA = n ∧ ω (1) + φ * δA, one sees that the term involving n do not contribute because of the antisymmetry of H. Therefore, the second term in (34) will vanish if H is regular and if the pull-back φ * δA on the future horizon is regular.…”