Linearized gravity in terms of differential forms

Abstract

Abstract.A technique to linearize gravitational field equations is developed in which the perturbation metric coefficients are treated as second rank, symmetric, 1-form fields belonging to the Minkowski background spacetime by using the exterior algebra of differential forms.

Nonminimal couplings, gravitational waves, and torsion in Horndeski’s theory

“…For flat backgrounds, linearized gravity in first-order formalism can be found in Ref. [37]. The separation that we achieve in eqs.…”

Impulsive gravitational waves in general massive 3D gravity

“…As an illustration of the expediency of the differential forms language, let us briefly discuss the linearization of the field equations ( 20) as a 2-form equation around the Minkowski background [26]. By using the field equations (20) with λ = 0 and ignoring the Cotton part temporarily for the sake of simplicity of the argument, the linearization of the NMG equations can readily be written as a 2-form equation in the Minkowski spacetime as…”

“…Moreover, the mass parameters m ∓ in Eq. ( 47), which are defined previously for flat background in (26), are now defined by the relations of the form…”

Abbott-Deser energy in connection with Thirring's superpotentials

“…where orthonormal coframe basis {ē a } stands for the natural Cartesian basis {dx a } for the flat background. Using the perturbation 1-forms φ a and assuming the flat background in the linearization formula discussed in the previous sections, the expression for the can be reduced to [16]…”

“…We now turn to a brief discussion of the AD construction involving background Killing vector fields. Let us assume that the gravitational Lagrangian density n-form L = L[g, λ] depends on the metric tensor whose field equations can be derived from coframe variations of the form * E a ≡ δL δe a (16) where E a ≡ E ab e b are the covector-valued 1-forms and λ denotes the cosmological constant.…”