Linearized propagation equations for metric fluctuations in a general (non-vacuum) background geometry
G. Fanizza, M. Gasperini, E. Pavone, L. Tedesco
Abstract
Abstract The linearized dynamical equation for metric perturbations in a fully general, non-vacuum, background geometry is obtained from the Hamilton variational principle applied to the action up to second order. We specialize our results to the case of traceless and transverse metric fluctuations, and we discuss how the intrinsic properties of the matter stress tensor can affect (and modify) the process of gravity wave propagation even in most conventional geometric scenarios, like (for instance) those described by a FLRW metric background. We provide explicit examples for fluid, scalar field and electromagnetic field sources.
Topics & Concepts
PhysicsMetric (unit)Friedmann–Lemaître–Robertson–Walker metricClassical mechanicsAction (physics)Scalar fieldScalar (mathematics)Tensor (intrinsic definition)Electromagnetic fieldField (mathematics)Einstein field equationsMetric tensorDynamical systems theoryWave propagationGravitational waveMathematical physicsTensor fieldVariational principleGeneral relativityTransverse planeGravitationTheoretical physicsCauchy stress tensorDynamical system (definition)Field equationEffective actionElectromagnetic tensorEinsteinGeometryEinstein tensorMathematical analysisFundamental theorem of Riemannian geometryCosmology and Gravitation TheoriesPulsars and Gravitational Waves ResearchAdvanced Differential Geometry Research