Retarded Green's Functions In Perturbed Spacetimes For Cosmology and Gravitational Physics

Abstract

Electromagnetic and gravitational radiation do not propagate solely on the null cone in a generic curved spacetime. They develop "tails," traveling at all speeds equal to and less than unity. If sizeable, this off-the-null-cone effect could mean objects at cosmological distances, such as supernovae, appear dimmer than they really are. Their light curves may be distorted relative to their flat spacetime counterparts. These in turn could affect how we infer the properties and evolution of the universe or the objects it contains. Within the gravitational context, the tail effect induces a self-force that causes a compact object orbiting a massive black hole to deviate from an otherwise geodesic path. This needs to be taken into account when modeling the gravitational waves expected from such sources. Motivated by these considerations, we develop perturbation theory for solving the massless scalar, photon and graviton retarded Green's functions in perturbed spacetimes, assuming these Green's functions are known in the background spacetime. In particular, we elaborate on the theory in perturbed Minkowski spacetime in significant detail; and apply our techniques to compute the retarded Green's functions in the weak field limit of the Kerr spacetime to first order in the black hole's mass and angular momentum. Our methods build on and generalizes work appearing in the literature on this topic to date, and lays the foundation for a thorough, first principles based, investigation of how light propagates over cosmological distances, within a spatially flat inhomogeneous Friedmann-Lemaître-Robertson-Walker (FLRW) universe. This perturbative scheme applied to the graviton Green's function, when pushed to higher orders, may provide approximate analytic (or semi-analytic) results for the self-force problem in the weak field limits of the Schwarzschild and Kerr black hole geometries.

23 pages, 5 figures. Significant updates in v2: Scalar, photon and graviton Green's functions calculated explicitly in Kerr black hole spacetime up to first order in mass and angular momentum (Sec. V); Visser's van Vleck determinant result shown to be equivalent to ours in Sec. II. v3: JWKB discussion moved to introduction; to be published in PRD

References in corpus (2)

• Radiation reaction and gravitational waves in the effective field theory approach
• Modification to the Luminosity Distance Redshift Relation in Modified Gravity Theories

Cited by in corpus (15)

• Self-force effects in post-Minkowskian scattering
• BMS-like symmetries in cosmology
• Galileon forces in the Solar System
• Transverse-Traceless Gravitational Waves In A Spatially Flat FLRW Universe: Causal Structure from Dimension Reduction
• More On Cosmological Gravitational Waves And Their Memories
• The Graviton Tail almost Completely Wags the Dog
• Dynamic Field Theory and Equations of Motion in Cosmology
• A Line Source In Minkowski For The de Sitter Spacetime Scalar Green's Function: Massless Minimally Coupled Case
• Non-perturbative results for the luminosity and area distances
• Finite-Size Effects On The Self-Force
• Gravitational glint: Detectable gravitational wave tails from stars and compact objects
• Rotations of the polarization of a gravitational wave propagating in Universe
• A Line Source in Minkowski for the de Sitter Spacetime Scalar Green's Function: Massive Case
• Scalar Wave Tails in Even Dimensional Weakly Curved Static Newtonian Spacetimes
• Late time tails and nonlinear memories in asymptotically de Sitter spacetimes