TY - JOUR

T1 - Retarded Green's functions in perturbed spacetimes for cosmology and gravitational physics

AU - Chu, Yi Zen

AU - Starkman, Glenn D.

PY - 2011/12/9

Y1 - 2011/12/9

N2 - 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 g μν=g ̄μν+h μν, assuming these Green's functions are known in the background spacetime g ̄μν. In particular, we elaborate on the theory in perturbed Minkowski spacetime in significant detail; and we 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 M and angular momentum S. Our methods build on and generalize work appearing in the literature on this topic to date, and lay 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 universe. This perturbative scheme applied to the graviton Green's function, when pushed to higher orders, may provide approximate analytic (or semianalytic) results for the self-force problem in the weak field limits of the Schwarzschild and Kerr black hole geometries.

AB - 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 g μν=g ̄μν+h μν, assuming these Green's functions are known in the background spacetime g ̄μν. In particular, we elaborate on the theory in perturbed Minkowski spacetime in significant detail; and we 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 M and angular momentum S. Our methods build on and generalize work appearing in the literature on this topic to date, and lay 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 universe. This perturbative scheme applied to the graviton Green's function, when pushed to higher orders, may provide approximate analytic (or semianalytic) results for the self-force problem in the weak field limits of the Schwarzschild and Kerr black hole geometries.

UR - http://www.scopus.com/inward/record.url?scp=84855312670&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.84.124020

DO - 10.1103/PhysRevD.84.124020

M3 - 期刊論文

AN - SCOPUS:84855312670

SN - 1550-7998

VL - 84

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 12

M1 - 124020

ER -