Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric chemically bond*

Journal Article · Fri May 01 00:00:00 EDT 1987 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(87)90214-4· OSTI ID:6510202

Dimock, J; Kay, B S

We consider the covariant Klein-Gordon equation (D'Alembertian/sub g/+m/sup 2/) phi = 0 of mass mgreater than or equal to0 on the exterior Schwarzschild spacetime of mass M. We introduce and study a set of outer and inner wave operators ..cap omega../sub 0//sup +- /, ..cap omega../sub 1//sup +- / (constructed in detail elsewhere) describing the asymptotic behavior of classical solutions: ..cap omega../sub 0//sup +- / for large distances and ..cap omega../sub 1//sup +- / near the Schwarzschild radius: as t..-->.. +- infinity. We re-interpret ..cap omega../sub 1//sup +- / on the Kruskal spacetime as solving a characteristic initial value problem for data on the future/past right horizon H-script/sup +- /. As a by-product, we prove (since we require it here) a stronger result than previously known concerning the stability of the Schwarzschild black hole against linearized (scalar) perturbations. Using ..cap omega../sub 0//sup +- /,..cap omega../sub 1//sup +- / we construct in and out and horizon fields for the corresponding quantum problem.

• Research Organization: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214
• OSTI ID: 6510202
• Journal Information: Ann. Phys. (N.Y.); (United States), Vol. 175:2
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
BOUNDARY-VALUE PROBLEMS
KLEIN-GORDON EQUATION
ASYMPTOTIC SOLUTIONS
SCALAR FIELDS
SCATTERING
HILBERT SPACE
MINKOWSKI SPACE
SCHWARZSCHILD METRIC
STABILITY
VACUUM STATES
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL SPACE
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
WAVE EQUATIONS
645400* - High Energy Physics- Field Theory