Asymptotic completeness of long range N-body systems. Main ideas of a proof

2008 ◽  
pp. 56-72 ◽  
Author(s):  
Jan Derezinski
Keyword(s):  
Long Range ◽  
Asymptotic Completeness ◽  
Main Ideas

SCATTERING OF MASSLESS DIRAC FIELDS BY A KERR BLACK HOLE

2004 ◽  
Vol 16 (01) ◽  
pp. 29-123 ◽  
Author(s):  
DIETRICH HÄFNER ◽  
JEAN-PHILIPPE NICOLAS
Keyword(s):  
Black Hole ◽  
Dirac Equation ◽  
Long Range ◽  
Unitary Transformation ◽  
Kerr Black Hole ◽  
Goursat Problem ◽  
Asymptotic Completeness ◽  
Conjugate Operator ◽  
Main Technique ◽  
Mourre Estimate

For the massless Dirac equation outside a slow Kerr black hole, we prove asymptotic completeness. We introduce a new Newman–Penrose tetrad in which the expression of the equation contains no artificial long-range perturbations. The main technique used is then a Mourre estimate. The geometry near the horizon requires us to apply a unitary transformation before we find ourselves in a situation where the generator of dilations is a good conjugate operator. The results are eventually re-interpreted geometrically to provide the solution to a Goursat problem on the Penrose compactified exterior.

scholarly journals Asymptotic completeness in long range scattering. II

1985 ◽  
Vol 18 (1) ◽  
pp. 57-87 ◽  
Author(s):  
Pl. Muthuramalingam ◽  
Kalyan B. Sinha
Keyword(s):  
Long Range ◽  
Asymptotic Completeness
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