ELFT HÍRADÓ

["Szabados,L." <lbszab AT rmki.kfki.hu>]

RELATIVITASELMELETI SZEMINARIUM


Eloado:  Prof Ezra T. Newman,
         University of Pittsburgh

Az eloadas cime:  A new unorthodox approach to equations of motion
                  via null infinity

t:       2007 oktober 15 (hetfo), 14.00
(x,y,z): KFKI RMKI III. epulet, tanacsterem


Kivonat:

We report on a recently discovered new structure associated with the 
asymptotic behavior of the Einstein or Einstein-Maxwell fields in the 
neighborhood of future null infinity. This structure, which is associated 
with asymptotically shearfree null congruences, appears to have 
significant physical interest or consequences.

Specifically, we first will discuss the existence, arising by analogy to 
that in algebraically special space-times, of a unique regular 
asymptotically shear-free null geodesic congruence in any asymptotically 
flat space-time. Associated with this congruence is a unique complex 
analytic curve defined in the space of complex Poincare translations which 
has its action on complexified null infinity, i.e., Penrose's 
(complexified) SCRI.

We then describe the surprising physical significance of this curve. The 
physical situation we are dealing with is a complicated 
gravitating-electromagnetic system viewed from null infinity.  This system 
possesses a Bondi asymptotic four-momentum. First of all, the curve yields 
kinematic meaning to the Bondi four-momentum, in the sense of P=Mv with v 
being the real part of worldline velocity. Furthermorer, from this curve 
we can define a (complex) center of mass for the entire system [and 
(complex) center of charge for the special case when the two coincide] 
with its equations of motion. The Bondi energy-momentum loss equation 
then yields explicit evolution equations for both the real and the 
imaginary parts of the curve. The imaginary part, which is interpreted as 
the spin-angular momentum, satisfies its own evolution equation while the 
real part yields equations of motion for a spinning particle - with spin 
coupling terms. Much of the physical identification arises from a 
comparison of the radiation terms - both electromagnetic and gravitational 
- with the variables associated with the complex worldline. We even obtain 
radiation reaction terms with the 'correct' numerical coefficients.