ELFT HÍRADÓ

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

RELATIVITÁSELMÉLETI SZEMINÁRIUM


Elõadó:  Prof James M Nester
         National Central University, Chungli, Taiwan

Az elõadás címe:  On the zeros of spinor fields and 
                  orthonormal frames 

t:       2006 április 13 (csütörtök), 14.00
(x,y,z): KFKI RMKI III. épület, tanácsterem

Kivonat: 

Some time ago (as a key ingredient in a positive energy
proof [1]) we proposed certain rotational gauge conditions for an
orthonormal frame on a Riemannian manifold [2].  However, except for
nearly flat spaces, it was not clear if the conditions could be
satisfied.  Then Dimakis and Muller-Hoissen [3] showed how to
construct such frames from solutions of the Dirac spinor equation
(which generally exist)---as long as the spinor field had no zero
points.  A later "proof" that zeros cannot happen [4] is not
convincing. Based on our recent examination of specific examples
described here we know that zeros can happen, but we argue that they
are not generic. Consequently the "special orthonormal frame" gauge
conditions can be used essentially without reservations.

References:

[1] J.M. Nester, Int. J. Mod. Phys. A 4 (1989) 1755
    Phys. Lett A 139 (1989) 112,
    Class. Quant. Grav.  8 (1991) L19.
[2] J.M. Nester,  J. Math. Phys. 30 (1989) 624.
[3] A. Dimakis and F. Muller-Hoissen, Phys. Lett. A  142 (1989) 73.
[4] V. Pelykh, J. Math Phys. 41 (2000) 5550.


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RELATIVITÁSELMÉLETI SZEMINÁRIUM


Elõadó:  Prof James M Nester
         National Central University, Chungli, Taiwan

Az elõadás címe:  On gravitational energy in a small region 

t:       2006 április 18 (kedd), 14.00
(x,y,z): KFKI RMKI III. epulet, tanacsterem

Kivonat:

The (quasi-)localization of energy for gravitating systems
remains an outstanding issue.  One of the desiderata (related to
positive energy) is that the small region vacuum limit should be
proportional the Bel-Robinson tensor with a positive coefficient.
Here we report on our investigation of this limit for certain
energy-momentum expressions.  Specifically we find that none of the
traditional pseudotensors satisfy this critera, however there are
certain linear combinations of them which do.  Moreover we can
construct a large number of new pseudotensors which do have this
desired Bel-Robinson vacuum limit.  In contrast to these rather
artificial constructs Moller's tetrad energy-momentum "tensor"
naturally has this property. This is also true for  one of our four
proposed covariant Hamiltonian boundary term quasi-local
energy-momentum expressions.  Thus the small region vacuum limit is
a fairly strong selection condition.