988 research outputs found
Nielsen equalizer theory
We extend the Nielsen theory of coincidence sets to equalizer sets, the
points where a given set of (more than 2) mappings agree. On manifolds, this
theory is interesting only for maps between spaces of different dimension, and
our results hold for sets of k maps on compact manifolds from dimension (k-1)n
to dimension n. We define the Nielsen equalizer number, which is a lower bound
for the minimal number of equalizer points when the maps are changed by
homotopies, and is in fact equal to this minimal number when the domain
manifold is not a surface.
As an application we give some results in Nielsen coincidence theory with
positive codimension. This includes a complete computation of the geometric
Nielsen number for maps between tori.Comment: + addendum, sync with published versio
The 3+1 decomposition of Conformal Yano-Killing tensors and "momentary" charges for spin-2 field
The "fully charged" spin-2 field solution is presented. This is an analog of
the Coulomb solution in electrodynamics and represents the "non-waving" part of
the spin-2 field theory. Basic facts and definitions of the spin--2 field and
conformal Yano-Killing tensors are introduced. Application of those two objects
provides a precise definition of quasi-local gravitational charge. Next, the
3+1 decomposition leads to the construction of the momentary gravitational
charges on initial surface which is applicable for Schwarzschild-like
spacetimes.Comment: 17 page
"Peeling property" for linearized gravity in null coordinates
A complete description of the linearized gravitational field on a flat
background is given in terms of gauge-independent quasilocal quantities. This
is an extension of the results from gr-qc/9801068. Asymptotic spherical
quasilocal parameterization of the Weyl field and its relation with Einstein
equations is presented. The field equations are equivalent to the wave
equation. A generalization for Schwarzschild background is developed and the
axial part of gravitational field is fully analyzed. In the case of axial
degree of freedom for linearized gravitational field the corresponding
generalization of the d'Alembert operator is a Regge-Wheeler equation. Finally,
the asymptotics at null infinity is investigated and strong peeling property
for axial waves is proved.Comment: 27 page
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