Singularities at real points of H space

Details Singularities at real points of H space Singularities at real points of H space

Feb 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980gregr..12...99t&link_type=abstract

General Relativity and Gravitation, vol. 12, Feb. 1980, p. 99-108.

Mathematics

3

Function Space, Gravitational Waves, Radiation Distribution, Singularity (Mathematics), Manifolds (Mathematics), Null Zones, Orbit Calculation, Particle Motion, Points (Mathematics), Quadrupoles

Scientific paper

A study is presented of the geometry of two-dimensional real subspaces in radiation fields possessing a twist-free axial symmetry for the case of quadrupole radiation fields for which determination of the shear-free slices reduces to the standard problem of determining orbits of a particle moving in a potential. In the presence of gravitational radiation, no shear-free slices of null infinity are present; however, a four-complex-dimensional set of shear-free slices of complexified null infinity exist which comprise the manifold H space. In general, there are no preferred real subspaces of H space associated with slices of real null infinity, but a two-parameter family of shear-free slices exist in radiation fields with a twist-free axial symmetry. Possible singularities caused by intense radiation fields are investigated; it was found that such singularities occur for radiation fields with the characteristic power of c to the 5th per G.

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