Rarita–Schwinger fields in algebraically special vacuum space‐times

The motion of massless spinning test particles is investigated using the Newman–Penrose formalism within the Mathisson–Papapetrou model extended to massless particles by Mashhoon and supplemented by the Pirani condition. When the "multipole reduction world line" lies along a principal null direction of an algebraically special vacuum space–time, the equations of motion can be explicitly integrated. Examples are given for some familiar space–times of this type in the interest of shedding some light on the consequences of this model.

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A note on Killing vectors in algebraically special vacuum space-times

General Relativity and Gravitation ◽

10.1007/bf00756531 ◽

1980 ◽

Vol 12 (7) ◽

pp. 575-580 ◽

Cited By ~ 3

Author(s):

Roberto Catenacci ◽

Annalisa Marzuoli ◽

Franco Salmistraro

Keyword(s):

Killing Vectors ◽

Special Vacuum ◽

Vacuum Space

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Hertz─Bromwich─Debye─Whittaker─Penrose potentials in general relativity

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1979.0101 ◽

1979 ◽

Vol 367 (1731) ◽

pp. 527-538 ◽

Cited By ~ 46

Keyword(s):

General Relativity ◽

Scalar Potential ◽

Space Time ◽

Physical Interest ◽

Gravitational Perturbations ◽

Special Vacuum ◽

Background Space ◽

Explicit Formulae ◽

Scalar Potentials ◽

Vacuum Space

The problem of deriving scalar potentials governing electromagnetic and gravitational perturbations of vacuum space-times is discussed. For the case of an algebraically special vacuum background space-time, explicit formulae for all quantities of physical interest are given in terms of derivaties of the scalar potential.

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Properties of shear-free congruences of null geodesics

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1976.0075 ◽

1976 ◽

Vol 349 (1658) ◽

pp. 309-318 ◽

Cited By ~ 21

Keyword(s):

Integrability Condition ◽

Field Equations ◽

Null Geodesics ◽

Conformal Curvature ◽

Special Vacuum ◽

Linearized Theory ◽

Vacuum Space

Associated with any shear-free congruence of null geodesics are two real bivectors. One of these describes the relation of the congruence to the conformal curvature, but the significance of the second bivector is less clear. The integrability condition is given for a certain class of spinor equations which arise in the presence of a shear-free congruence of null geodesics. This integrability condition leads to a basis-free proof of the Goldberg-Sachs theorem and related results. Comparing the field equations for algebraically special vacuum space-times with those for the corresponding field types in linearized theory, it is seen that the functional freedom in the fields is the same.

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