scholarly journals The Bach equations in spin-coefficient form

2018 ◽  
Vol 35 (12) ◽  
pp. 125010
Author(s):  
Hamish Forbes
Keyword(s):  
Spin Coefficient

Angular momentum in general relativity I. Definition and asymptotic behaviour

1977 ◽  
Vol 354 (1679) ◽  
pp. 379-405 ◽  
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Angular Momentum ◽  
Asymptotic Behaviour ◽  
Event Horizon ◽  
Conservation Law ◽  
General Definition ◽  
Field Equations ◽  
Spin Coefficient ◽  
Coefficient Formalism

Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptoticallyflat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.

Some solutions of the Lanczos vacuum wave equation

1994 ◽  
Vol 447 (1931) ◽  
pp. 577-585 ◽  
Keyword(s):  
Wave Equation ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Spin Coefficient ◽  
Independent Components ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Non Local ◽  
Weyl Conformal Curvature Tensor ◽  
Gauge Conditions

In general relativity the non-local part of the gravitational field is described by the 10 degrees of freedom of the Weyl conformal curvature tensor C abcd . In every space-time the Weyl field C abcd is derivable from a potential L abc which has at most 16 algebraically independent components reducing to 10 degrees of freedom when the six gauge conditions L ab s ; s = 0 are imposed. The potential L abc discov­ered by Lanczos was shown by Illge to have an extremely simple vacuum wave equation, namely, □ L abc ≡ g sm L abc ; s ; m = 0. Using tensor, spinor and spin-coefficient methods we give some solutions of this new vacuum wave equation in some spacetimes containing one or more preferred vector fields.

Theoretical studies in nuclear structure IV. Wave functions for the nuclear p -shell Part A. ‹ p n │ p n-1 p › fractional parentage coefficients

1951 ◽  
Vol 209 (1099) ◽  
pp. 502-524 ◽  
Keyword(s):  
Direct Method ◽  
Wave Functions ◽  
Irreducible Representations ◽  
Reciprocal Relation ◽  
Spin Coefficient ◽  
Linear Combinations ◽  
Orthogonal Representation ◽  
Fractional Parentage ◽  
Complete Set ◽  
A Charge

A complete set of wave functions is constructed for the whole of the nuclear p -shell (from p 3 to p 12 ). Following Racah, the wave functions for p n are expressed as linear combinations of totally antisymmetric wave functions for p n-1 , vector-coupled to the wave functions of the remaining particle. The coefficients in the linear combination are expressed as the product of an orbital coefficient, a charge-spin- coefficient and a weight factor equal to the square root of the ratio of the dimensions of two irreducible representations of permutation groups. Using the Young-Yamanouchi orthogonal representation of the permutation group, the orbital and charge-spin coefficients may be calculated independently. Specialization of the new method to the atomic p -shell and an alternative direct method of calculating the total parentage coefficients are described in the appendices. A reciprocal relation for the special unitary group, simplifying the calculation of both the orbital and the charge-spin coefficients, is described in an Addendum.

SPACE–TIMES WITH A TWO-DIMENSIONAL GROUP OF CONFORMAL MOTIONS

1996 ◽  
Vol 11 (05) ◽  
pp. 845-861 ◽  
Author(s):  
CHARALAMPOS KOLASSIS ◽  
GARRY LUDWIG
Keyword(s):  
Simple Proof ◽  
Sufficient Conditions ◽  
Conformal Killing ◽  
Two Dimensional ◽  
Spin Coefficient ◽  
Dimensional Group ◽  
Star Operation ◽  
Conformal Killing Vectors ◽  
Necessary And Sufficient ◽  
Coefficient Formalism

The necessary and sufficient conditions for a space–time to admit a two-dimensional group of conformal motions (and, in particular, of homothetic motions) acting on nonnull orbits are found in the compacted spin-coefficient formalism. Although the discussion is restricted to the case of spacelike orbits, similar results are readily obtained for timelike orbits via the (modified) Sachs star operation. A number of theorems are obtained dealing with such topics as the Gaussian curvature of the group orbits, orthogonal transitivity, and hypersurface orthogonality of the conformal Killing vectors. A simple proof is presented of a generalization of a theorem due to Papapetrou.

scholarly journals Spin-coefficient formalism

Scholarpedia ◽  
2009 ◽  
Vol 4 (6) ◽  
pp. 7445 ◽  
Author(s):  
Ezra Newman ◽  
Roger Penrose
Keyword(s):  
Spin Coefficient ◽  
Coefficient Formalism
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