Structural equations for Killing tensors of order two. II

Journal Article · Fri Aug 01 04:00:00 EDT 1975 · J. Math. Phys. (N.Y.), v. 16, no. 8, pp. 1625-1629

DOI:https://doi.org/10.1063/1.522731· OSTI ID:4141269

Hauser, I; Malhiot, R J

In a preceding paper, a new form of the structural equations for any Killing tensor of order two have been derived; these equations constitute a system analogous to the Killing vector equations Nabla/sub alpha/ K/sub beta/ = $omega$/sub alpha beta/ = -$omega$/sub beta alpha/ and Nabla/sub gamma/ $omega$/ sub alpha beta = R/sub alpha beta gamma delta/ K/sup delta/. The first integrability condition for the Killing tensor structural equations is now derived. The structural equations and the integrability condition have forms which can readily be expressed in terms of a null tetrad to furnish a Killing tensor parallel of the Newman--Penrose equations; this is briefly described. The integrability condition implies the new result, for any given space--time, that the dimension of the set of second-order Killing tensors attains its maximum possible value of 50 only if the space--time is of constant curvature. Potential applications of the structural equations are discussed. (auth)

• Research Organization: Illinois Inst. of Tech., Chicago
• NSA Number: NSA-33-008651
• OSTI ID: 4141269
• Journal Information: J. Math. Phys. (N.Y.), v. 16, no. 8, pp. 1625-1629, Journal Name: J. Math. Phys. (N.Y.), v. 16, no. 8, pp. 1625-1629; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

*SPACE-TIME-- TENSORS
644003*
N76300* --Physics (Theoretical)--Gravitation & General Relativity