Physics
Scientific paper
Dec 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980gregr..12.1043t&link_type=abstract
General Relativity and Gravitation, Volume 12, Issue 12, pp.1043-1054
Physics
3
Scientific paper
The spin-two particle is described by a symmetric tensorh μυ subject to the subsidiary conditionsh {α/α}=∂α h αβ=0. Their covariant generalization and the “wave equation” have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh μυ a symmetric third-rank tensorλГ μυ =λГ υμ as well as a vector fieldA μ have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh μυ ,λГ μυ andA μ independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh μυ as well as the generalization of the wave equationD λ D λ h αβ + 2R αμυβ h μυ -R {α/λ} h λβ -R {α/λ} h αλ +g αβ R μυ h μυ +Rh αβ =m 2 h αβ Finally, variation with respect tog μυ yields the energy-momentum tensor.
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