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Gravitational Field Equations of Fourth Order and Supersymmetry
Author(s) -
v. Borzeszkowski H. V.,
Treder H.J.,
Yourgrau W.
Publication year - 1978
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19784900607
Subject(s) - graviton , physics , mathematical physics , gravitation , planck mass , supersymmetry , einstein , gravitational field , field equation , einstein field equations , theoretical physics , classical mechanics , quantum mechanics
We discuss the field equations which stem from a variational principle containing the quadratic terms α R μν R μν and β R 2 besides the Einstein‐Hilbert Lagrangian R . Comparison of this theory with a pure theory of fourth order shows that R must necessarily be included if we wish to interpret the field equations as gravitational equations. The Einstein‐Bach‐Weyl theory (α = −3β) has the property of being a theory of “supergravitation”. Apart from gravitons without rest‐mass, we have here only one additional kind of particles with rest‐mass. Their mass may be determined by Planck' slength ( hG/c 3 ) 1/2 . The occurrence of those particles results from the breakdown of a “supersymmetry”, that is of the conform invariance. The Einstein tensor E μν R μν −1/2 g μν R can be regarded as a source of the gravitons without rest‐mass.