caa a22 4500 469065680 CHVBK 20180323132908.0 cr unu---uuuuu 170328e19921201xx s 000 0 eng 10.1007/BF02722853 doi (NATIONALLICENCE)springer-10.1007/BF02722853 Buchdahl H. Department of Physics and Theoretical Physics Faculty of Science, Australian National University, GFO Box 4, 2601, Canberra, A.C.T., Australia aut P -variations and asymmetric connexions [Elektronische Daten] [H. Buchdahl] Summary: In the general theory of relativity the field equations are generated by a variational principle in which the metric tensorg ij is subjected to variation, the linear connexion $$\Gamma _{ab} ^c $$ being a certain prescribed function ofg ij and its derivatives. In a known variant of this,g ij and $$\Gamma _{ab} ^c $$ are initially taken as mutually independent and therefore varied independently of each other (<<P-variation>>), subject to the condition that $$\Gamma _{ab} ^c $$ remain symmetric. One is therefore operating in anL 4 which is always anA 4. When the LagrangianL is linear,i.e. depends linearly on the curvature tensor, the variational principle narrows theA 4 down to being aV 4. WhenL is not linear the method ofP-variation is in general not viable. This paper deals with the consequences of abandoning the stipulation that $$\Gamma _{ab} ^c $$ must be symmetric, so that at the outset one is dealing with a generalL 4. Because of the difficulties or contradictions to which nonlinear Lagrangians lead, a general seven-parameter family of nominally <<linear>> LagrangiansL * is specified as analogue of the linear Lagrangian of the general relativity theory. The principal results emerging from this relate, first, to the nonmetricity, in particular the condition onL * which will ensure that theL 4 is aU 4; and, second, to the relation between angular momentum and torsion for various values of the parameters. Società Italiana di Fisica, 1992 PACS 04.20 General relativity nationallicence PACS 04.50 Unified field. Theories and other theories of gravitation nationallicence PACS 04.90 Other topics in relativity and gravitation nationallicence Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/12(1992-12-01), 1427-1435 107:12<1427 1992 107 40764 https://doi.org/10.1007/BF02722853 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02722853 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Buchdahl H. Department of Physics and Theoretical Physics Faculty of Science, Australian National University, GFO Box 4, 2601, Canberra, A.C.T., Australia aut NATIONALLICENCE 773 0- Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/12(1992-12-01), 1427-1435 107:12<1427 1992 107 40764 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer