The quadratic Lagrangians in General Relativity

Details The quadratic Lagrangians in General Relativity The quadratic Lagrangians in General Relativity

Jun 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971cmaph..22..115f&link_type=abstract

Communications in Mathematical Physics, Volume 22, Issue 2, pp.115-120

Mathematics

Mathematical Physics

4

Scientific paper

The solutions of the General Relativity equations with quadratic Lagrangians R iklmRiklm, RikRik, R2 are studied. It is shown that nontrivial Euclidian (at r → ∞) solution of the theory equations does not exist when T≠0 ( T is a trace of the energy-momentum tensor of matter). The Schwarzschild solution is not an external part of a total solution when T≠0. Under condition T= R=0 Lagrangians R iklmRiklm, RikRik lead to the identical field equations, so there exist the only quadratic Lagrangian and the only field equations. This equation has a solution with an external part being a standard Schwarzschild solution for the statical spherically symmetric case.

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