Non-linear Lagrangians and the significance of the metric

Details Non-linear Lagrangians and the significance of the metric Non-linear Lagrangians and the significance of the metric

Dec 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988cqgra...5l.197b&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 5, Dec. 1, 1988, p. L197-L199.

Physics

33

Einstein Equations, Gravitation Theory, Metric Space, Tensor Analysis, Euler-Lagrange Equation, Geodesy, Matter (Physics), Nonlinear Equations

Scientific paper

Recent investigations of nonlinear general-relativistic gravitational Lagrangians have focused on the fact that these theories can be recast in standard Einstein form if the metric is redefined. It has been claimed that this result shows that these other theories are equivalent to the standard Einstein theory with additional fields. However, in this letter it is pointed out that the coupling to matter defines what the physically measured metric will be, so that the freedom of identification of an arbitrarily defined 2-tensor field as the metric is not justified. Simply, geodesics provide an operational definition of the metric.

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