We consider monochromatic, plane gravitational waves in a conformally invariant theory of general relativity. We show that the simple, standard ansatz for the metric, usually that which is taken for the linearized theory of these waves, is reducible to the metric of Minkowski spacetime via a sequence of conformal and coordinate transformations. This implies that we have in fact, exact plane wave solutions. However they are simply coordinate/conformal artifacts. As a consequence, they carry no energy.
CONFORMAL GRAVITY AND GRAVITATIONAL WAVES
FABBRI, LUCA;
2012-01-01
Abstract
We consider monochromatic, plane gravitational waves in a conformally invariant theory of general relativity. We show that the simple, standard ansatz for the metric, usually that which is taken for the linearized theory of these waves, is reducible to the metric of Minkowski spacetime via a sequence of conformal and coordinate transformations. This implies that we have in fact, exact plane wave solutions. However they are simply coordinate/conformal artifacts. As a consequence, they carry no energy.
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