Monochromatic plane-fronted waves in conformal gravity are pure gauge

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

5 pages, no figures, version published, substantial changes to the presentation, conclusions unaltered, title changed

Scientific paper

10.1103/PhysRevD.83.104046

We consider plane-fronted, monochromatic gravitational waves on a Minkowski background, in a conformally invariant theory of general relativity. By this we mean waves of the form: $g_{\mu\nu}=\eta_{\mu\nu}+\epsilon_{\mu\nu}F(k\cdotx)$, where $\epsilon_{\mu\nu}$ is a constant polarization tensor, and $k_\mu$ is a lightlike vector. We also assume the coordinate gauge condition $|g|-1/4\partial_\tau(|g|1/4g^{\sigma\tau})=0$ which is the conformal analog of the harmonic gauge condition $g^{\mu\nu}\Gamma_{\mu\nu}^\sigma=-|g|-1/2\partial_\tau(|g|1/2g^{\sigma\tau})=0, where $\det[g_{\mu\nu}]\equivg$. Requiring additionally the conformal gauge condition $g=-1$ surprisingly implies that the waves are both transverse and traceless. Although the ansatz for the metric is eminently reasonable when considering perturbative gravitational waves, we show that the metric is reducible to the metric of Minkowski space-time via a sequence of coordinate transformations which respect the gauge conditions, without any perturbative approximation that \in{\mu}{\nu} be small. 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. Our result does not imply that conformal gravity does not have gravitational wave phenomena. A different, more generalized ansatz for the deviation, taking into account the fourth-order nature of the field equation, which has the form $g_{\mu\nu}=\eta_{\mu\nu}+B_{\mu\nu}(n\cdotx)G(k\cdotx)$, indeed yields waves which carry energy and momentum [P.D. Mannheim, Gen. Relativ. Gravit. 43, 703 (2010)]. It is just surprising that transverse, traceless, plane-fronted gravitational waves, those that would be used in any standard, perturbative, quantum analysis of the theory, simply do not exist.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Monochromatic plane-fronted waves in conformal gravity are pure gauge does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Monochromatic plane-fronted waves in conformal gravity are pure gauge, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monochromatic plane-fronted waves in conformal gravity are pure gauge will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-193266

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.