- #1
timmdeeg
Gold Member
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In his article The Ricci and Weyl Tensors John Baez states that the tidal stretching and squashing caused by gravitational waves would not change the volume as there is 'only' Weyl- but no Ricci-curvature. No additional meaning is mentioned.
But, beeing not an expert I still have no good understanding, what Weyl-curvature really means and would appreciate any help.
If I think of spacetime curvature I have effects like Shapiro-Delay/time dilation/the sum of light ray triangles etc. in my mind. But it seems that the Weyl curvature is not responsible for anything else than the tidal effects happening in the x-y-plane, the transverse plane of the wave. Is that right? Perhaps it is sufficient to say, a plane is not curved. The MTW talkes about the plane-wave solution.
Otherwise gravitational wave measurements should be obscured by Shapiro-Delay/time dilation to a certain extent.
But on the other side and this puzzles me, gravitational waves are called "ripples of spacetime curvature". From this I would expect the spacetime curvature to oszillate locally between positive and negative values as the wave passes by, which should be measurable by light ray triangles, e.g. However is that right? And if so, in which plane? In the transverse plane or in the plane in which the wave propagates?
But, beeing not an expert I still have no good understanding, what Weyl-curvature really means and would appreciate any help.
If I think of spacetime curvature I have effects like Shapiro-Delay/time dilation/the sum of light ray triangles etc. in my mind. But it seems that the Weyl curvature is not responsible for anything else than the tidal effects happening in the x-y-plane, the transverse plane of the wave. Is that right? Perhaps it is sufficient to say, a plane is not curved. The MTW talkes about the plane-wave solution.
Otherwise gravitational wave measurements should be obscured by Shapiro-Delay/time dilation to a certain extent.
But on the other side and this puzzles me, gravitational waves are called "ripples of spacetime curvature". From this I would expect the spacetime curvature to oszillate locally between positive and negative values as the wave passes by, which should be measurable by light ray triangles, e.g. However is that right? And if so, in which plane? In the transverse plane or in the plane in which the wave propagates?