2011 Student Research Conference:
24th Annual Student Research Conference

Weyl Curvature and Invariance of Spacelike 3-Volume Under Geodesic Flow
Joseph A. Palmer
Dr. Kevin Easley, Faculty Mentor

We prove an observation of Penrose that spacelike 3-volume is preserved under geodesic flow in Ricci-flat spacetimes. While volume is preserved, the shape is not; the deformation of spacelike 3-volumes is measured by the Weyl curvature tensor, the only non-trivial component of the Riemann curvature tensor to persist in Ricci-flat spacetimes. The result will be shown to have a simple, geometrically appealing interpretation when considering free fall near the Earth or a similar gravitating body.

Keywords: Differential Geometry, Weyl Curvature, General Relativity, geodesic flow


Presentation Type: Oral Paper

Session: 40-2
Location: MG 1096
Time: 3:00

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