Tuesday, June 8, 2010

Weak-field GR near the centre of a light planar mass - Greg Egan

"In Newtonian gravity, an infinite planar mass of uniform density σ produces a uniform gravitational field: at every point in space, test particles experience an acceleration of magnitude 2 π σ (in units where G=1), directed towards the plane and orthogonal to its surface.

Is there an analogous situation in General Relativity, and if so, in what ways does it depart from the Newtonian case? In fact there are at least two exact solutions of Einstein's equation that deserve to be called “infinite plane” solutions [1], but they both have exotic aspects (a cosmological constant, and relativistic pressures) that make them less similar to the Newtonian case than we might wish, if we're not interested in a strictly infinite plane for its own sake, but only in the mathematical simplicity that it yields."

5 out of 5


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