Do the Ricci and energy-momentum tensors have "duality'' in the context of their Lie symmetries?

Details Do the Ricci and energy-momentum tensors have "duality'' in the context of their Lie symmetries? Do the Ricci and energy-momentum tensors have "duality'' in the context of their Lie symmetries?

2010-11-23

arxiv.org/abs/1011.5163v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

The Ricci and energy-momentum tensors have the same algebraic symmetries. In the Einstein equations they look ``dual'' to each other, in that interchanging them and inverting the gravitational coupling leaves the equations invariant. It may then be expected that their differential symmetry Lie algebras would also be identical. Using cylindrically symmetric static spacetimes it is shown that they are not identical and neither algebra is a subset of the other.

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