# What is the curvature scalar $\Psi_{4}$?

What is the curvature scalar $\Psi_{4}$?

Is it related to the scalar curvature $R$?

What does its real and imaginary parts represent?

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## 1 Answer

It's one of the Weyl curvature scalars or coefficients, see the first page of http://arxiv.org/abs/1105.0781 - They're some "doubly light-like", see the formulae, components of the Weyl tensor, and because the Ricci scalar is specifically removed from the Weyl tensor, you may be sure that $\Psi_4$ isn't related to $R$. But both $R$ and $\Psi_n$ are linear combinations of components of the Riemann tensor.

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2
Typically, for the "natural" tetrad coordinate choices, $\psi_{4}$ represents terms related to radiation. But it is obviously something that his highly coordinate-dependent. – Jerry Schirmer Sep 29 '12 at 16:44
– user12345 Sep 30 '12 at 14:34
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