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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

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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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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
Lubo\v{s}, thank you for the time you took to answer my question :) May I add a follow-up? In this paper (which is similar to the one you cited), it says (on p.21) that the $\Psi_{4} = \ddot{h}_{+} - i\ddot{h}_{\times}$ which I understand. However, the author plots (in Fig. 18) the real part of the $l=n=2$ component of $\Psi_{4}$. Is there a way I can think of this quantity in terms of $h$, $h_{+}$ or $h_{\times}$? – user12345 Sep 30 '12 at 14:34

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