Weyl scalar

From Wikipedia, the free encyclopedia

You have new messages (last change).

The Weyl scalars form a set of five scalar quantities,

\Psi_0, \ldots, \Psi_4,

describing the curvature of a four-dimensional spacetime. They are part of the Newman-Penrose Formalism for general relativity.

A particularly important case is the Weyl scalar Ψ4, which is defined as

\Psi_4 = -C_{\alpha\beta\gamma\delta} n^\alpha \bar{m}^\beta n^\gamma \bar{m}^\delta\ .

It can be shown to describe outgoing gravitational radiation (in an asymptotically flat spacetime) as

\Psi_4 = \frac{1}{2}\left( \ddot{h}_{\hat{\theta} \hat{\theta}} - \ddot{h}_{\hat{\phi} \hat{\phi}} \right) + i \ddot{h}_{\hat{\theta}\hat{\phi}} = -\ddot{h}_+ + i \ddot{h}_\times\ .

Here, h + and h_\times are the "plus" and "cross" polarizations of gravitational radiation, and the double dots represent double time-differentiation.

For more details, see the article on the Newman-Penrose Formalism.

This relativity-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org../../../w/e/y/Weyl_scalar.html"