Proving Spin Coefficient Transformation for Null Rotation with l Fixed

[Ravi Panchal]

In Newmann-Penrose formalism, a Null rotation with $l$ fixed is
$$l^a−>l^a\\
n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\
m^a−>m^a+cl^a\\
\bar{m}^a−>\bar{m}^a+\bar{c}l^a$$
Using this transformation, how to prove?
$$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$
Ref: 2-Spinors by P.O'Donell, p.no, 65

 

[PeterDonis]

One quick note on LaTeX: LaTeX inline in a paragraph is delimited with two pound signs (2 #), not $. I've fixed the OP of this thread accordingly.