10 - Wednesday

Today I'm getting back into research. I've partly reviewed my work during honours but Josh provided me with a recent paper from the arXiv that uses conformal transformations of the Vaidya metric to perform Bogoliubov transforms with exact solutions. They do this by using the conformal coupling of QFT to the spacetime:

\[\phi_{;\mu\nu}g^{\mu\nu}+\frac{1}{6}R\phi=0\]

Including the conformal term allows the field to be found in the static case, and to then use a rescaling of the spacetime to find the evaporating (Vaidya) case. Conformally coupled fields are invariant under conformal transforms of the form:

\[\tilde{g}_{\mu\nu}=\Omega^2(x)g_{\mu\nu},\hspace{0.5cm}\tilde{\phi}=\Omega^{-1}(x)\phi\]