I am trying to put the Kerr metric into the famous Bondi gauge, which is given for instance by the formula (6.2.10) at page 154 of the following paper: https://arxiv.org/abs/1801.01714. Now, Barnich and Troessaert in their paper BMS charge algebra (https://arxiv.org/abs/1106.0213) did the calculations, which can be found in Appendix D and F of the paper. My questions are: 1) In the original metric the determinant of the angular part is different from the unit sphere metric determinant, hence they redefine the radial coordinate. I managed to work out all the new metric coefficients except for $g_{u\theta}$; in particular, I don't understand from where the new leading order coefficient $\frac{a\cos{\theta}}{2\sin^2{\theta}}$ comes from. Any help to understand this transformation would be very appreciated. 2) As one can see in Appendix F (it is pretty straightforward to calculate thiz), $C^{AB}C_{AB}=\frac{2a^2}{\sin^2{\theta}}$. However, in the Bondi gauge one has that the coefficient of the power $r^{-2}$ in $g_{ur}$ should be $\frac{C^{AB}C_{AB}}{16}=\frac{a^2}{8\sin^2{\theta}}$, and in the metric found by Barnich the same coefficient is actually $a^2(\frac{1}{2}-\cos^2{\theta})$. These are very different, unless I am missing some property of sinusoidal functions. Can anyone help me to solve this incongruence?

Thanks for any help or hints!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.