Kavli Affiliate: Anthony Lasenby
| Summary:
We investigate the conditions under which a hypersurface becomes null through the use of coordinate transformations. We demonstrate that, in static spacetimes, the correct criterion for a surface to be null is $g_tt = 0$, rather than $g^rr = 0$, in agreement with the results of Vollick. We further show that, if a Kruskal-like coordinate exists, the proxy condition $g^rr = 0$ is equivalent to $g_tt = 0$ if $partial_r g_tt neq 0$ and both $g^rr$ and $g_tt$ vanish at the same rate near the horizon. Our method extends naturally to axisymmetric stationary spacetimes, for which we demonstrate that the condition $detbig(h_abbig) = 0$ for the induced metric on a null hypersurface is recovered. By contrast with the induced metric approach, our method provides a physical perspective that connects the general null condition with its underlying relationship to photon geodesics.
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