Kavli Affiliate: Anthony Lasenby
| First 5 Authors: Yi-Hsiung Hsu, Will Barker, Michael Hobson, 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~$detbig(h_{ab}big) = 0$ 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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