2025/04/17 by Hsu, Yi-Hsiung, Barker, Will, Hobson, Michael +1
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2504.13255
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 gtt = 0, rather than grr = 0, in agreement with the results of Vollick. We further show that, if a Kruskal-like coordinate exists, the proxy condition grr = 0 is equivalent to gtt = 0 if ∂r gtt ≠ 0 and both grr and gtt vanish at the same rate near the horizon. Our method extends naturally to axisymmetric stationary spacetimes, for which we demonstrate that the condition det(hab) = 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.