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We investigate photon surfaces and their stability in a less symmetric spacetime, a general static warped product with a warping function acting on a Riemannian submanifold of codimension two.
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In the current paper, we assume f ( r ) , h ( r ) > 0 f(r),\ h(r)>0 for simplicity. The condition h ( r ) > 0 h(r)>0 is necessary for a hypersurface of r = const . r=\mathrm{const.} to be timelike. The condition f ( r ) > 0 f(r)>0 is necessary for the metric g g to have Lorentzian signature if we require the metric γ i j \gamma_{ij} to have Riemannian signature. One can instead assume that f ( r ) < 0 f(r)<0 , h ( r ) > 0 h(r)>0 , and γ i j \gamma_{ij} is Lorentzian. Since our analysis does not depend on the signature, the analysis in that case should be parallel
Cited in the paper.
P. V. P. Cunha, E. Berti, and C. A. R. Herdeiro, Phys. Rev. Lett. 119
2017
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H. Yoshino, K. Izumi, T. Shiromizu, and Y. Tomikawa, Prog. Theor. Exp. Phys. 2017
2017
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T. Shiromizu, Y. Tomikawa, K. Izumi, and H. Yoshino, Prog. Theor. Exp. Phys. 2017
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J. Fine and B. Premoselli, J. Amer. Math. Soc. 33
2020
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