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arXiv · 2004.00086

On Schwarzschild causality in higher dimensions

Peter Cameron·Maciej Dunajski
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Abstract

We show that the causal properties of asymptotically flat spacetimes depend on their dimensionality: while the time-like future of any point in the past conformal infinity $\mathcal{I}^-$ contains the whole of the future conformal infinity $\mathcal{I}^+$ in $(2+1)$ and $(3+1)$ dimensional Schwarzschild spacetimes, this property (which we call the Penrose property) does not hold for $(d+1)$ dimensional Schwarzschild if $d>3$. We also show that the Penrose property holds for the Kerr solution in $(3+1)$ dimensions, and discuss the connection with scattering theory in the presence of positive mass.

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Peter Cameron, Maciej Dunajski. 2020-09-04. On Schwarzschild causality in higher dimensions. https://doi.org/10.1088/1361-6382%2Fabb4b8

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