A 12-lecture mini-course providing an overview of advanced topics relevant to current research in General Relativity. The course will focus exclusively on classical aspects of gravity and, towards the end, on the quantum behaviour of particles/fields in gravitational backgrounds. The course will run from 20 March to 28 April 2023. Video recordings are available from the ICTS website for the series, https://www.icts.res.in/lectures/AGR2023
Monday 27 March 2023
My notes, updated after today's lecture, are available in the shared folder (see previous post).
I think an example of a physical scenario wherein spacetime lacks global hyperbolicity is provided in this paper by Penrose 'A Remarkable Property of Plane Waves in General Relativity' (https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.37.215).
Further, Gibbons in 'Quantized fields propagating in plane-wave spacetimes' (https://link.springer.com/article/10.1007/BF01629249) shows how we can still consider "substitute Cauchy surfaces" in such spacetimes, depending on the question we are interested in.
I think an example of a physical scenario wherein spacetime lacks global hyperbolicity is provided in this paper by Penrose 'A Remarkable Property of Plane Waves in General Relativity' (https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.37.215).
ReplyDeleteFurther, Gibbons in 'Quantized fields propagating in plane-wave spacetimes' (https://link.springer.com/article/10.1007/BF01629249) shows how we can still consider "substitute Cauchy surfaces" in such spacetimes, depending on the question we are interested in.
Yes, and actually the plane wave is a limit of AdS, so this problem will already arise when we consider AdS/dS spacetimes.
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