- #31
Mike Holland
- 114
- 1
Ok, thanks Peter. I am a follower of the frozen star heresy, and thought you might be coming out of the closet!
Future null infinity confusion
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Discussion Overview
The discussion revolves around the concepts of event horizons, Killing horizons, and future null infinity within the context of general relativity. Participants explore the definitions and implications of these concepts, particularly focusing on their mathematical and physical interpretations in various spacetimes, including Schwarzschild and Rindler coordinates.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants express confusion regarding the definition of future null infinity, particularly the notion of the "end" of a geodesic as the affine parameter approaches infinity.
- There is a discussion about whether the definition of future null infinity includes events on the photon sphere, with some arguing that it does not since the photon sphere is within the original spacetime and does not reach the conformal boundaries.
- One participant clarifies that in conformally completed spacetime, geodesics that have no endpoints in the original spacetime can have endpoints on the conformal boundaries.
- Another participant notes that for a null geodesic to be considered as reaching future null infinity, it must correspond to distinct events along the geodesic, which is not the case for circular photon orbits.
- There is a mention of Rindler coordinates, where every null surface is a Killing horizon, but none are event horizons, as all events in Minkowski spacetime can send light signals to future null infinity.
- Some participants discuss the uniqueness of Killing horizons in relation to specific Killing vector fields and how they differ in various spacetimes.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the implications of future null infinity concerning the photon sphere, with some asserting it does not reach future null infinity while others express uncertainty about how the rules enforce this conclusion. There are competing views on the definitions and characteristics of event and Killing horizons.
Contextual Notes
Participants note that the definitions and concepts discussed are tied to mathematical procedures like conformal completion and Penrose diagrams, which may introduce additional complexities not fully resolved in the discussion.
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