Model Near-Colliding Ultra-Relativistic BHs w/ Colliding PP Waves

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Discussion Overview

The discussion revolves around the modeling of near-colliding ultra-relativistic black holes using the collision of plane-fronted (pp) waves, particularly referencing the Aichelburg-Sexl solution. Participants explore the implications of such a model and question the outcomes of potential collisions, as well as the appropriate coordinate charts for analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that modeling near-colliding ultra-relativistic black holes with colliding pp waves is reasonable, based on the Aichelburg-Sexl ultraboost space-time.
  • There is uncertainty regarding the appropriate coordinate chart for analyzing a pair of colliding pp waves, as standard charts are typically centered on a single pp wave.
  • A participant references a theorem by Tipler, suggesting that curvature singularities in colliding plane wave solutions imply that a "near miss" collision may not exist, as it would lead to the formation of a larger black hole.
  • Another participant notes that the terminology used to describe the collision, such as "near miss," may be ambiguous compared to "non-zero impact factor," which is used in relevant literature.
  • Discussion of a linked paper indicates it primarily addresses head-on collisions, raising questions about its applicability to the scenario of interest.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of modeling near-colliding black holes with pp waves and the implications of such models, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

There are limitations regarding the definitions and assumptions used in the discussion, particularly concerning the coordinate charts and the implications of curvature singularities in the context of black hole collisions.

pervect
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How reasonable would it be to model near-colliding of ultra-relativistic black holes by the collision of pp waves? Wkiki, for instance, says that the Aichelburg-Sexl ultraboost space-time models the space-time near an ultra-relativistic black hole, and that it's a type of pp wave spacetime, though it's not plane symmetric. This suggests that a pair of colliding pp waves (modelled on the Aichelburg-Sexl solution) might be a good model for a "near-miss" collision of ultra-relativistic black holes.

A related question is if we know anything definite about the results of such a collision. I gather there's quite a lot written about colliding pp waves, but it's unclear if anything that's been written would apply to this hypothetical scneario.
 
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pervect said:
a pair of colliding pp waves (modelled on the Aichelburg-Sexl solution) might be a good model for a "near-miss" collision of ultra-relativistic black holes.

I would agree, but I'm not sure what coordinate chart would be used, since the standard charts used for the ultraboost solution are "centered" on the single pp wave. Any chart used for a pair of colliding pp-waves would need to be "centered" on (heuristically) the center of mass of the system (so, heuristically, both pp-waves would be "moving" in such a chart), and I'm not sure if there's a known chart that does that.
 
pervect said:
A related question is if we know anything definite about the results of such a collision.

In a paper by Yurtsever [1], he refers to a theorem by Tipler that says that curvature singularities appear in generic colliding plane wave solutions. That would seem to me to suggest that there could not be such a thing as a "near miss" ultrarelativistic BH collision--if the holes approach close enough that a pair of colliding pp-waves is a viable model, the collision would have to produce a single larger hole (corresponding to the curvature singularity from the wave collision). But this is all very heuristic and I'm not sure how much it has been studied.

[1] https://journals.aps.org/prd/abstract/10.1103/PhysRevD.37.2803
 
Ibix said:
The second paper linked by @PAllen in this thread seems to have relevant discussion.

I noticed that paper and started to read it - it seems to be in line with my thinking, but I've just skimmed it so far. My description of a collision as "a near miss" is a bit ambiguous, the paper in question uses "non-zero impact factor" to describe the situation I had in mind. That description is more precise, but probably not too intuitive.
 
From my reading, except for discussion of other literature in the intro, the paper I linked only covers head on collisions.
 

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