Interpretation of (X,T) coordinates in Kruskal diagram

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Discussion Overview

The discussion revolves around the interpretation of the (X, T) coordinates in the Kruskal diagram, particularly in the context of black hole physics. Participants explore the implications of these coordinates for observers free-falling near the event horizon, examining the nature of proper time and the relationship between Kruskal-Szekeres coordinates and local inertial frames.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question what is meant by "naturally used" in relation to the (X, T) coordinates and whether this applies only as the observer crosses the event horizon.
  • One participant suggests that "naturally used" could refer to matching local frames with the observer's worldline, but notes that this does not apply to Kruskal-Szekeres coordinates for freely falling observers.
  • Another participant discusses the possibility of scaling and offsetting Kruskal coordinates to match a local inertial frame centered on an event on the horizon, emphasizing that this is only valid within that local frame.
  • There is a contention regarding the definition of T as the proper time of the observer, with some participants asserting that this is incorrect due to the presence of a r-dependent prefactor in the metric.
  • Some participants propose that the coordinates (X, T) may correspond to standard Minkowski coordinates, while others clarify that these are specifically Kruskal-Szekeres coordinates.
  • There is discussion about the need for transformations to relate Kruskal coordinates to Minkowski coordinates in local frames, with some participants asserting that they coincide only under specific conditions.

Areas of Agreement / Disagreement

Participants express differing interpretations of the (X, T) coordinates and their relationship to proper time and local inertial frames. There is no consensus on the definitions and implications of these coordinates, and multiple competing views remain throughout the discussion.

Contextual Notes

Limitations include the dependence on specific transformations to relate Kruskal coordinates to local inertial frames, as well as the ambiguity surrounding the definition of proper time in this context.

  • #31
Sagittarius A-Star said:
I can't find in the video the following of what you quoted in the OP from the book
Me too. That statement is still a mystery to me.
 
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  • #35
Sagittarius A-Star said:
It seems that Susskind uses the same capital letters X, T for both, the locally applied standard Minkowski diagram in your posting #12 and the Kruskal diagram in your posting #8, which includes the upper quadrant containing the singularity.
I think that this is just what he does.
 
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