Black Hole Time Dilation: Light-ray Interpretation

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SUMMARY

The discussion centers on the concept of time dilation in black holes, specifically how infinite curvature in spacetime leads to infinite time dilation. It posits that a light ray traveling radially towards a black hole's center must traverse an infinitely long proper radial distance due to the extreme curvature, effectively halting time as perceived from an external observer's frame of reference. The Schwarzschild metric is highlighted as a crucial mathematical framework for understanding these phenomena.

PREREQUISITES
  • Understanding of general relativity principles
  • Familiarity with the Schwarzschild metric
  • Basic knowledge of spacetime geometry
  • Concept of proper distance in curved spacetime
NEXT STEPS
  • Study the implications of the Schwarzschild metric on black hole physics
  • Explore the concept of proper distance in general relativity
  • Investigate the effects of time dilation near massive objects
  • Read about the mathematical formulations of spacetime curvature
USEFUL FOR

Physicists, astrophysicists, and students of general relativity seeking to deepen their understanding of black hole dynamics and the nature of time in extreme gravitational fields.

Alexrey
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I know that a black hole creates infinite curvature in spacetime and hence infinite time dilation. I was wondering though, if I could think of this stopping of time due to the fact that a light ray moving radially towards the centre of a black hole would have to travel infinitely far along the coordinate system's proper radial axis to reach the black hole's centre, as the infinite curvature would produce a proper radial distance tending to infinity as the light ray gets closer to the singularity?
 
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Probably best for you to look at:
http://www.jimhaldenwang.com/black_hole.htm
... introduction to space-time geometry inside and close to a black hole.

Don't be too intimidated by the math - scroll till it starts talking about the Schwarzschild metric.
 
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