How Long Until You Hit the Black Hole?

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SUMMARY

The discussion focuses on calculating the time experienced by an observer falling into a black hole of mass M, specifically the time measured on their watch as they cross the event horizon. The key approach involves integrating the metric from the horizon to the singularity at r=0. The participant confirms that understanding the metric is essential for measuring distance and time in this context, indicating that integration is the correct method to determine the time until the observer reaches the singularity.

PREREQUISITES
  • General Relativity principles
  • Understanding of black hole metrics
  • Integration techniques in calculus
  • Concept of event horizons
NEXT STEPS
  • Study Schwarzschild metric in detail
  • Learn about time dilation effects near black holes
  • Explore the mathematical integration of spacetime intervals
  • Investigate the implications of singularities in General Relativity
USEFUL FOR

Physics students, astrophysicists, and anyone interested in the dynamics of black holes and the effects of gravity on time perception.

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Homework Statement



Starting from rest at a great distance, you plunge straight towards a black hole of mass M. You set your watch to noon as you determine that you are crossing the horizon. How much more time do you have (as measured on your watch) until the instant of crunch?

Homework Equations



Nothing else is given in the problem. I thought I would need to know the metric.

The Attempt at a Solution



If I understand correctly the metric tells me how to measure distance and time so I would just integrate from the r=horizon to r=0 to get the time? Am I on the right track?
 
Physics news on Phys.org
I think yes.You should integrate.
 

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