Time dilation inside the second horizon of the BH

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SUMMARY

This discussion centers on the phenomenon of time dilation experienced by Alice as she freely falls into a rotating black hole (BH) and crosses the second horizon. While Alice hovers near the naked ring singularity, Bob's journey to meet her is influenced by the BH's rotation, creating scenarios where their meeting time varies significantly. The discussion emphasizes the coordinate-independent nature of time dilation in this context, highlighting the complexities of their interactions based on the BH's gravitational effects.

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  • Understanding of general relativity and its implications on time dilation
  • Familiarity with the concept of black holes, particularly rotating black holes
  • Knowledge of singularities and their properties in astrophysics
  • Basic grasp of coordinate systems in physics
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  • Research the effects of rotating black holes on time dilation using Kerr metric
  • Explore the concept of naked singularities and their implications in theoretical physics
  • Study the relationship between gravitational fields and time perception in general relativity
  • Investigate the synchronization of events in non-inertial reference frames
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Astronomers, physicists, and students of theoretical physics interested in the effects of black holes on time and space, as well as those exploring advanced concepts in general relativity.

Dmitry67
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Here is an example, where time dilation is coordinate-independent.

Alice freely falls into the rotating BH. When she crosses the second horizon, she stops and hovers (enjoying the spectacular view of the naked ring singularity). As ring actually repels in some places, she would be safe and probably can even switch off her engines.

Bob waits 1 day, or 1 year, and does the same. How long Alice would wait his arrival?

Note: as BH is rotating, when Bob arrives Alice can be on the opposite side of BH, so we look at the scenarios where Bob is lucky, or 'in sync' with the rotation, so they meet.
 
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Hm... No ideas?
 

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