Tidal forces near a black hole

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SUMMARY

The discussion focuses on calculating tidal forces near a black hole horizon using the black hole metric g_{\mu\nu}. To determine these tidal forces, one must compute the Riemann tensor R_{abcd} in the comoving frame. The tidal tensor can then be derived by contracting the Riemann tensor with the four-velocity U^b, specifically using U^0 = -1. This method provides a precise framework for analyzing tidal effects in the vicinity of black holes.

PREREQUISITES
  • Understanding of general relativity and black hole metrics
  • Familiarity with the Riemann tensor and its properties
  • Knowledge of four-velocity concepts in relativistic physics
  • Ability to perform tensor contractions in a comoving frame
NEXT STEPS
  • Study the properties of the Riemann tensor in general relativity
  • Learn about the implications of tidal forces in astrophysical contexts
  • Explore the mathematical framework of black hole metrics
  • Investigate the role of four-velocity in relativistic physics
USEFUL FOR

Physicists, astrophysicists, and students of general relativity who are interested in the effects of tidal forces near black holes and their implications in theoretical physics.

praharmitra
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Given a black hole metric [tex]g_{\mu\nu}[/tex] how does one calculate the tidal forces near the black hole horizon? Is there any more quantities that may be required to answer this?
 
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praharmitra said:
Given a black hole metric [tex]g_{\mu\nu}[/tex] how does one calculate the tidal forces near the black hole horizon? Is there any more quantities that may be required to answer this?

Yes, you need to calculate the Riemann tensor Rabcd in the comoving frame and then contract it with U0=-1 to give the tidal tensor

[tex] E_{ac}=R_{abcd}\ U^b\ U^d[/tex]
 

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