TOV Equation in (2+1)-dimensions for Perfect Fluids

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SUMMARY

The discussion focuses on deriving the Tolman-Oppenheimer-Volkov (TOV) equation for perfect fluids in a static, circularly symmetric (2+1)-dimensional spacetime. The Schwarzschild metric serves as the foundational framework for this derivation. A participant initially struggled with the phi component of the Schwarzschild metric but ultimately found a solution. This indicates that the adaptation of the metric is crucial for achieving the desired results in lower-dimensional spacetimes.

PREREQUISITES
  • Understanding of the Schwarzschild metric
  • Familiarity with perfect fluid dynamics in general relativity
  • Knowledge of (2+1)-dimensional spacetime concepts
  • Basic grasp of the TOV equation and its significance
NEXT STEPS
  • Study the implications of the TOV equation in (2+1)-dimensional spacetimes
  • Explore the derivation of the Schwarzschild metric in various dimensions
  • Investigate the properties of perfect fluids in general relativity
  • Learn about circular symmetry in gravitational theories
USEFUL FOR

Physicists, particularly those specializing in general relativity, cosmologists, and students tackling advanced topics in theoretical physics will benefit from this discussion.

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Homework Statement


Consider a perfect fluid in a static, circularly symmetric (2+1)-dimensional spacetime.

Derive the analogue of the Tolman-Oppenheimer-Volkov (TOV) equation for (2+1)-dimensions

Homework Equations


Schwarzschild metric

The Attempt at a Solution


Okay. I'm trying to think this through. I've replaced the phi component of the schwarzchild metric with some random variable because we only need circular symmetry. but where do I go from here?
 
Nevermind. I have solved it!
 

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