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

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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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