The paper extends Perelman's entropy functionals to 4D Lorentzian spacetimes and proves long-time well-posedness of Ricci flow using gradient flow properties of the coupled system.
Ricci flow and black holes.Classical and Quantum Gravity, 23(23):6683–6707, 2006
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Well-posedness of Ricci Flow in Lorentzian Spacetime and its Entropy Formula
The paper extends Perelman's entropy functionals to 4D Lorentzian spacetimes and proves long-time well-posedness of Ricci flow using gradient flow properties of the coupled system.