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The Ricci flow (RF) is a flow equation which describe a diffusive process acting on the Riemannian metric driven by its Ricci curvature. This equation was introduced by Richard Hamilton in 1982 as a tool for proving the Thurston's geometrization conjecture for closed 3-manifolds. The equation c...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/7081 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The Ricci flow (RF) is a flow equation which describe a diffusive process acting on the Riemannian metric driven by its Ricci curvature. This equation was introduced by Richard Hamilton in 1982 as a tool for proving the Thurston's geometrization conjecture for closed 3-manifolds. The equation can be applied in general relativity. We derive a spherical solution of the RF equation in four dimensional spacetime and compare it with the solution of Einstein's equation. As the result, we found that the solution of Einstein's equation, i.e the Schwarzschild solution, is just a limiting case of the RF solution. The Divergence of the Einstein tensor which derived from the RF solution is zero. It means that this solution satisfy the Bianchi identity and energy-momentum conservation law, so the solution has a physical meaning. |
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