Quantum no-singularity theorem from geometric flows

In this letter, we analyze the classical geometric flows as a dynamical system. We obtain an action for such a dynamical system, such that its equation of motion would be the Raychaudhuri equation. As the Raychaudhuri equation is the basis of singularity theorems, and we can analyze it as equations of motion of a dynamical system, we are able to understand the quantum behavior of singularities. Thus, quantizing these geometric flows, we can demonstrate that a quantum spacetime is complete (non-singular).

225 Math (Ordinary Differential Equations)

This upper level course provides an introduction to the theory, solution and application of ordinary differential equations. Topics discussed in the course include methods of solving first-order differential equations, higher-order differential equations, modeling with first-order and higher-order differential equations, series solution of linear equations, systems of linear first order differential equations, and numerical solutions of ordinary differential equations. Applications of differential equations in physics, biology, and economics are presented.

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