Quantum Geometric Flows
We develop a novel approach to quantum geometry based on geometric flows, and we propose
that this quantum geometry can be used to describe quantum gravity. Thus, we first identify
the degrees of freedom for the dynamical system describing such geometric flows. We then are
able to demonstrate that Raychaudhuri equation is the classical field equation obtained from
the Hamiltonian (and action) of such a dynamical system. As we have the full Hamiltonian
(and action) for the geometric flows, we are able to quantize this system using a functional
Schr\"{o}dinger’s equation. Unlike the Wheeler-DeWitt equation, this Schr\"{o}dinger’s
equation for geometric flows has an intrinsic definition of time. We also comment on the
Ehrenfest limit of this Schr\"{o}dinger’s equation describing quantum geometric flows, and
its implications for the Hawking-Penrose singularity theorems.
We also discuss the implications of this formalism to cosmology and Black holes
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