Gravitational Time Dilation from Closed-String Condensates, Perelman's Entropy Functional, and Dirac–Born–Infeld Brane Pullback Geometry
Year: 2026
Type: preprint
Abstract: In relativistic gravity and string theory, a foundational structural question concerns how the macroscopic curvature of spacetime and the slowing of physical clocks near a massive body emerge from microscopic quantum degrees of freedom. In this treatise, we establish a self-contained mathematical architecture that unifies the coherent condensation of boundaryless closed gravitational strings in the bulk manifold with the worldvolume dynamics of open matter and gauge strings anchored to a three-dimensional spacetime membrane. Whereas elementary fermions and gauge bosons are represented by open strings whose endpoints are constrained to move on the three-dimensional membrane via Dirichlet and Neumann boundary conditions, gravitons are closed string loops devoid of endpoints that propagate freely throughout the ambient bulk spacetime. We demonstrate that a macroscopic Glauber–Polyakov coherent condensate of massless closed-string graviton and scalar dilaton excitations deforms the flat background geometry into a curved weighted Riemannian manifold. By introducing Grigori Perelman’s entropy functional on a Bakry–Émery weighted manifold equipped with the dilaton-deformed volume measure, we prove that the one-loop conformal Weyl invariance of the closed-string worldsheet is variationally equivalent to the monotonic gradient flow of Perelman’s entropy functional, whose stationary equilibrium enforces the vanishing of the generalized Bakry–Émery Ricci curvature tensor. Finally, we prove that when this stationary closed-string bulk metric is pulled back onto the three-dimensional membrane via the Dirac–Born–Infeld worldvolume action, the Arnowitt–Deser–Misner temporal lapse function at the open-string endpoints is governed directly by the local density of the closed-string graviton condensate. Consequently, as a physical clock composed of membrane-anchored open strings approaches a massive gravitational source, the increasing local concentration of closed-string graviton modes reduces the induced temporal lapse function on the membrane, providing a rigorous variational derivation of gravitational time dilation and frequency redshift from first principles.
Author: Tanan, Yassin
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225652077
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