We study coupled geometric flows involving the metric, dilaton, and flux fields arising from worl... more We study coupled geometric flows involving the metric, dilaton, and flux fields arising from worldsheet β-functions in string theory. Extending the Ricci flow formalism, we derive parabolic evolution equations governing these fields and prove short-time existence and uniqueness for SU(3)-structure compactifications. We establish monotonicity properties of flow functionals analogous to Perelman's entropy and identify conditions for moduli stabilization in type II backgrounds. Our results unify Ricci-type flow techniques with flux compactifications and suggest new mathematical tools for analyzing dynamical string backgrounds and quantum gravity.
This study explores the influence of relativistic rotational effects on black hole entropy. Speci... more This study explores the influence of relativistic rotational effects on black hole entropy. Specifically, we investigate how the event horizon geometry of Kerr black holes, modified by angular momentum, affects entropy relative to non-rotating Schwarzschild black holes. Using the Bekenstein-Hawking entropy framework and invoking a heuristic analogy to length contraction from special relativity, we propose that increasing angular momentum geometrically contracts the event horizon. This leads to a reduction in its surface area and associated entropy. This geometricthermodynamic relationship offers an intuitive lens to understand the interplay between rotation, gravity, and thermodynamics in black holes.
This work explores the interplay between gravity and probability. Specifically, we investigate ho... more This work explores the interplay between gravity and probability. Specifically, we investigate how the probability distribution of a physical system can become distorted in the presence of a gravitational field. Drawing upon fundamental principles of probability theory, we analyze the modifications introduced by active gravitational influences. Our study leverages key concepts from general relativity, including the Ricci tensor and the energy-momentum tensor, to provide a theoretical framework for understanding this distortion. By proposing a geometric interpretation of probability, this work aims to stimulate new perspectives on the structure and behavior of probabilistic systems.
This paper investigates the relationship between gravitational wave energy and metric affineness ... more This paper investigates the relationship between gravitational wave energy and metric affineness in active gravitational fields. We present a novel analysis of gravitational wave behavior when propagating through regions of varying energy density. Our findings suggest a significant correlation between metric variations and gravitational wave energy attenuation, particularly in regions characterized by affine geometry. We provide theoretical frameworks supported by mathematical models to demonstrate how gravitational field strength influences wave propagation and energy dissipation.
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preprint by Rohit D