Zeno-Gravity Correspondence: Zeno's Dichotomy Paradox and Gravitational red-shift near Event Horizon

TL;DR

This paper establishes a novel analogy between Zeno's Dichotomy paradox and gravitational red-shift near a black hole's event horizon, providing an intuitive understanding of complex relativistic effects through a classical paradox.

Contribution

It introduces the Zeno-Gravity correspondence, linking Zeno's paradox to gravitational red-shift, offering a simplified, educational perspective on relativistic phenomena without advanced mathematics.

Findings

Mapped Zeno's paradox to gravitational red-shift effects

Clarified the concept of coordinate time near the event horizon

Provided an intuitive explanation of gravitational effects without differential geometry

Abstract

We relate Zeno's Dichotomy paradox with gravitational red-shift near event horizon in a spherically symmetric space-time. A dictionary of this connection, henceforth called as Zeno-Gravity correspondence, has been built up. The infinite sequence of Zeno's paradox gets mapped to the effect of infinite gravitational red-shift near event horizon and the infinite amount of co-ordinate time the light/particle takes to reach the horizon, starting from a finite distance away from the horizon. Utilizing the dictionary, we elucidate the concept of gravitational red-shift and co-ordinate chart, not covering the whole manifold in a more transparent student-friendly manner without using sophisticated machinery of differential geometry.