Quantum time dilation in the near-horizon region of a black hole

TL;DR

This paper derives a quantum time dilation relation for clocks near a black hole horizon, connecting quantum effects with classical and flat spacetime limits.

Contribution

It introduces a quantum time dilation formula applicable in the near-horizon region of black holes using Rindler metric and conformal tortoise coordinates.

Findings

Quantum time dilation relation derived for near-horizon black hole region

Relation reduces to classical and flat spacetime limits

Provides a bridge between quantum and classical gravitational effects

Abstract

In this work, we obtain a relation for average quantum time dilation between two clocks A and B in the near-horizon region of a black hole supported by the Rindler metric and conformal tortoise coordinate. It is indicated that this relation is identified with time dilation in classical and flat background limits.