# Quantum Tunnelling for Hawking Radiation from Both Static and Dynamic Black Holes

## TL;DR

This paper investigates Hawking radiation via quantum tunnelling from static and dynamic black holes, incorporating quantum corrections and deriving a modified entropy formula.

## Contribution

It introduces a unified approach to quantum tunnelling for both static and dynamic black holes, including quantum corrections beyond semiclassical approximation.

## Key findings

- Quantum corrections modify Hawking temperature and entropy.
- Different order correction terms satisfy the same differential equation.
- Derived a general modified black hole entropy formula.

## Abstract

The paper deals with Hawking radiation from both a general static black hole and a nonstatic spherically symmetric black hole. In case of static black hole, tunnelling of nonzero mass particles is considered and due to complicated calculations, quantum corrections are calculated only up to the first order. The results are compared with those for massless particles near the horizon. On the other hand, for dynamical black hole, quantum corrections are incorporated using the Hamilton-Jacobi method beyond semiclassical approximation. It is found that different order correction terms satisfy identical differential equation and are solved by a typical technique. Finally, using the law of black hole mechanics, a general modified form of the black hole entropy is obtained considering modified Hawking temperature.