# Energy distribution and thermodynamics of the quantum-corrected Schwarzschild black hole

## TL;DR

This paper explores how quantum vacuum fluctuations affect the energy distribution and thermodynamics of Schwarzschild black holes, revealing that quantum corrections increase energies and temperature-related properties.

## Contribution

It introduces quantum vacuum fluctuation corrections into Schwarzschild black hole thermodynamics and compares different energy prescriptions, highlighting their differences.

## Key findings

- Quantum fluctuations increase black hole energies.
- Einstein and Møller energies differ due to quantum effects.
- Quantum correction factor influences temperature and heat capacity.

## Abstract

In this work, energy distribution and thermodynamics are investigated in the Schwarzschild black hole spacetime when considering corrections due to quantum vacuum fluctuations. The Einstein and M{\o}ller prescriptions were used to derive the expressions of the energy in the background. The temperature and heat capacity were also derived. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, all the energies increase and Einstein energy differs from M{\o}ller's one. Moreover, when increasing the quantum correction factor ($a$), the difference between Einstein and M{\o}ller energies, the Unruh-Verlinde temperature as well as the heat capacity of the black hole increase while the Hawking temperature remains unchanged.