A Note on Temperature and Energy of 4-dimensional Black Holes from Entropic Force

TL;DR

This paper explores the temperature and energy on holographic screens for 4D black holes using Verlinde's entropic force, revealing a generalized temperature and a modified force law involving a reduced mass.

Contribution

It introduces a generalized Hawking temperature on holographic screens and demonstrates that the entropic force depends on a reduced black hole mass, not the total mass.

Findings

Unruh-Verlinde temperature equals Hawking temperature on the horizon.

Energy on holographic screens relates to reduced mass M_0, not total mass M.

Entropic force formula modified to include reduced mass M_0.

Abstract

We investigate the temperature and energy on holographic screens for 4-dimensional black holes with the entropic force idea proposed by Verlinde. We find that the "Unruh-Verlinde temperature" is equal to the Hawking temperature on the horizon and can be considered as a generalized Hawking temperature on the holographic screen outside the horizons. The energy on the holographic screen is not the black hole mass $M$ but the reduced mass $M_0$, which is related to the black hole parameters. With the replacement of the black hole mass $M$ by the reduced mass $M_0$, the entropic force can be written as $F=\frac{GmM_0}{r^2}$, which could be tested by experiments.