Black Holes and Photons with Entropic Force

TL;DR

This paper explores entropic force effects on black holes and photons, deriving new relations for black hole radius changes and proposing a unified entropy change rule, extending entropic force concepts to massless particles like photons.

Contribution

It introduces a new relation for black hole radius change due to entropic forces and extends the entropic force framework to photons, unifying entropy concepts across dimensions.

Findings

Derived a relation for black hole radius change under entropic influence.

Proposed a unified entropy change rule applicable in various dimensions.

Extended entropic force concept to photons, attributing an effective gravitational mass.

Abstract

We study entropic force effects on black holes and photons. We find that application of an entropic analysis restricts the radial change $\Delta R$ of a black hole of radius $R_{\mathrm{H}}$, due to a test particle of a Schwartzchild radius $R_{h}$ moving towards the black hole by $\Delta x$ near black body surface, to be given by a relation $R_{\mathrm{H}} \Delta R= R_h \Delta x/2$, or ${\Delta R}/{\lambdabar_M} = {\Delta x}/{2 \lambdabar_m}$. We suggest a new rule regarding entropy changes in different dimensions, $\Delta S= 2\pi k D \Delta l /\lambdabar,$ which unifies Verlinde's conjecture and the black hole entropy formula. We also propose to extend the entropic force idea to massless particles such as a photon. We find that there is an entropic force on a photon of energy $E_\gamma$, with $F=G M m_{\gamma}/R^2$, and therefore the photon has an effective gravitational mass $m_\gamma = E_\gamma/c^2$.