Black Holes and Photons with Entropic Force

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 $\Delta R/{\text{lambdabar}}_M=\Delta x/2{\text{lambdabar}}_m$. We suggest a new rule regarding entropy changes in different dimensions, $\Delta S=2\pi kD\Delta l/\text{lambdabar},$ 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 $F=GM{m}_{\gamma }/R^2$, and therefore the photon has an effective gravitational mass $m_{\gamma }=E_{\gamma }/c^2$.

Comments: 4 Latex pages, no figure.