Black Holes and Photons with Entropic Force

We study entropic force effects on black holes and photons. We find that application of an entropic analysis restricts the radial change $\mathrm{\Delta }R$ 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 $\mathrm{\Delta }x$ 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 $F=GM{m}_{\gamma }\mathrm{/}{R}^2$, and therefore the photon has an effective gravitational mass $m_{\gamma }=E_{\gamma }\mathrm{/}{c}^2$.