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 $ΔR$ 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 $Δx$ near black body surface, to be given by a relation $R_{\mathrm{H}} ΔR= R_h Δx/2$, or ${ΔR}/{\lambdabar_M} = {Δx}/{2 \lambdabar_m}$. We suggest a new rule regarding entropy changes in different dimensions, $ΔS= 2πk D Δl /\lambdabar,$ 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 $E_γ$, with $F=G M m_γ/R^2$, and therefore the photon has an effective gravitational mass $m_γ= E_γ/c^2$.

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