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 ${ΔR}/{\lambdabar_M} = {Δx}/{2 \lambdabar_m}$. 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 $E_{\gamma }$, with $F=GM{m}_{\gamma }/R^2$, and therefore the photon has an effective gravitational mass $m_{\gamma }=E_{\gamma }/c^2$.

4 Latex pages, no figure.

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• Thermodynamical Aspects of Gravity: New insights
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