Extended Uncertainty Principle Black Holes

Abstract

An Extended Uncertainty Principle inspired Schwarzschild metric that allows for large scale modifications to gravitation is presented. At a new fundamental length scale $\Ls$, the usual black hole characteristics (horizon radius, ISCO, and photosphere) deviate from their general relativistic counterparts by an additional term proportional to $\frac{G^3M^3}{\Ls^2}$ for $\hbar=c=1$. If the scale is $\Ls\sim10^{13}$m, EUP modifications become relevant for black holes of mass $M \geq 10^{6}~M_\odot$. This would affect the characteristics of most known supermassive black holes, and thus presents a unique set of experimental signatures that could be tested by the Event Horizon Telescope and similar future collaborations. The Newtonian potential is similarly modified, and it is shown that for values of $\Ls$ in the range considered, the effect will emerge at about 1~kpc from the galactic center, coincident with the flattening of the Milky Way's rotation curve. This suggests that the EUP could contribute to dark matter effects.