# Extended Uncertainty Principle Black Holes

## TL;DR

This paper proposes an Extended Uncertainty Principle inspired modification to the Schwarzschild metric, predicting large-scale deviations in black hole and galactic dynamics that could be tested observationally and may relate to dark matter phenomena.

## Contribution

It introduces a new EUP-inspired metric that modifies black hole and galactic gravitational characteristics at large scales, linking quantum principles to astrophysical observations.

## Key findings

- Deviations in black hole properties become significant for supermassive black holes with M ≥ 10^6 solar masses.
- Modified Newtonian potential could explain galactic rotation curve flattening.
- Potential observational signatures detectable by Event Horizon Telescope and similar instruments.

## 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.