Stringy Forces in the Black Hole Interior

Abstract

Effective field theories break down inside large black holes on macroscopic scales when tidal forces are string-sized. If $r_0$ is the horizon radius and ${\alpha }^{\prime }$ is the square of the string scale, the 4D Schwarzschild interior is strongly curved at $(r_0{\alpha }^{\prime }{)}^{1/3}$. Infalling massless probes that reach this scale stretch and become excited strings. I generalize this picture for a wide class of black hole solutions in string theory. For the black hole dual to the large-$N$ BFSS model in a thermal state, and denoting ${\ell }_P$ the Planck length, tidal forces are stringy at $r_0{\left(\frac{r_0}{N^{1/3}{\ell }_P}\right)}^{3/11}$, which is greater than the scale where string perturbation theory breaks down for sufficiently large $r_0/{\ell }_P$. For 4D Kerr, there is a range of spin parameters for which the inner horizon is to the future of the scale of stringy curvature. These results specify the portion of black hole interior solutions where effective field theory can be used; beyond these scales, one must resort to other methods.

arXiv comment33 pages, 3 figures. V2: Added references, edited appendix, made more than 20 sentences more precise. V3: Added two figures that compare inner horizons to scales of strong curvature, matches with the published version

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