String-theoretic breakdown of effective field theory near black hole horizons

We investigate the validity of the equivalence principle near horizons in string theory, analyzing the breakdown of effective field theory caused by longitudinal string spreading effects. An experiment is set up where a detector is thrown into a black hole a long time after an early infalling string. Light cone gauge calculations, taken at face value, indicate a detectable level of root-mean-square longitudinal spreading of the initial string as measured by the late infaller. This results from the large relative boost between the string and detector in the near-horizon region, which develops automatically despite their modest initial energies outside the black hole and the weak curvature in the geometry. We subject this scenario to basic consistency checks, using these to obtain a relatively conservative criterion for its detectability. In a companion paper, we exhibit longitudinal nonlocality in well-defined gauge-invariant S-matrix calculations, obtaining results consistent with the predicted spreading albeit not in a direct analog of the black hole process. We discuss applications of this effect to the firewall paradox, and estimate the time and distance scales it predicts for new physics near black hole and cosmological horizons.

Figure 1

Two configurations in which we assess the detectability of the spreading of the red string by the blue detector, as described in the text. (a) Direction of relative motion along the prescribed light cone directions $x^{\pm }$. (b) Direction of relative motion transverse to $x^{\pm }$.

Figure 2

Two illustrative processes from the paper [13]. They exhibit properties which fit with longitudinal spreading and are difficult to interpret purely in terms of transverse string spreading as described in the text.

Figure 3

The black hole with Kruskal light cone coordinates indicated.

Figure 4

Illustration of the proposed thought experiment. The early and late strings are displayed in red and blue respectively. The zigzag lines indicate the spreading of the early string as detectable by the late string, which only develops sufficient resolution to see it in the near-horizon region. The dotted line is a constant $r$ locus from which both detector and string may be dropped at different times.

Figure 5

Proportions in our setup. The separation between 1 and 2 is much larger than the intersection of string 1’s worldsheet with the horizon, our condition (3.7).

Figure 6

Trajectories 1 and 2 in the late de Sitter universe. For small values of the global spatial coordinate $\theta$, the trajectories fall across the indicated observer horizon at a late global time, so that the spatial slices are nearly flat as in our observed Universe. Within that regime, the hierarchy $\frac{{\theta }_2}{{\theta }_1}\ll 1$ leads to a large relative boost at the horizon, generated by the cosmological background.