Strings near black holes are Carrollian

Abstract

We demonstrate that strings near the horizon of a Schwarzschild black hole, when viewed by a stationary observer at infinity, probe a string Carroll geometry, where the effective lightspeed is given by the distance from the horizon. We expand the Polyakov action in powers of this lightspeed to find a theory of Carrollian strings. We show that the string shrinks to a point to leading order near the horizon, which follows a null geodesic in a two-dimensional Rindler space. At the next-to-leading order the string oscillates in the embedding fields associated with the near-horizon two-sphere.

Figures (1)

• Figure 1: An asymptotic observer sees a closed string shrinking to a point as it approaches the near-horizon region, which looks like 2d Rindler space times a 2-sphere. In this regime, the string effectively probes a string Carroll geometry. The distance from the horizon $\epsilon$ provides an effective speed of light.