Strings near black holes are Carrollian -- Part II

TL;DR

This paper explores how classical strings behave near black hole horizons, revealing a Carrollian regime characterized by two types of strings with distinct worldsheet geometries, and extends this understanding to various black hole solutions.

Contribution

It introduces a novel Carrollian string framework near black hole horizons, identifying magnetic and electric Carroll strings and demonstrating their relevance to different black hole geometries.

Findings

Two types of Carroll strings: magnetic with Lorentzian worldsheet, electric with Carrollian worldsheet.

Near-horizon geometry of 4D black holes matches the string Carroll expansion.

The framework applies to Kerr and Reissner-Nordström black holes, indicating broad applicability.

Abstract

We study classical closed bosonic strings probing the near-horizon region of a non-extremal black hole and show that this corresponds to understanding string theory in the Carroll regime. This is done by first performing a Carroll expansion and then a near-horizon expansion of a closed relativistic string, subsequently showing that they agree. Concretely, we expand the phase space action in powers of $c^2$, where $c$ is the speed of light, assuming that the target space admits a string Carroll expansion (where two directions are singled out) and show that there exist two different Carroll strings: a magnetic and an electric string. The magnetic string has a Lorentzian worldsheet, whereas the worldsheet of the electric string is Carrollian. The geometry near the horizon of a four-dimensional (4D) Schwarzschild black hole takes the form of a string Carroll expansion (a 2D Rindler space fibred over a 2-sphere). We show that the solution space of relativistic strings near the horizon bifurcates and the two sectors precisely match with the magnetic/electric Carroll strings with an appropriate target space. Magnetic Carroll strings near a black hole shrink to a point on the two-sphere and either follow null geodesics or turn into folded strings on the 2D Rindler spacetime. Electric Carroll strings wrap the two-sphere and follow a massive geodesic in the Rindler space. Finally, we show that 4D non-extremal Kerr and Reissner-Nordstr\"om black holes also admit string Carroll expansions near their outer horizons, indicating that our formulation extends to generic non-extremal black holes.