Tachyons and Black Hole Horizons in Gauge Theory

TL;DR

This paper proposes that Schwarzschild horizons in M(atrix) theory appear as tachyon instability regions (TIRs) in the gauge-theory description, providing a concrete absorption-based signature for the horizon. By analyzing D-brane absorption mechanisms and evaluating explicit configurations—including $N=2$ systems, spherical membranes, and Gaussian random matrices—the authors show that tachyon regions can be macroscopic and correlated with the horizon scale, while extremal cases rely on string-pair creation rather than tachyons. They develop a framework to compute $M^2$ for off-diagonal modes and demonstrate that tachyons arise in physically relevant backgrounds, supporting a gauge-theory notion of a horizon via tachyon condensation and subsequent thermalization. The work suggests a gauge-theoretic indicator for horizons, with potential extensions to non-extremal D-brane black holes and AdS/CFT contexts, where tachyon dynamics could encode horizon physics.

Abstract

Any probe which crosses the horizon of a black hole should be absorbed. In M(atrix) theory, for 0-brane probes of Schwarzschild black holes, we argue that the relevant absorption mechanism is a tachyon instability which sets in at the horizon. We give qualitative arguments, and some quantitative large-N calculations, in support of this claim. The tachyon instability provides an attractive mechanism for infalling matter to be captured and thermalized by a Schwarzschild black hole.

Figures (1)

• Figure 1: The eigenvalue distribution $\rho_A({\tilde{\lambda}})$. Equivalently, the density of stretched string states vs. (mass)$^2$ for a probe at the center of a Gaussian ensemble.