Accelerating Branes and the String/Black Hole Transition

TL;DR

This paper explores how string theory predicts a transition from black holes to string states as temperature increases, using D-brane dynamics and tachyon condensates to model the smearing of horizons and the non-normalizability of black hole states.

Contribution

It introduces a novel perspective on the string/black hole transition by linking tachyon condensates and horizon smearing to temperature effects and non-normalizability of black hole states.

Findings

Horizon smearing grows with Hawking temperature.

At the Hagedorn temperature, black holes become non-normalizable.

Stringy effects dominate near the transition point.

Abstract

String theory in Euclidean flat space with a spacelike linear dilaton contains a D1-brane which looks like a semi-infinite hairpin. In addition to its curved shape, this ``hairpin brane'' has a condensate of the open string tachyon stretched between its two sides. The tachyon smears the brane and shifts the location of its tip. The Minkowski continuation of the hairpin brane describes a D0-brane freely falling in a linear dilaton background. Effects that in Euclidean space are attributed to the tachyon condensate, give rise in the Minkowski case to a stringy smearing of the trajectory of the D-brane by an amount that grows as its acceleration increases. When the Unruh temperature of the brane reaches the Hagedorn temperature of perturbative string theory in the throat, the rolling D-brane state becomes non-normalizable. We propose that black holes in string theory exhibit similar properties. The Euclidean black hole solution has a condensate of a tachyon winding around Euclidean time. The Minkowski manifestation of this condensate is a smearing of the geometry in a layer around the horizon. As the Hawking temperature, T_{bh}, increases, the width of this layer grows. When T_{bh} reaches the Hagedorn temperature, the size of this ``smeared horizon'' diverges, and the black hole becomes non-normalizable. This provides a new point of view on the string/black hole transition.