Abstract

A mini-review devoted to some implications of the Hagedorn temperature for black hole physics. The existence of a limiting temperature is a generic feature of string models. The Hagedorn temperature was introduced first in the context of hadronic physics. Nowadays, the emphasis is shifted to fundamental strings which might be a necessary ingredient to obtain a consistent theory of black holes. The point is that, in field theory, the local temperature close to the horizon could be arbitrarily high, and this observation is difficult to reconcile with the finiteness of the entropy of black holes. After preliminary remarks, we review our recent attempt to evaluate the entropy of large black holes in terms of fundamental strings. We also speculate on implications for dynamics of large- N c gauge theories arising within holographic models.

Highlights

  • 1.1 From hadrons to black holesThis talk was presented at a session devoted to the 50th anniversary of the introduction of the Hagedorn temperature [1]

  • The Hagedorn temperature TH was discussed in connection with hadronic physics

  • We will discuss the physics of black holes, or, more precisely, the properties of the black-hole horizon

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Summary

From hadrons to black holes

This talk was presented at a session devoted to the 50th anniversary of the introduction of the Hagedorn temperature [1]. The local temperature close to the horizon can be arbitrarily high, and this is known to be inconsistent with finiteness of the Bekenstein-Hawking entropy of black holes, see, in particular, [2][3]. The inconsistency becomes manifest at the gravitational scale, or at T ∼ MPlanck This observation serves as a motivation [4] to introduce strings at this scale. It is within this framework that we make our remarks on the explicit evaluation of the Bekenstein-Hawking entropy, see [5] and references therein. In the Introduction we describe briefly how the notion of a limiting temperature arises within a generic string picture.

Hagedorn temperature
Hagedorn temperature and strings
Limiting temperature vs phase transition
Black holes and limiting temperature
Stringy horizon
Main results
Main tool: thermal scalar
Thermal scalar in curved space
Picture emerging

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