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Non-extremal fuzzballs and ergoregion emission

Borun D. Chowdhury, Samir D. Mathur

Abstract

In the traditional picture of black holes Hawking radiation is created by pair creation from the vacuum at the horizon. In the fuzzball proposal, individual microstates do not have a horizon with the `vacuum' state in its vicinity. For a special family of non-extremal microstates it was recently found that emission occurs due to pair creation in an ergoregion, rather than at a horizon. In this paper we extend this result to a slightly larger class of microstates, again finding exact agreement between the emission in the gravity picture and the CFT dual. We write down an expression for emission from geometries with ergoregions, in terms of the leading falloff behavior of the wavefunctions in the fuzzball region. Finally, we describe another family of nonextremal microstates and find their ergoregion.

Non-extremal fuzzballs and ergoregion emission

Abstract

In the traditional picture of black holes Hawking radiation is created by pair creation from the vacuum at the horizon. In the fuzzball proposal, individual microstates do not have a horizon with the `vacuum' state in its vicinity. For a special family of non-extremal microstates it was recently found that emission occurs due to pair creation in an ergoregion, rather than at a horizon. In this paper we extend this result to a slightly larger class of microstates, again finding exact agreement between the emission in the gravity picture and the CFT dual. We write down an expression for emission from geometries with ergoregions, in terms of the leading falloff behavior of the wavefunctions in the fuzzball region. Finally, we describe another family of nonextremal microstates and find their ergoregion.

Paper Structure

This paper contains 36 sections, 121 equations, 6 figures.

Table of Contents

  1. Introduction
  2. The microstate geometry
  3. The supergravity solution
  4. The large R limit
  5. The inner and outer regions
  6. Inner Region: $r^2 \ll \sqrt{Q_1 Q_5}$
  7. The Outer Region: $r^2 \gg \sqrt{Q_1Q_5}$
  8. The ergoregion
  9. The classical instability
  10. The CFT description for the state and for the emitted scalar
  11. The D1-D5 CFT
  12. The CFT state
  13. The orbifold CFT
  14. Spectral flow
  15. Spectral flow of the component string
  16. ...and 21 more sections

Figures (6)

  • Figure 1: The NS vacuum is shown in (a) and the chiral primary state is shown in (b).
  • Figure 2: The ground state in the twisted Ramond sector.
  • Figure 3: The initial state of the CFT; each component string has a certain winding number and left and right fermionic excitations.
  • Figure 4: The state of the CFT after one 'final state' component string has been produced.
  • Figure 5: A generic stationary geometry (in the large $R$ limit).
  • ...and 1 more figures