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Brane-world creation and black holes

Jaume Garriga, Misao Sasaki

TL;DR

We address the quantum creation of an inflating brane-world in an AdS$_5$ bulk and its subsequent evolution. The work constructs a de Sitter-brane instanton by gluing two AdS patches along a 4-sphere, analyzes the KK graviton spectrum and finds a mass gap $m=(3/2)H$, and extends to a Nariai-brane instanton describing pair creation of 'black cigars'; it also studies Schwarzschild-AdS bulk thermal instantons and interprets the extra 'radiation-like' term in the brane Friedmann equation via AdS/CFT. In the large-instanton limit the 5D action reduces to the 4D action and the entropies agree, supporting holographic unity between bulk and boundary. The results reinforce that brane-world cosmology reproduces standard 4D results in the low-energy limit, while providing semiclassical mechanisms for brane creation and explicit predictions for KK spectra and nucleation rates.

Abstract

An inflating brane-world can be created from ``nothing'' together with its Anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap $m=(3/2) H$, where $H$ is the Hubble rate. We consider the analog of the Nariai solution and argue that it describes pair production of ``Black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing, or the production of AdS black holes in the vicinity of a pre-existing inflating brane-world. The Lorentzian evolution of the brane-world after creation is briefly discussed. An additional "integration constant" in the Friedmann equation -accompanying a term which dilutes like radiation- describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. This could be a 5-dimensional black hole or a "parallel" brane-world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the $AdS/CFT$ correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.

Brane-world creation and black holes

TL;DR

We address the quantum creation of an inflating brane-world in an AdS bulk and its subsequent evolution. The work constructs a de Sitter-brane instanton by gluing two AdS patches along a 4-sphere, analyzes the KK graviton spectrum and finds a mass gap , and extends to a Nariai-brane instanton describing pair creation of 'black cigars'; it also studies Schwarzschild-AdS bulk thermal instantons and interprets the extra 'radiation-like' term in the brane Friedmann equation via AdS/CFT. In the large-instanton limit the 5D action reduces to the 4D action and the entropies agree, supporting holographic unity between bulk and boundary. The results reinforce that brane-world cosmology reproduces standard 4D results in the low-energy limit, while providing semiclassical mechanisms for brane creation and explicit predictions for KK spectra and nucleation rates.

Abstract

An inflating brane-world can be created from ``nothing'' together with its Anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap , where is the Hubble rate. We consider the analog of the Nariai solution and argue that it describes pair production of ``Black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing, or the production of AdS black holes in the vicinity of a pre-existing inflating brane-world. The Lorentzian evolution of the brane-world after creation is briefly discussed. An additional "integration constant" in the Friedmann equation -accompanying a term which dilutes like radiation- describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. This could be a 5-dimensional black hole or a "parallel" brane-world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.

Paper Structure

This paper contains 4 sections, 54 equations, 2 figures.

Table of Contents

  1. Introduction
  2. de Sitter-brane instanton
  3. Pair production of "black cigars"
  4. AdS black holes and thermal instantons

Figures (2)

  • Figure 1: De Sitter-brane instanton. The thick vertical circle at $r=r_0$ represents the 4-sphere brane at which the two identical 5-dimensional anti-de Sitter spaces are glued. The $\chi=\pi/2$ hypersurface is the nucleation geometry.
  • Figure 2: Conformal diagram of the inflating brane-world (at $r=r_0$) created from nothing. Each point in the figure represents a 3-sphere.