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dS/CFT at uniform energy density and a de Sitter "bluewall"

Diptarka Das, Sumit R. Das, K. Narayan

TL;DR

The paper investigates bulk duals in dS/CFT that correspond to a CFT on a circle with uniform energy density, by constructing asymptotically de Sitter spacetimes that arise via analytic continuation from Euclidean AdS black branes. A key result is that, for odd spacetime dimensions, the holographic energy-momentum tensor can be real even when the bulk metric is complex, while for even dimensions it remains imaginary, and the Fefferman–Graham expansion links normalizable bulk modes to the boundary $T_{ij}$. The authors also introduce a real-parameter branch, the de Sitter bluewall, which features two asymptotic de Sitter regions connected by Cauchy horizons and timelike singularities, and they show that late-time infalling observers experience an exponentially large blueshift near the horizons, indicating a blue-shift instability. These findings illuminate how holographic stress tensors encode horizon-like instabilities in dS/CFT and illustrate the role of regularity conditions and analytic continuation in defining the dual description.

Abstract

We describe a class of spacetimes that are asymptotically de Sitter in the Poincare slicing. Assuming that a dS/CFT correspondence exists, we argue that these are gravity duals to a CFT on a circle leading to uniform energy-momentum density, and are equivalent to an analytic continuation of the Euclidean AdS black brane. These are solutions with a complex parameter which then gives a real energy-momentum density. We also discuss a related solution with the parameter continued to a real number, which we refer to as a de Sitter "bluewall". This spacetime has two asymptotic de Sitter universes and Cauchy horizons cloaking timelike singularities. We argue that the Cauchy horizons give rise to a blue-shift instability.

dS/CFT at uniform energy density and a de Sitter "bluewall"

TL;DR

The paper investigates bulk duals in dS/CFT that correspond to a CFT on a circle with uniform energy density, by constructing asymptotically de Sitter spacetimes that arise via analytic continuation from Euclidean AdS black branes. A key result is that, for odd spacetime dimensions, the holographic energy-momentum tensor can be real even when the bulk metric is complex, while for even dimensions it remains imaginary, and the Fefferman–Graham expansion links normalizable bulk modes to the boundary . The authors also introduce a real-parameter branch, the de Sitter bluewall, which features two asymptotic de Sitter regions connected by Cauchy horizons and timelike singularities, and they show that late-time infalling observers experience an exponentially large blueshift near the horizons, indicating a blue-shift instability. These findings illuminate how holographic stress tensors encode horizon-like instabilities in dS/CFT and illustrate the role of regularity conditions and analytic continuation in defining the dual description.

Abstract

We describe a class of spacetimes that are asymptotically de Sitter in the Poincare slicing. Assuming that a dS/CFT correspondence exists, we argue that these are gravity duals to a CFT on a circle leading to uniform energy-momentum density, and are equivalent to an analytic continuation of the Euclidean AdS black brane. These are solutions with a complex parameter which then gives a real energy-momentum density. We also discuss a related solution with the parameter continued to a real number, which we refer to as a de Sitter "bluewall". This spacetime has two asymptotic de Sitter universes and Cauchy horizons cloaking timelike singularities. We argue that the Cauchy horizons give rise to a blue-shift instability.

Paper Structure

This paper contains 4 sections, 39 equations, 2 figures.

Table of Contents

  1. Introduction and summary
  2. $dS/CFT$ at uniform energy-momentum density
  3. Real parameter $C$: a de Sitter "bluewall"
  4. de Sitter "bluewall" details

Figures (2)

  • Figure 1: de Sitter "bluewall" Penrose diagram. This resembles the Penrose diagram of the $AdS$ Schwarzschild black brane rotated by ${\pi\over 2}$.
  • Figure 2: Trajectories in the de Sitter bluewall and the Cauchy horizon. Observers $P_1$ are static while $P_2$ has $w$-momentum $p_w$, crosses the horizon, turns around inside and appears to re-emerge in the future universe. Also shown are incoming lightrays from infinity which "crowd near" the Cauchy horizon.