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Reconstructing Minkowski Space-Time

Sergey N. Solodukhin

TL;DR

The paper develops a holographic description of Minkowski space by anchoring bulk Ricci-flat geometry to boundary data on the light-cone, then reduces linear gravitational perturbations to a tower of field equations on de Sitter slices. It identifies explicit holographic data for massless, partially massless, and massive graviton sectors, organized in λ-dependent pairs that map to boundary stress-tensor-like operators and sources on S^-_d and S^+_d, with precise interrelations and Ward identities. The analysis extends to the asymptotic black hole form, revealing how mass information is encoded in specific holographic modes (notably λ=d−1) and illustrating how the S-matrix of bulk gravity can be reconstructed from boundary correlators. Overall, this framework proposes a concrete, causality-respecting route to reconstruct and potentially quantize asymptotically flat gravity from boundary data on light-cone holographic screens.

Abstract

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of the light-cone. We focus on the gravitational aspects of the duality. Specifically, we identify the gravitational holographic data and provide the way Minkowski space-time (understood in more general context as a Ricci-flat space) is reconstructed from the data. In order to avoid the complexity of non-linear Einstein equations we consider linear perturbations and do the analysis for the perturbations. The analysis proceeds in two steps. We first reduce the problem in Minkowski space to an infinite set of field equations on de Sitter space one dimension lower. These equations are quite remarkable: they describe massless and massive gravitons in de Sitter space. In particular, the partially massless graviton appears naturally in this reduction. In the second step we solve the graviton field equations and identify the holographic boundary data. Finally, we consider the asymptotic form of the black hole space-time and identify the way the information about the mass of the static gravitational configuration is encoded in the holographic data.

Reconstructing Minkowski Space-Time

TL;DR

The paper develops a holographic description of Minkowski space by anchoring bulk Ricci-flat geometry to boundary data on the light-cone, then reduces linear gravitational perturbations to a tower of field equations on de Sitter slices. It identifies explicit holographic data for massless, partially massless, and massive graviton sectors, organized in λ-dependent pairs that map to boundary stress-tensor-like operators and sources on S^-_d and S^+_d, with precise interrelations and Ward identities. The analysis extends to the asymptotic black hole form, revealing how mass information is encoded in specific holographic modes (notably λ=d−1) and illustrating how the S-matrix of bulk gravity can be reconstructed from boundary correlators. Overall, this framework proposes a concrete, causality-respecting route to reconstruct and potentially quantize asymptotically flat gravity from boundary data on light-cone holographic screens.

Abstract

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of the light-cone. We focus on the gravitational aspects of the duality. Specifically, we identify the gravitational holographic data and provide the way Minkowski space-time (understood in more general context as a Ricci-flat space) is reconstructed from the data. In order to avoid the complexity of non-linear Einstein equations we consider linear perturbations and do the analysis for the perturbations. The analysis proceeds in two steps. We first reduce the problem in Minkowski space to an infinite set of field equations on de Sitter space one dimension lower. These equations are quite remarkable: they describe massless and massive gravitons in de Sitter space. In particular, the partially massless graviton appears naturally in this reduction. In the second step we solve the graviton field equations and identify the holographic boundary data. Finally, we consider the asymptotic form of the black hole space-time and identify the way the information about the mass of the static gravitational configuration is encoded in the holographic data.

Paper Structure

This paper contains 12 sections, 192 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Holographic reconstruction as a boundary value problem
  3. Holographic description in Minkowski space
  4. Reconstruction of metric: linear perturbation analysis
  5. First step: reduction to field equations on de Sitter slice
  6. Second step: solving field equations on de Sitter slice
  7. $\lambda=0$: Massless graviton in de Sitter space
  8. $\lambda=1$: Partially massless graviton in de Sitter space
  9. $\lambda\neq 0,1$: Massive graviton in de Sitter space
  10. Summary
  11. Asymptotic form of the black hole metric
  12. Conclusion

Figures (1)

  • Figure 1: Minkowski space-time with a choice of the light-cone. The boundary sphere $S^+_d$ ($S^-_d$) lies in the intersection of the light-cone and the future (past) null-infinity.