# The Stretched Horizon Limit

**Authors:** Dionysios Anninos, Damián A. Galante, Silvia Georgescu, Chawakorn Maneerat, Andrew Svesko  
**arXiv:** [2512.16738](https://arxiv.org/abs/2512.16738)  
**Date:** 2025-12-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2512.16738v1/

## Key points

- The paper explores four-dimensional general relativity with a positive cosmological constant ($Λ$) in the presence of a boundary ($Γ$) of finite spatial size.
- Specific boundary conditions dictate the conformal class of the induced metric and the trace of the extrinsic curvature along $Γ".
- The parameter ${K}{Λ^{-\frac{1}{2}}}$ is crucial in determining the proximity of $Γ$ to the horizon.
- Two scenarios are explored: one where $Γ$ encloses a portion of the static patch just before the cosmological horizon (pole patch), and another where $Γ$ encompasses only the region near the cosmological horizon (cosmic patch).
- In their investigation, ordinary normal modes, a novel type of boundary gapless mode, and boundary soft modes characterized by specific frequencies are identified for the pole patch scenario.
- Minkowskian behavior is reinstated for angular momenta $l \gtrsim {K}{Λ^{-\frac{1}{2}}}$ to mitigate growing modes.
- Sound and shear fluid-dynamical modes are identified in the cosmic patch scenario, interpreted as manifestations of a conformal fluid with specific viscosity ratios.
- Non-linear treatments within the fluid dynamical sector reveal a scaling regime where stretched horizon gravitational dynamics follow a universal Rindler geometry independent of specific infilling horizon details.
- Quantitative distinctions between cosmological and black hole horizons outside the Rindler regime are briefly touched upon.

## Summary

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The paper "The Stretched Horizon Limit" by Dionysios Anninos, Damián A. Galante, Silvia Georgescu, Chawakorn Maneerat, and Andrew Svesko explores the realm of four-dimensional general relativity with a positive cosmological constant ($Λ$) in the presence of a boundary ($Γ$) of finite spatial size. The strategically positioned boundary near a cosmological event horizon is governed by specific boundary conditions that dictate the conformal class of the induced metric and the trace of the extrinsic curvature along $Γ$. The parameter ${K}{Λ^{-\frac{1}{2}}}$ plays a crucial role in determining the proximity of $Γ$ to the horizon. The study provides an exhaustive analysis of linearized gravitational perturbations within this setup, exploring two distinct scenarios: one where $Γ$ encloses a portion of the static patch just before the cosmological horizon (pole patch), and another where $Γ$ encompasses only the region near the cosmological horizon (cosmic patch). In their investigation of the pole patch, the authors uncover a layered hierarchy of modes including ordinary normal modes, a novel type of boundary gapless mode, and boundary soft modes characterized by frequencies close to $\pm 2πi T_{\text{dS}}$, with $T_{\text{dS}}$ representing the horizon temperature. They also demonstrate that Minkowskian behavior is reinstated for angular momenta $l \gtrsim {K}{Λ^{-\frac{1}{2}}}$—a parameter that can be significantly increased—to mitigate previously identified growing modes. Transitioning to the cosmic patch, they identify sound and shear fluid-dynamical modes which they interpret as manifestations of a conformal fluid exhibiting a shear viscosity over entropy density ratio of $\tfracη{s} = \tfrac{1}{4π}$ alongside vanishing bulk viscosity ($ζ=0$). The authors also explore non-linear treatments within the fluid dynamical sector and describe a scaling regime where stretched horizon gravitational dynamics are dictated by a universal Rindler geometry independent of specific infilling horizon details. Finally, they briefly touch upon quantitative distinctions between cosmological and black hole horizons outside the Rindler regime. This comprehensive study sheds light on intricate gravitational dynamics near boundaries in four-dimensional general relativity with implications for both cosmology and black hole physics.