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<p>The holographic complexity of a static spherically symmetric black hole, defined as the volume of an extremal surface, grows linearly with time at late times in general relativity. The growth comes from a region at a constant transverse area inside the black hole and continues forever in the classical theory. In this region the volume complexity of any spherically symmetric black hole in <i>d</i> + 1 spacetime dimensions reduces to a geodesic length in an effective two-dimensional JT-gravity theory. The length in JT-gravity has been argued to saturate at very late times via non-perturbative corrections obtained from a random matrix description of the gravity theory. The same argument, applied to our effective JT-gravity description of the volume complexity, leads to complexity saturation at times of exponential order in the Bekenstein-Hawking entropy of a <i>d</i> + 1-dimensional black hole. Along the way, we explore a simple toy model for complexity growth, based on a discretisation of Nielsen complexity geometry, that can be analytically shown to exhibit the expected late-time complexity saturation.</p>

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Late-time saturation of black hole complexity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月7日

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  • Friðrik Freyr Gautason,
  • Vyshnav Mohan,
  • Lárus Thorlacius

摘要

The holographic complexity of a static spherically symmetric black hole, defined as the volume of an extremal surface, grows linearly with time at late times in general relativity. The growth comes from a region at a constant transverse area inside the black hole and continues forever in the classical theory. In this region the volume complexity of any spherically symmetric black hole in d + 1 spacetime dimensions reduces to a geodesic length in an effective two-dimensional JT-gravity theory. The length in JT-gravity has been argued to saturate at very late times via non-perturbative corrections obtained from a random matrix description of the gravity theory. The same argument, applied to our effective JT-gravity description of the volume complexity, leads to complexity saturation at times of exponential order in the Bekenstein-Hawking entropy of a d + 1-dimensional black hole. Along the way, we explore a simple toy model for complexity growth, based on a discretisation of Nielsen complexity geometry, that can be analytically shown to exhibit the expected late-time complexity saturation.