2025/02/24 by Gautason, Friðrik Freyr, Mohan, Vyshnav, Thorlacius, Lárus · 3 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2502.17179
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.