Complexity Growth Rate in Lovelock Gravity

TL;DR

This paper calculates the late-time growth of complexity in charged black holes within Lovelock gravity using the 'Complexity = Action' approach, revealing dependencies on internal energies and Lovelock couplings.

Contribution

It extends the complexity growth analysis to Lovelock gravity, providing explicit formulas and identifying conditions where complexity growth halts.

Findings

Growth rate reduces to a difference of internal energies.

Reproduces the $2M/\pi$ result with Lovelock corrections.

Identifies a minimum mass threshold for complexity growth.

Abstract

Using the "Complexity = Action" framework we compute the late time growth of complexity for charged black holes in Lovelock gravity. Our calculation is facilitated by the fact that the null boundaries of the Wheeler-DeWitt patch do not contribute at late times and essential contributions coming from the joints are now understood arXiv:1803.00172. The late time growth rate reduces to a difference of internal energies associated with the inner and outer horizons, and in the limit where the mass is much larger than the charge, we reproduce the celebrated result of $2M/\pi$ with corrections proportional to the highest Lovelock coupling in even (boundary) dimensions. We find in some cases a minimum mass below which complexity remains effectively constant, even if the black hole contains a non-degenerate horizon.