Strong energy condition and complexity growth bound in holography

TL;DR

This paper demonstrates that under certain conditions, the strong energy condition ensures that Schwarzschild black holes maximize action growth rate, supporting the holographic complexity-action conjecture.

Contribution

It establishes a link between the strong energy condition and maximal complexity growth in black holes, providing theoretical evidence for the complexity-action conjecture.

Findings

Strong energy condition guarantees maximal action growth in Schwarzschild black holes.

Supports the holographic complexity-action conjecture.

Provides conditions under which black holes saturate complexity growth bounds.

Abstract

This paper proves that if eternal neutral black holes satisfy some general conditions and matter fields only appear in the outside of the Killing horizon, the strong energy condition is a sufficient condition to insure that the vacuum Schwarzschild black hole has the fastest action growth of the same total energy. This result is consistent with the bound of computational complexity growth rate and gives a strong evidence for the holographic complexity-action conjecture.