Complexity Conjecture of Regular Electric Black Holes

TL;DR

This paper explores the complexity growth rate of four-dimensional regular electric black holes in different frames, analyzing their action growth, energy modifications, and asymptotic behavior under various conjectures.

Contribution

It introduces the study of action growth rates for electric black holes in P frame and examines the effects on Lloyd bound and complexity conjectures.

Findings

Action growth rate analyzed for electric black holes in P frame.

Energy modifications due to non-zero trace of energy-momentum tensor.

Asymptotic behavior of complexity studied for static and rotating black holes.

Abstract

Recently, the action growth rate of a variety of four-dimensional regular magnetic black holes in F frame is obtained in [1]. Here, we study the action growth rate of a four-dimensional regular electric black hole in P frame that is the Legendre transformation of F frame. We also investigate the action growth rates of the Wheeler-De Witt patch for such black hole configurations at the late time and examine the Lloyd bound on the rate of quantum computation. We show that although the form of the Lloyd bound formula remains unaltered, the energy modifies due to a non-vanishing trace of the energy-momentum tensor and some extra terms may appear in the total growth action. We also investigate the asymptotic behavior of complexity in two conjectures for static and rotating regular black holes.