Chemistry and Complexity for Solitons in AdS$_5$

TL;DR

This paper explores gravitational solitons in five-dimensional supergravity, analyzing their thermodynamic properties and holographic complexity, revealing similarities with black holes and novel behaviors in complexity measures.

Contribution

It introduces the study of asymptotically AdS$_5$ gravitational solitons, deriving mass formulas, and examining their holographic complexity within the complexity equals action and volume conjectures.

Findings

Complex mass and variation formulas analogous to black holes.

Complexity of formation scales as V^{3/4} for large solitons.

Distinct behaviors observed between volume and action complexity measures.

Abstract

Minimal $D=5$ supergravity admits asymptotically globally AdS$_5$ gravitational solitons (strictly stationary, geodesically complete spacetimes with positive mass). We show that, like asymptotically flat gravitational solitons, these solutions satisfy mass and mass variation formulas analogous to those satisfied by AdS black holes. A thermodynamic volume associated to the non-trivial topology of the spacetime plays an important role in this construction. We then consider these solitons within the holographic ``complexity equals action'' and ``complexity equals volume'' conjectures as simple examples of spacetimes with nontrivial rotation and topology. We find distinct behaviours for the volume and action, with the counterterm for null boundaries playing a significant role in the latter case. For large solitons we find that both proposals yield a complexity of formation proportional to a power of the thermodynamic volume, $V^{3/4}$. In fact, up to numerical prefactors, the result coincides with the analogous one for large black holes.