Dual Charges for AdS Spacetimes and the First Law of Black Hole Mechanics

TL;DR

This paper extends the concept of dual charges to asymptotically AdS spacetimes, revealing their relation to NUT parameters and proposing a complex first law of black hole mechanics.

Contribution

It demonstrates the behavior of dual charges in AdS spacetimes and introduces a complex first law of black hole mechanics involving NUT charges.

Findings

Dual charges vanish at leading order in AdS with Dirichlet boundary.

In Taub-NUT-AdS solutions, dual charges are non-zero and linked to NUT parameters.

A complex first law of black hole mechanics is proposed.

Abstract

We apply the recent derivations of dual charges in asymptotically flat spacetimes to asymptotically locally AdS spacetimes. In contrast to the results in the flat case, in the AdS case with a Dirichlet boundary the dual charge contribution vanishes at the leading order. However, by focusing on the Taub-NUT-AdS solution, we show that nevertheless, more generally, the dual charge is non-vanishing and corresponds to the NUT parameter. We propose a complex first law of black mechanics in the presence of NUT charges that is inspired by the naturally complex nature of the charges derived using Hamiltonian methods.