# The First Law for Rotating NUTs

## TL;DR

This paper develops a comprehensive thermodynamic first law for rotating Taub--NUT solutions, incorporating asymmetric Misner strings and their charges, revealing new contributions to angular momentum beyond traditional Noether charges.

## Contribution

It introduces a full cohomogeneity first law for rotating NUT spacetimes, accounting for Misner string asymmetries and their gravitational charges, a novel extension in gravitational thermodynamics.

## Key findings

- Derived a full cohomogeneity first law for rotating NUTs.
- Identified non-trivial contributions to angular momentum from Misner strings.
- Allowed for asymmetric Misner string distributions and variable strengths.

## Abstract

We address a long-standing problem of describing the thermodynamics of rotating Taub--NUT solutions. The obtained first law is of full cohomogeneity and allows for asymmetric distributions of Misner strings as well as their potential variable strengths---encoded in the gravitational Misner charges. Notably, the angular momentum is no longer given by the Noether charge over the sphere at infinity and picks up non-trivial contributions from Misner strings.