Soliton mechanics

TL;DR

This paper explores the mechanics of five-dimensional spacetimes with non-trivial 2-cycles, deriving a first law that includes contributions from solitonic bubbles and providing explicit calculations of physical quantities.

Contribution

It introduces a new mass variation formula for spacetimes with bubbles, extending black hole mechanics to include solitonic structures and their associated fluxes.

Findings

Derived a first law of soliton and black hole mechanics.

Explicitly calculated angular momenta and charges in bubble spacetimes.

Demonstrated the importance of regularity conditions for the formulae.

Abstract

The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have non-zero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This `first law of black hole and soliton mechanics' contains new intensive and extensive quantities associated to each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulae relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.