Soliton mechanics

The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess nontrivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have nonzero 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 with each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulas 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.