Soliton mechanics

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. * sdgg82@mun.ca † uh1681@mun.ca ‡ hkkunduri@mun.ca 1 arXiv:1609.08500v1 [hep-th]

Chemistry and Complexity for Solitons in AdS$_5$

“…Considering the first law, the thermodynamic volume plays a role in the first law analogous to that in the black hole case. Interestingly, we find that the first law holds only if the variations respect the regularity of the spacetime, commensurate with previous results for the asymptotically flat case [26].…”

“…The local solutions above can be made to describe rotating black holes by taking appropriate ranges of the parameters (p, q, j). Alternatively, as first observed by Ross [15], one may choose parameters so that a complete Lorentzian metric is obtained (the resulting solitons are AdS generalizations of the solitons considered in [26]). To do this, we require that the S 1 direction parameterized by the ψ coordinate smoothly degenerates on an S 2 in the spacetime at some radius r = r 0 .…”

5-dimensional space-periodic solutions of the static vacuum Einstein equations

“…Similar results hold for the Einstein-Maxwell equations when D = 4. However, in higher dimensional supergravity theories, horizonless soliton solutions can possess nontrivial 2-cycle 'bubbles' that are supported by magnetic flux supplied by Maxwell fields [11]. Here, a gravitational soliton refers to a nontrivial, globally stationary, geodesically complete spacetime.…”

Spacetime Topology and the Laws of Black Hole-Soliton Mechanics

“…Indeed, additional terms in the Smarr relation and first law for black rings were originally observed by Emparan [18] and later given a derivation by Copsey and Horowitz [19]. In contrast here the extra terms arise in a natural way as a consequence of the structure of the orbit space, as has recently been shown in [20]. Finally, it is interesting that variations of intensive variables (e.g., δΦ I i [D]) appear in the first law, rather than those of extensive quantities.…”

“…The Killing field ∂ ψ degenerates at r = r 0 and the manifold near that point is diffeormorphic to R t × S 2 × {pt} provided there is no conical singularity at r = r 0 , which requires [20] 1…”