Localisation of Soft Charges, and Thermodynamics of Softly Hairy Black Holes

Understand

Large gauge transformations (LGT) in asymptotically flat space are generated by charges defined at asymptotic infinity.

• No method for unambiguously localising these charges into the interior of spacetime has previously been established.
• We determine what this method must be, and use it to find localised expressions for the LGT charges.
• Applying the same principle to the case of a charged black hole spacetime leads to angle-dependent generalisations of the Smarr formula and the first law of black hole mechanics, both of which have important thermodynamical implications.