Einstein–Skyrme black hole’s novel first law of Skyrmion’s black hole thermodynamics

Abstract We investigate the thermodynamics and phase structure of an extremely rare exact, static and spherically symmetric black hole solution in the Einstein–Skyrme theory. The solution is characterized by two matter-sector couplings: K , which controls the strength of the Skyrme field and induces a solid-angle-deficit-like factor $$1-8\pi K$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mn>8</mml:mn> <mml:mi>π</mml:mi> <mml:mi