Conformal Symmetry for Black Holes in Four Dimensions and Irrelevant Deformations

Understand

It has been argued several times in the past that the structure of the entropy formula for general non-extremal asymptotically flat black holes in four dimensions can be understood in terms of an underlying conformal symmetry.

• A recent implementation of this idea, carried out by Cveti\v{c} and Larsen, involves the replacement of a conformal factor in the original geometry by an alternative conformal factor in such a way that the near-horizon behavior and thermodynamic properties of the black hole remain unchanged, while only the asymptotics or "environment" of the geometry are modified.
• The solution thus obtained, dubbed "subtracted geometry", uplifts to an asymptotically AdS$_{3}\times S^{2}$ black hole in five dimensions, and an AdS/CFT interpretation is then possible.
• Building on this intuition we show that, at least in the static case, the replacement of the conformal factor can be implemented dynamically by means of an interpolating flow which we construct explicitly.