Abstract
We introduce a new entropy formula for Kerr black holes inspired by recent results for 3-dimensional black holes and cosmologies with soft Heisenberg hair. We show that also Kerr–Taub–NUT black holes obey the same formula.
Highlights
A new horizon entropy formula has emerged [1] S = 2π J0+ + J0− (1)that is more universal than the Bekenstein–Hawking [2, 3] or Wald’s [4, 5] entropy formulas, albeit only in three dimensions
Formula (1) was first derived for black holes in 3-dimensional Anti-de Sitter space within Einstein gravity [1] inspired by related earlier discussions of near horizon boundary conditions [6, 7] and the concept of soft hair [8]
Besides the entropy itself Cardyology simplifies [1, 9, 13] including log-corrections [14], while semi-classical considerations allow for Hardyology [15,16,17,18], by which we mean a counting of explicitly constructed semi-classical black hole microstates that combinatorially reduces to partitions of large integers
Summary
That is more universal than the Bekenstein–Hawking [2, 3] or Wald’s [4, 5] entropy formulas, albeit only in three dimensions. Most results so far apply only to three spacetime dimensions, with the exception of [18] that applies Hardyology to extremal Kerr black holes. The main purpose of this proceedings contribution is to make modest progress towards lifting the exciting results in three dimensions to four dimensions by providing an analog of the entropy formula (1) for non-extremal Kerr black holes. That is equivalent to the Bekenstein–Hawking law or Wald’s entropy, but expressed in terms of zero mode charges of u(1) current algebras that are expected to appear in a suitable near horizon description of non-extremal Kerr.
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