Mechanics of multidimensional isolated horizons

Abstract

Recently, a multidimensional generalization of the isolated horizon framework has been proposed Pawłowski 2005 Class. Quantum Grav. 22 1573-98). Therein the geometric description was easily generalized to higher dimensions and the structure of the constraints induced by the Einstein equations was analysed. In particular, the geometric version of the zeroth law of black-hole thermodynamics was proved. In this work, we show how the IH mechanics can be formulated in a dimension-independent fashion and derive the first law of BH thermodynamics for arbitrarily dimensional IH. We also propose a definition of energy for non-rotating horizons.

BF theory explanation of the entropy for rotating isolated horizons

“…15 For the internal gauge transformation, Eq. (20) is still valid for higher dimension for the same reason.…”

Black Holes in Higher Dimensions

“…The formalism of isolated horizons and the laws of black-hole mechanics for them, have been Living Reviews in Relativity http://www.livingreviews.org/lrr-2008-6 extended to higher dimensions in [182,170], and then to five-dimensional Einstein-Maxwell theory with the Chern-Simons term [183] and anti-de Sitter asymptotics [5].…”

Mechanics of higher dimensional black holes in asymptotically anti-de Sitter spacetimes

“…The second condition requires that the rotation 1-form also be 'time-independent'. (For further details, see [3,4,18]. )…”

“…First consider the integral of j(δ 1 , δ 2 ) over ∆ ′ . Now we can take over arguments from the isolated horizon analysis of [3,4,18] in a straightforward manner because they are insensitive to the precise number of space-time dimensions and the value of the cosmological constant. We therefore simply provide the final result.…”