Entropy of higher dimensional nonrotating isolated horizons from loop quantum gravity

Abstract

In this paper, we extend the calculation of the entropy of the nonrotating isolated horizons in 4 dimensional spacetime to that in a higher dimensional spacetime. We show that the boundary degrees of freedom on an isolated horizon can be described effectively by a punctured SO(1, 1) BF theory. Then the entropy of the nonrotating isolated horizon can be calculated out by counting the microstates. It satisfies the Bekenstein-Hawking law.

Reformulation of boundary BF theory approach to statistical explanation of the entropy of isolated horizons

“…Their internal degrees of freedom are traced out and the number of their boundary degrees of freedom gives the entropy of the IH. In contrast, in the previous approach [20,21,24,36] since only the Palatini action is considered, the symplectic form has two terms, the bulk term and the boundary term. The resulted Hilbert space is also the tensor product of the bulk and the boundary Hilbert space.…”

“…The reason is that the eigenvalue equation (4.1) for the flux operator is different from the Ref. [21] with a factor 2, so the flux operator have the same eigenvalues, thus the same physics. We choose this form since it gives the same value for both SU(2) in 4 dimension and SO(D) in arbitrary dimension.…”

“…Recently, a new approach to calculate the entropy of IHs in the framework of loop quantum gravity is proposed [20,21]. In this approach, the entropy of an IH is attributed to the number of degrees of freedom of the quantized SO(1,1) BF theory instead of the Chern-Simons theory.…”

Conformal field theory on the horizon of a BTZ black hole

“…In the previous work [24][25][26][27][28][29][30], it was shown that the boundary degrees of freedom can also be described by a BF theory. Since both the BF theory and the massless scalar field theory are on the horizon, the relation between those two theories need further investigated.…”

Holographic equipartition from first order action

“…This action is closely related to loop quantum gravity [14][15][16][17]. Another advantage is that, when considering a black hole, the boundary degrees of freedom can be described by a SO(1, 1) BF theory [18][19][20][21][22]. In the following section we set 8πG = 1.…”