THE SU(2) INVARIANT PRESYMPLECTIC STRUCTURE OF SPHERICAL ISOLATED HORIZONS

摘要

In this work we concentrate and further develop the theory of isolated horizons in the context of loop quantum gravity. Recently, we have proposed a new computation of BH entropy in loop quantum gravity (LQG) that avoids the internal gauge-fixing used in prior works~2 and makes the underlying structure more transparent.We show, in particular, that the degrees of freedom of Type I isolated horizons can be encoded (along the lines of the standard treatment) in an SU(2) boundary connection. The results of this work clarify the relationship between the theory of isolated horizons and SU(2) Chern-Simons theory first explored in Ref. 3, and vindicates Krasnov's original intuition that SU(2) Chern-Simons should be used to describe the degrees of freedom of gravity at the horizon. Moreover, our work makes the relationship with the usual treatment of degrees of freedom in loop quantum gravity clear-cut.In the present work, we provide a full detail derivation of the result of our resent work and discuss several important issues that were only briefly mentioned then.