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Loop-quantum-gravity vertex amplitude.
TLDR
This work presents an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly.
Asymptotics and Hamiltonians in a First order formalism
We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle for general relativity is well defined
Multipole moments of isolated horizons
To every axi-symmetric isolated horizon we associate two sets of numbers, Mn and Jn with n = 0, 1, 2, ..., representing its mass and angular momentum multipoles. They provide a diffeomorphism
Black hole entropy from the SU(2)-invariant formulation of type I isolated horizons
A detailed analysis of the spherically symmetric isolated horizon system is performed in terms of the connection formulation of general relativity. The system is shown to admit a manifestly SU(2)
Black hole entropy and SU(2) Chern-Simons theory.
TLDR
This work shows that this boundary condition given on a null surface representing the event horizon can be treated in a manifestly SU(2) invariant manner and settles previous controversies concerning the counting of states.
LETTER TO THE EDITOR: Quantum horizons and black-hole entropy: inclusion of distortion and rotation
Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry is spherical, they are called type I while if it is axi-symmetric, they are called type II. The
Generic isolated horizons in loop quantum gravity
Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the
Regularization and finiteness of the Lorentzian loop quantum gravity vertices
We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of doing so, a natural regularization of the vertices
Uniqueness of the Representation in Homogeneous Isotropic LQC
We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) is the GNS-representation that corresponds to the unique state on the reduced quantum holonomy-flux
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