46 research outputs found
Radiation from quantum weakly dynamical horizons in LQG
Using the recent thermodynamical study of isolated horizons by Ghosh and
Perez, we provide a statistical mechanical analysis of isolated horizons near
equilibrium in the grand canonical ensemble. By matching the description of the
dynamical phase in terms of weakly dynamical horizons with this local
statistical framework, we introduce a notion of temperature in terms of the
local surface gravity. This provides further support to the recovering of the
semiclassical area law just by means of thermodynamical considerations.
Moreover, it allows us to study the radiation process generated by the LQG
dynamics near the horizon, providing a quantum gravity description of the
horizon evaporation. For large black holes, the spectrum we derive presents a
discrete structure which could be potentially observable and might be preserved
even after the inclusion of all the relevant transition lines.Comment: 9 pages, 2 figure
Black Holes as Quantum Gravity Condensates
We model spherically symmetric black holes within the group field theory
formalism for quantum gravity via generalised condensate states, involving sums
over arbitrarily refined graphs (dual to 3d triangulations). The construction
relies heavily on both the combinatorial tools of random tensor models and the
quantum geometric data of loop quantum gravity, both part of the group field
theory formalism. Armed with the detailed microscopic structure, we compute the
entropy associated with the black hole horizon, which turns out to be
equivalently the Boltzmann entropy of its microscopic degrees of freedom and
the entanglement entropy between the inside and outside regions. We recover the
area law under very general conditions, as well as the Bekenstein-Hawking
formula. The result is also shown to be generically independent of any specific
value of the Immirzi parameter.Comment: 22 page
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
We review the black hole entropy calculation in the framework of Loop Quantum
Gravity based on the quasi-local definition of a black hole encoded in the
isolated horizon formalism. We show, by means of the covariant phase space
framework, the appearance in the conserved symplectic structure of a boundary
term corresponding to a Chern-Simons theory on the horizon and present its
quantization both in the U(1) gauge fixed version and in the fully SU(2)
invariant one. We then describe the boundary degrees of freedom counting
techniques developed for an infinite value of the Chern-Simons level case and,
less rigorously, for the case of a finite value. This allows us to perform a
comparison between the U(1) and SU(2) approaches and provide a state of the art
analysis of their common features and different implications for the entropy
calculations. In particular, we comment on different points of view regarding
the nature of the horizon degrees of freedom and the role played by the
Barbero-Immirzi parameter. We conclude by presenting some of the most recent
results concerning possible observational tests for theory
CFT/Gravity Correspondence on the Isolated Horizon
A quantum isolated horizon can be modelled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localised at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational flux degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new nongeometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Immirzi parameter. This allows us to recover the Bekenstein-Hawking entropy formula without the large quantum gravity corrections associated with the number of punctures. © 2014 The Authors
Orthogonal gauge fixing of first order gravity
We consider the first order connection formulation of 4D general relativity
in the "orthogonal" gauge. We show how the partial gauge fixing of the phase
space canonical coordinates leads to the appearance of second class constraints
in the theory. We employ the gauge unfixing procedure in order to successfully
complete the Dirac treatment of the system. While equivalent to the inversion
of the Dirac matrix, the gauge unfixing allows us to work directly with the
reduced phase space and the ordinary Poisson bracket. At the same time, we
explicitly derive the new set of residual first class constraints preserving
the partial gauge fixing, which are linear combinations of the original
constraints, and these turn out to contain nonlinear terms. While providing an
explicit example of how to consistently recast general relativity in a given
partial gauge, the main motivation of this classical analysis is the
application of the Quantum Reduced Loop Gravity program to a Schwarzschild
black hole geometry.Comment: 14 pages; 'radial gauge' replaced with 'orthogonal gauge' to avoid
confusion with previous literature, on which we comment on more extensively.
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