220 research outputs found
Modelling gravity on a hyper-cubic lattice
We present an elegant and simple dynamical model of symmetric, non-degenerate
(n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic
lattice with nearest-neighbor interactions. We show how this model is related
to General Relativity, and discuss multiple ways in which it can be useful for
studying gravity, both classical and quantum. In particular, we show that the
dynamics of the model when all matrices are close to the identity corresponds
exactly to a finite-difference discretization of weak-field gravity in harmonic
gauge. We also show that the action which defines the full dynamics of the
model corresponds to the Einstein-Hilbert action to leading order in the
lattice spacing, and use this observation to define a lattice analogue of the
Ricci scalar and Einstein tensor. Finally, we perform a mean-field analysis of
the statistical mechanics of this model.Comment: 5 page
Emergence of a 4D World from Causal Quantum Gravity
Causal Dynamical Triangulations in four dimensions provide a
background-independent definition of the sum over geometries in nonperturbative
quantum gravity, with a positive cosmological constant. We present evidence
that a macroscopic four-dimensional world emerges from this theory dynamically.Comment: 11 pages, 3 figures; some short clarifying comments added; final
version to appear in Phys. Rev. Let
Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations
We present a possibility of coupling a point-like, non-singular, mass
distribution to four-dimensional quantum gravity in the nonperturbative setting
of causal dynamical triangulations (CDT). In order to provide a point of
comparison for the classical limit of the matter-coupled CDT model, we derive
the spatial volume profile of the Euclidean Schwarzschild-de Sitter space glued
to an interior matter solution. The volume profile is calculated with respect
to a specific proper-time foliation matching the global time slicing present in
CDT. It deviates in a characteristic manner from that of the pure-gravity
model. The appearance of coordinate caustics and the compactness of the mass
distribution in lattice units put an upper bound on the total mass for which
these calculations are expected to be valid. We also discuss some of the
implementation details for numerically measuring the expectation value of the
volume profiles in the framework of CDT when coupled appropriately to the
matter source.Comment: 26 pages, 9 figures, updated published versio
Coherent States for Black Holes
We determine coherent states peaked at classical space-time of the
Schwarzschild black hole in the frame-work of canonical quantisation of general
relativity. The information about the horizon is naturally encoded in the phase
space variables, and the perturbative quantum fluctuations around the classical
geometry depend on the distance from the horizon. For small black holes, space
near the vicinity of the singularity appears discrete with the singular point
excluded from the spectrum.Comment: 48 pages, 18+1 figures, some modifications, references adde
The spectrum of quantum black holes and quasinormal modes
The spectrum of multiple level transitions of the quantum black hole is
considered, and the line widths calculated. Initial evidence is found for these
higher order transitions in the spectrum of quasinormal modes for Schwarzschild
and Kerr black holes, further bolstering the idea that there exists a
correspondence principle between quantum transitions and classical ``ringing
modes''. Several puzzles are noted, including a fine-tuning problem between the
line width and the level degeneracy. A more general explanation is provided for
why setting the Immirzi parameter of loop quantum gravity from the black hole
spectrum necessarily gives the correct value for the black hole entropy.Comment: 5 pages, 5 figures, version to appear in Phys. Rev.
A new perspective on matter coupling in 2d quantum gravity
We provide compelling evidence that a previously introduced model of
non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional)
flat-space behaviour when coupled to Ising spins. The evidence comes from both
a high-temperature expansion and from Monte Carlo simulations of the combined
gravity-matter system. This weak-coupling behaviour lends further support to
the conclusion that the Lorentzian model is a genuine alternative to Liouville
quantum gravity in two dimensions, with a different, and much `smoother'
critical behaviour.Comment: 24 pages, 7 figures (postscript
From covariant to canonical formulations of discrete gravity
Starting from an action for discretized gravity we derive a canonical
formalism that exactly reproduces the dynamics and (broken) symmetries of the
covariant formalism. For linearized Regge calculus on a flat background --
which exhibits exact gauge symmetries -- we derive local and first class
constraints for arbitrary triangulated Cauchy surfaces. These constraints have
a clear geometric interpretation and are a first step towards obtaining
anomaly--free constraint algebras for canonical lattice gravity. Taking higher
order dynamics into account the symmetries of the action are broken. This
results in consistency conditions on the background gauge parameters arising
from the lowest non--linear equations of motion. In the canonical framework the
constraints to quadratic order turn out to depend on the background gauge
parameters and are therefore pseudo constraints. These considerations are
important for connecting path integral and canonical quantizations of gravity,
in particular if one attempts a perturbative expansion.Comment: 37 pages, 5 figures (minor modifications, matches published version +
updated references
Discrete approaches to quantum gravity in four dimensions
The construction of a consistent theory of quantum gravity is a problem in
theoretical physics that has so far defied all attempts at resolution. One
ansatz to try to obtain a non-trivial quantum theory proceeds via a
discretization of space-time and the Einstein action. I review here three major
areas of research: gauge-theoretic approaches, both in a path-integral and a
Hamiltonian formulation, quantum Regge calculus, and the method of dynamical
triangulations, confining attention to work that is strictly four-dimensional,
strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the
author welcomes any comments and suggestion
From Big Bang to Asymptotic de Sitter: Complete Cosmologies in a Quantum Gravity Framework
Using the Einstein-Hilbert approximation of asymptotically safe quantum
gravity we present a consistent renormalization group based framework for the
inclusion of quantum gravitational effects into the cosmological field
equations. Relating the renormalization group scale to cosmological time via a
dynamical cutoff identification this framework applies to all stages of the
cosmological evolution. The very early universe is found to contain a period of
``oscillatory inflation'' with an infinite sequence of time intervals during
which the expansion alternates between acceleration and deceleration. For
asymptotically late times we identify a mechanism which prevents the universe
from leaving the domain of validity of the Einstein-Hilbert approximation and
obtain a classical de Sitter era.Comment: 47 pages, 17 figure
Spin Networks and Quantum Gravity
We introduce a new basis on the state space of non-perturbative quantum
gravity. The states of this basis are linearly independent, are well defined in
both the loop representation and the connection representation, and are labeled
by a generalization of Penrose's spin netoworks. The new basis fully reduces
the spinor identities (SU(2) Mandelstam identities) and simplifies calculations
in non-perturbative quantum gravity. In particular, it allows a simple
expression for the exact solutions of the Hamiltonian constraint
(Wheeler-DeWitt equation) that have been discovered in the loop representation.
Since the states in this basis diagnolize operators that represent the three
geometry of space, such as the area and volumes of arbitrary surfaces and
regions, these states provide a discrete picture of quantum geometry at the
Planck scale.Comment: 42 page
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