49 research outputs found
Pentahedral volume, chaos, and quantum gravity
We show that chaotic classical dynamics associated to the volume of discrete
grains of space leads to quantal spectra that are gapped between zero and
nonzero volume. This strengthens the connection between spectral discreteness
in the quantum geometry of gravity and tame ultraviolet behavior. We complete a
detailed analysis of the geometry of a pentahedron, providing new insights into
the volume operator and evidence of classical chaos in the dynamics it
generates. These results reveal an unexplored realm of application for chaos in
quantum gravity.Comment: 8 pages, 5 figures, small revisions made and typos fixed, updated to
include appendice
Quantum Gravity Effects around Sagittarius A*
Recent VLBI observations have resolved Sagittarius A* at horizon scales. The
Event Horizon Telescope is expected to provide increasingly good images of the
region around the Schwarzschild radius of Sgr A* soon. A number of
authors have recently pointed out the possibility that non-perturbative quantum
gravitational phenomena could affect the space surrounding a black hole. Here
we point out that the existence of a region around where these
effects should be maximal.Comment: 5 pages; Received honorable mention in the Gravity Research
Foundation 2016 Awards for Essays on Gravitatio
Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
We show that there is a classical metric satisfying the Einstein equations
outside a finite spacetime region where matter collapses into a black hole and
then emerges from a white hole. We compute this metric explicitly. We show how
quantum theory determines the (long) time for the process to happen. A black
hole can thus quantum-tunnel into a white hole. For this to happen, quantum
gravity should affect the metric also in a small region outside the horizon: we
show that contrary to what is commonly assumed, this is not forbidden by
causality or by the semiclassical approximation, because quantum effects can
pile up over a long time. This scenario alters radically the discussion on the
black hole information puzzle.Comment: 10 pages, 5 figure
Death and resurrection of the zeroth principle of thermodynamics
The zeroth principle of thermodynamics in the form "temperature is uniform at
equilibrium" is notoriously violated in relativistic gravity. Temperature
uniformity is often derived from the maximization of the total number of
microstates of two interacting systems under energy exchanges. Here we discuss
a generalized version of this derivation, based on informational notions, which
remains valid in the general context. The result is based on the observation
that the time taken by any system to move to a distinguishable (nearly
orthogonal) quantum state is a universal quantity that depends solely on the
temperature. At equilibrium the net information flow between two systems must
vanish, and this happens when two systems transit the same number of
distinguishable states in the course of their interaction.Comment: 5 pages, 2 figure
Coupling and thermal equilibrium in general-covariant systems
A fully general-covariant formulation of statistical mechanics is still
lacking. We take a step toward this theory by studying the meaning of
statistical equilibrium for coupled, parametrized systems. We discuss how to
couple parametrized systems. We express the thermalization hypothesis in a
general-covariant context. This takes the form of vanishing of information
flux. An interesting relation emerges between thermal equilibrium and gauge.Comment: 8 pages, 3 figure
Holographic description of boundary gravitons in (3+1) dimensions
Gravity is uniquely situated in between classical topological field theories
and standard local field theories. This can be seen in the the quasi-local
nature of gravitational observables, but is nowhere more apparent than in
gravity's holographic formulation. Holography holds promise for simplifying
computations in quantum gravity. While holographic descriptions of
three-dimensional spacetimes and of spacetimes with a negative cosmological
constant are well-developed, a complete boundary description of zero curvature,
four-dimensional spacetime is not currently available. Building on previous
work in three-dimensions, we provide a new route to four-dimensional holography
and its boundary gravitons. Using Regge calculus linearized around a flat
Euclidean background with the topology of a solid hyper-torus, we obtain the
effective action for a dual boundary theory which describes the dynamics of the
boundary gravitons. Remarkably, in the continuum limit and at large radii this
boundary theory is local and closely analogous to the corresponding result in
three-dimensions. The boundary effective action has a degenerate kinetic term
that leads to singularities in the one-loop partition function that are
independent of the discretization. These results establish a rich boundary
dynamics for four-dimensional flat holography.Comment: 43 pages, 3 figures, 1 tabl
Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks
Prominent approaches to quantum gravity struggle when it comes to
incorporating a positive cosmological constant in their models. Using
quantization of a complex Chern-Simons theory we
include a cosmological constant, of either sign, into a model of quantum
gravity.Comment: 5 pages and 2 figure
SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
We study the expectation value of a nonplanar Wilson graph operator in
SL(2,C) Chern-Simons theory on . In particular we analyze its asymptotic
behaviour in the double-scaling limit in which both the representation labels
and the Chern-Simons coupling are taken to be large, but with fixed ratio. When
the Wilson graph operator has a specific form, motivated by loop quantum
gravity, the critical point equations obtained in this double-scaling limit
describe a very specific class of flat connection on the graph complement
manifold. We find that flat connections in this class are in correspondence
with the geometries of constant curvature 4-simplices. The result is fully
non-perturbative from the perspective of the reconstructed geometry. We also
show that the asymptotic behavior of the amplitude contains at the leading
order an oscillatory part proportional to the Regge action for the single
4-simplex in the presence of a cosmological constant. In particular, the
cosmological term contains the full-fledged curved volume of the 4-simplex.
Interestingly, the volume term stems from the asymptotics of the Chern-Simons
action. This can be understood as arising from the relation between
Chern-Simons theory on the boundary of a region, and a theory defined by an
action in the bulk. Another peculiarity of our approach is that the sign
of the curvature of the reconstructed geometry, and hence of the cosmological
constant in the Regge action, is not fixed a priori, but rather emerges
semiclassically and dynamically from the solution of the equations of motion.
In other words, this work suggests a relation between 4-dimensional loop
quantum gravity with a cosmological constant and SL(2,C) Chern-Simons theory in
3-dimensions with knotted graph defects.Comment: 54+11 pages, 9 figure