7 research outputs found
Quantization of Midisuperspace Models
We give a comprehensive review of the quantization of midisuperspace models.
Though the main focus of the paper is on quantum aspects, we also provide an
introduction to several classical points related to the definition of these
models. We cover some important issues, in particular, the use of the principle
of symmetric criticality as a very useful tool to obtain the required
Hamiltonian formulations. Two main types of reductions are discussed: those
involving metrics with two Killing vector fields and spherically symmetric
models. We also review the more general models obtained by coupling matter
fields to these systems. Throughout the paper we give separate discussions for
standard quantizations using geometrodynamical variables and those relying on
loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit
Loop Quantum Cosmology
Quantum gravity is expected to be necessary in order to understand situations
where classical general relativity breaks down. In particular in cosmology one
has to deal with initial singularities, i.e. the fact that the backward
evolution of a classical space-time inevitably comes to an end after a finite
amount of proper time. This presents a breakdown of the classical picture and
requires an extended theory for a meaningful description. Since small length
scales and high curvatures are involved, quantum effects must play a role. Not
only the singularity itself but also the surrounding space-time is then
modified. One particular realization is loop quantum cosmology, an application
of loop quantum gravity to homogeneous systems, which removes classical
singularities. Its implications can be studied at different levels. Main
effects are introduced into effective classical equations which allow to avoid
interpretational problems of quantum theory. They give rise to new kinds of
early universe phenomenology with applications to inflation and cyclic models.
To resolve classical singularities and to understand the structure of geometry
around them, the quantum description is necessary. Classical evolution is then
replaced by a difference equation for a wave function which allows to extend
space-time beyond classical singularities. One main question is how these
homogeneous scenarios are related to full loop quantum gravity, which can be
dealt with at the level of distributional symmetric states. Finally, the new
structure of space-time arising in loop quantum gravity and its application to
cosmology sheds new light on more general issues such as time.Comment: 104 pages, 10 figures; online version, containing 6 movies, available
at http://relativity.livingreviews.org/Articles/lrr-2005-11
The Spin Foam Approach to Quantum Gravity
This article reviews the present status of the spin foam approach to the
quantization of gravity. Special attention is payed to the pedagogical
presentation of the recently introduced new models for four dimensional quantum
gravity. The models are motivated by a suitable implementation of the path
integral quantization of the Plebanski formulation of gravity on a simplicial
regularization. The article also includes a self-contained treatment of the 2+1
gravity. The simple nature of the latter provides the basis and a perspective
for the analysis of both conceptual and technical issues that remain open in
four dimensions.Comment: To appear in Living Reviews in Relativit
Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ∼ 10^{-5} – 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger