1,090 research outputs found
Isolated and Dynamical Horizons and Their Applications
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in an unified manner. In this framework, evolving black holes are modeled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity; suggested a phenomenological model for hairy black holes; provided novel techniques to extract physics from numerical simulations; and led to new laws governing the dynamics of black holes in exact general relativity
Gauss Linking Number and Electro-magnetic Uncertainty Principle
It is shown that there is a precise sense in which the Heisenberg uncertainty
between fluxes of electric and magnetic fields through finite surfaces is given
by (one-half times) the Gauss linking number of the loops that bound
these surfaces. To regularize the relevant operators, one is naturally led to
assign a framing to each loop. The uncertainty between the fluxes of electric
and magnetic fields through a single surface is then given by the self-linking
number of the framed loop which bounds the surface.Comment: 13 pages, Revtex file, 3 eps figure
Two physical characteristics of numerical apparent horizons
This article translates some recent results on quasilocal horizons into the
language of general relativity so as to make them more useful to
numerical relativists. In particular quantities are described which
characterize how quickly an apparent horizon is evolving and how close it is to
either equilibrium or extremality.Comment: 6 pages, 2 figures, conference proceedings loosely based on talk
given at Theory Canada III (Edmonton, Alberta, 2007). V2: Minor changes in
response to referees comments to improve clarity and fix typos. One reference
adde
Laws Governing Isolated Horizons: Inclusion of Dilaton Couplings
Mechanics of non-rotating black holes was recently generalized by replacing
the static event horizons used in standard treatments with `isolated horizons.'
This framework is extended to incorporate dilaton couplings. Since there can be
gravitational and matter radiation outside isolated horizons, now the
fundamental parameters of the horizon, used in mechanics, must be defined using
only the local structure of the horizon, without reference to infinity. This
task is accomplished and the zeroth and first laws are established. To
complement the previous work, the entire discussion is formulated tensorially,
without any reference to spinors.Comment: Some typos corrected, references updated. Some minor clarifications
added. 20 pages, 1 figure, Revtex fil
Non-minimally coupled scalar fields and isolated horizons
The isolated horizon framework is extended to include non-minimally coupled
scalar fields. As expected from the analysis based on Killing horizons, entropy
is no longer given just by (a quarter of) the horizon area but also depends on
the scalar field. In a subsequent paper these results will serve as a point of
departure for a statistical mechanical derivation of entropy using quantum
geometry.Comment: 14 pages, 1 figure, revtex4. References and minor clarifications
adde
Quantum Loop Representation for Fermions coupled to Einstein-Maxwell field
Quantization of the system comprising gravitational, fermionic and
electromagnetic fields is developed in the loop representation. As a result we
obtain a natural unified quantum theory. Gravitational field is treated in the
framework of Ashtekar formalism; fermions are described by two Grassmann-valued
fields. We define a -algebra of configurational variables whose
generators are associated with oriented loops and curves; ``open'' states --
curves -- are necessary to embrace the fermionic degrees of freedom. Quantum
representation space is constructed as a space of cylindrical functionals on
the spectrum of this -algebra. Choosing the basis of ``loop'' states we
describe the representation space as the space of oriented loops and curves;
then configurational and momentum loop variables become in this basis the
operators of creation and annihilation of loops and curves. The important
difference of the representation constructed from the loop representation of
pure gravity is that the momentum loop operators act in our case simply by
joining loops in the only compatible with their orientaiton way, while in the
case of pure gravity this action is more complicated.Comment: 28 pages, REVTeX 3.0, 15 uuencoded ps-figures. The construction of
the representation has been changed so that the representation space became
irreducible. One part is removed because it developed into a separate paper;
some corrections adde
Quantum Theory of Gravity I: Area Operators
A new functional calculus, developed recently for a fully non-perturbative
treatment of quantum gravity, is used to begin a systematic construction of a
quantum theory of geometry. Regulated operators corresponding to areas of
2-surfaces are introduced and shown to be self-adjoint on the underlying
(kinematical) Hilbert space of states. It is shown that their spectra are {\it
purely} discrete indicating that the underlying quantum geometry is far from
what the continuum picture might suggest. Indeed, the fundamental excitations
of quantum geometry are 1-dimensional, rather like polymers, and the
3-dimensional continuum geometry emerges only on coarse graining. The full
Hilbert space admits an orthonormal decomposition into finite dimensional
sub-spaces which can be interpreted as the spaces of states of spin systems.
Using this property, the complete spectrum of the area operators is evaluated.
The general framework constructed here will be used in a subsequent paper to
discuss 3-dimensional geometric operators, e.g., the ones corresponding to
volumes of regions.Comment: 33 pages, ReVTeX, Section 4 Revised: New results on the effect of
topology of a surface on the eigenvalues and eigenfunctions of its area
operator included. The proof of the bound on the level spacing of eigenvalues
(for large areas) simplified and its ramification to the Bekenstein-Mukhanov
analysis of black-hole evaporation made more explicit. To appear in CQ
Fundamental properties and applications of quasi-local black hole horizons
The traditional description of black holes in terms of event horizons is
inadequate for many physical applications, especially when studying black holes
in non-stationary spacetimes. In these cases, it is often more useful to use
the quasi-local notions of trapped and marginally trapped surfaces, which lead
naturally to the framework of trapping, isolated, and dynamical horizons. This
framework allows us to analyze diverse facets of black holes in a unified
manner and to significantly generalize several results in black hole physics.
It also leads to a number of applications in mathematical general relativity,
numerical relativity, astrophysics, and quantum gravity. In this review, I will
discuss the basic ideas and recent developments in this framework, and
summarize some of its applications with an emphasis on numerical relativity.Comment: 14 pages, 2 figures. Based on a talk presented at the 18th
International Conference on General Relativity and Gravitation, 8-13 July
2007, Sydney, Australi
THE VOLUME OPERATOR IN DISCRETIZED QUANTUM GRAVITY
We investigate the spectral properties of the volume operator in quantum
gravity in the framework of a previously introduced lattice discretization. The
presence of a well-defined scalar product in this approach permits us to make
definite statements about the hermiticity of quantum operators. We find that
the spectrum of the volume operator is discrete, but that the nature of its
eigenstates differs from that found in an earlier continuum treatment.Comment: 15 pages, TeX, 3 figures (postscript, compressed and uu-encoded), May
9
Real and complex connections for canonical gravity
Both real and complex connections have been used for canonical gravity: the
complex connection has SL(2,C) as gauge group, while the real connection has
SU(2) as gauge group. We show that there is an arbitrary parameter
which enters in the definition of the real connection, in the Poisson brackets,
and therefore in the scale of the discrete spectra one finds for areas and
volumes in the corresponding quantum theory. A value for could be could
be singled out in the quantum theory by the Hamiltonian constraint, or by the
rotation to the complex Ashtekar connection.Comment: 8 pages, RevTeX, no figure
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