2,430 research outputs found
Renormalization and Essential Singularity
In usual dimensional counting, momentum has dimension one. But a function
f(x), when differentiated n times, does not always behave like one with its
power smaller by n. This inevitable uncertainty may be essential in general
theory of renormalization, including quantum gravity. As an example, we
classify possible singularities of a potential for the Schr\"{o}dinger
equation, assuming that the potential V has at least one class eigen
function. The result crucially depends on the analytic property of the eigen
function near its 0 point.Comment: 12 pages, no figures, PTPTeX with amsfonts. 2 pages added for detail
Twistors, special relativity, conformal symmetry and minimal coupling - a review
An approach to special relativistic dynamics using the language of spinors
and twistors is presented. Exploiting the natural conformally invariant
symplectic structure of the twistor space, a model is constructed which
describes a relativistic massive, spinning and charged particle, minimally
coupled to an external electro-magnetic field. On the two-twistor phase space
the relativistic Hamiltonian dynamics is generated by a Poincare scalar
function obtained from the classical limit (appropriately defined by us) of the
second order, to an external electro-magnetic field minimally coupled, Dirac
operator. In the so defined relativistic classical limit there are no Grassman
variables. Besides, the arising equation that describes dynamics of the
relativistic spin differs significantly from the so called Thomas Bergman
Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything
else in the papper) on page 23 delete
Weak Cosmic Censorship: As Strong as Ever
Spacetime singularities that arise in gravitational collapse are always
hidden inside of black holes. This is the essence of the weak cosmic censorship
conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one
of the most important open questions in general relativity. In this Letter, we
reanalyze extreme situations which have been considered as counterexamples to
the weak cosmic censorship conjecture. In particular, we consider the
absorption of scalar particles with large angular momentum by a black hole.
Ignoring back reaction effects may lead one to conclude that the incident wave
may overspin the black hole, thereby exposing its inner singularity to distant
observers. However, we show that when back reaction effects are properly taken
into account, the stability of the black-hole event horizon is irrefutable. We
therefore conclude that cosmic censorship is actually respected in this type of
gedanken experiments.Comment: 4 page
Geodesic motion in General Relativity: LARES in Earth's gravity
According to General Relativity, as distinct from Newtonian gravity, motion
under gravity is treated by a theory that deals, initially, only with test
particles. At the same time, satellite measurements deal with extended bodies.
We discuss the correspondence between geodesic motion in General Relativity and
the motion of an extended body by means of the Ehlers-Geroch theorem, and in
the context of the recently launched LAser RElativity Satellite (LARES). Being
possibly the highest mean density orbiting body in the Solar system, this
satellite provides the best realization of a test particle ever reached
experimentally and provides a unique possibility for testing the predictions of
General Relativity.Comment: 4 pages, 1 imag
Linearized gravity and gauge conditions
In this paper we consider the field equations for linearized gravity and
other integer spin fields on the Kerr spacetime, and more generally on
spacetimes of Petrov type D. We give a derivation, using the GHP formalism, of
decoupled field equations for the linearized Weyl scalars for all spin weights
and identify the gauge source functions occuring in these. For the spin weight
0 Weyl scalar, imposing a generalized harmonic coordinate gauge yields a
generalization of the Regge-Wheeler equation. Specializing to the Schwarzschild
case, we derive the gauge invariant Regge-Wheeler and Zerilli equation directly
from the equation for the spin 0 scalar.Comment: 24 pages, corresponds to published versio
CR Structures and Asymptotically Flat Space-Times
We discuss the unique existence, arising by analogy to that in algebraically
special space-times, of a CR structure realized on null infinity for any
asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page
The frictional Schr\"odinger-Newton equation in models of wave function collapse
Replacing the Newtonian coupling G by -iG, the Schrodinger-Newton equation
becomes ``frictional''. Instead of the reversible Schrodinger-Newton equation,
we advocate its frictional version to generate the set of pointer states for
macroscopic quantum bodies.Comment: 6pp LaTeX for J.Phys.Conf.Ser.+2 figs. Talk given at the Int.
Workshop DICE2006 "Quantum Mechanics between Decoherence and Determinism: new
aspects from particle physics to cosmology" Piombino, Sept 11-15, 200
Note on (conformally) semi-symmetric spacetimes
We provide a simple proof that conformally semi-symmetric spacetimes are
actually semi-symmetric. We also present a complete refined classification of
the semi-symmetric spacetimes.Comment: 5 pages, no figure
A Maximally Symmetric Vector Propagator
We derive the propagator for a massive vector field on a de Sitter background
of arbitrary dimension. This propagator is de Sitter invariant and possesses
the proper flat spacetime and massless limits. Moreover, the retarded Green's
function inferred from it produces the correct classical response to a test
source. Our result is expressed in a tensor basis which is convenient for
performing quantum field theory computations using dimensional regularization.Comment: 21 pages, no figures, uses LaTeX 2 epsilon, version 2 has an error in
eqn (86) corrected and an updated reference lis
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. III. On the determination of radiation
We discuss the issue of radiation extraction in asymptotically flat
space-times within the framework of conformal methods for numerical relativity.
Our aim is to show that there exists a well defined and accurate extraction
procedure which mimics the physical measurement process. It operates entirely
intrisically within \scri^+ so that there is no further approximation
necessary apart from the basic assumption that the arena be an asymptotically
flat space-time. We define the notion of a detector at infinity by idealising
local observers in Minkowski space. A detailed discussion is presented for
Maxwell fields and the generalisation to linearised and full gravity is
performed by way of the similar structure of the asymptotic fields.Comment: LaTeX2e,13 pages,2 figure
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