278 research outputs found
Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle
Causal fermion systems are introduced as a general mathematical framework for
formulating relativistic quantum theory. By specializing, we recover earlier
notions like fermion systems in discrete space-time, the fermionic projector
and causal variational principles. We review how an effect of spontaneous
structure formation gives rise to a topology and a causal structure in
space-time. Moreover, we outline how to construct a spin connection and
curvature, leading to a proposal for a "quantum geometry" in the Lorentzian
setting. We review recent numerical and analytical results on the support of
minimizers of causal variational principles which reveal a "quantization
effect" resulting in a discreteness of space-time. A brief survey is given on
the correspondence to quantum field theory and gauge theories.Comment: 23 pages, LaTeX, 2 figures, footnote added on page
A Rigorous Treatment of Energy Extraction from a Rotating Black Hole
The Cauchy problem is considered for the scalar wave equation in the Kerr
geometry. We prove that by choosing a suitable wave packet as initial data, one
can extract energy from the black hole, thereby putting supperradiance, the
wave analogue of the Penrose process, into a rigorous mathematical framework.
We quantify the maximal energy gain. We also compute the infinitesimal change
of mass and angular momentum of the black hole, in agreement with
Christodoulou's result for the Penrose process. The main mathematical tool is
our previously derived integral representation of the wave propagator.Comment: 19 pages, LaTeX, proof of Propositions 2.3 and 3.1 given in more
detai
An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry
We consider the scalar wave equation in the Kerr geometry for Cauchy data
which is smooth and compactly supported outside the event horizon. We derive an
integral representation which expresses the solution as a superposition of
solutions of the radial and angular ODEs which arise in the separation of
variables. In particular, we prove completeness of the solutions of the
separated ODEs.
This integral representation is a suitable starting point for a detailed
analysis of the long-time dynamics of scalar waves in the Kerr geometry.Comment: 41 pages, 4 figures, minor correction
A Discussion on Dirac Field Theory, No-Go Theorems and Renormalizability
We study Dirac field equations coupled to electrodynamics with metric and
torsion fields: we discuss how special spinorial solutions are incompatible
with torsion; eventually these results will be used to sketch a discussion on
the problem of renormalizability of point-like particles.Comment: 10 page
Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials
A method is presented for obtaining rigorous error estimates for approximate
solutions of the Riccati equation, with real or complex potentials. Our main
tool is to derive invariant region estimates for complex solutions of the
Riccati equation. We explain the general strategy for applying these estimates
and illustrate the method in typical examples, where the approximate solutions
are obtained by glueing together WKB and Airy solutions of corresponding
one-dimensional Schrodinger equations. Our method is motivated by and has
applications to the analysis of linear wave equations in the geometry of a
rotating black hole.Comment: 23 pages, LaTeX, 13 figures, minor improvements (published version
The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker Universe
We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and
separate the spatial and time variables. In the case of a closed universe, the
spatial dependence is solved explicitly, giving rise to a discrete set of
solutions. We compute the probability integral and analyze a space-time
normalization integral. This analysis allows us to introduce the fermionic
projector in a closed Friedmann-Robertson-Walker geometry and to specify its
global normalization as well as its local form.Comment: 22 pages, LaTeX, sign error in equation (3.7) correcte
Absence of Stationary, Spherically Symmetric Black Hole Solutions for Einstein-Dirac-Yang/Mills Equations with Angular Momentum
We study a stationary, spherically symmetric system of (2j+1) massive Dirac particles, each having angular momentum j, j=1,2,..., in a classical gravitational and SU(2) Yang-Mills field. We show that for any black hole solution of the associated Einstein-Dirac-Yang/Mills equations, the spinors must vanish identically outside of the event horizon
Superconducting Hair on Charged Black String Background
Behaviour of Dirac fermions in the background of a charged black string
penetrated by an Abelian Higgs vortex is elaborated. One finds the evidence
that the system under consideration can support fermion fields acting like a
superconducting cosmic string in the sence that a nontrivial Dirac fermion
field can be carried by the system in question. The case of nonextremal and
extremal black string vortex systems were considered. The influence of electric
and Higgs charge, the winding number and the fermion mass on the fermion
localization near the black string event horizon was studied. It turned out
that the extreme charged black string expelled fermion fields more violently
comparing to the nonextremal one.Comment: RevTex, 16 pages, 12 figures, to be published in Phys.REvD1
The repulsive nature of naked singularities from the point of view of Quantum Mechanics
We use the Dirac equation coupled to a background metric to examine what
happens to quantum mechanical observables like the probability density and the
radial current in the vicinity of a naked singularity of the
Reissner-Nordstr\"{o}m type. We find that the wave function of the Dirac
particle is regular in the point of the singularity. We show that the
probability density is exactly zero at the singularity reflecting
quantum-mechanically the repulsive nature of the naked singularity.
Furthermore, the surface integral of the radial current over a sphere in the
vicinity of the naked singularity turns out to be also zero.Comment: 11 page
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