374 research outputs found
On Further Generalization of the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
A rigidity theorem that applies to smooth electrovac spacetimes which
represent either (A) an asymptotically flat stationary black hole or (B) a
cosmological spacetime with a compact Cauchy horizon ruled by closed null
geodesics was given in a recent work \cite{frw}. Here we enlarge the framework
of the corresponding investigations by allowing the presence of other type of
matter fields. In the first part the matter fields are involved merely
implicitly via the assumption that the dominant energy condition is satisfied.
In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian] Higgs
(E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and
Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event
horizon or, respectively, the compact Cauchy horizon of the considered
spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is
proven that there exists a Killing vector field in a one-sided neighborhood of
the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector
field is normal to the horizon, moreover, the associated matter fields are also
shown to be invariant with respect to it. The presented results provide
generalizations of the rigidity theorems of Hawking (for case A) and of
Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity
of both the black hole rigidity scenario and the strong cosmic censor
conjecture of classical general relativity.Comment: 25 pages, LaTex, a shortened version, including a new proof for lemma
5.1, the additional case of Einstein-Yang-Mills-Higgs systems is also
covered, to appear in Class. Quant. Gra
Fluctuations in subsystems of the zero temperature XX chain: Emergence of an effective temperature
Fluctuations in subsystems of the zero temperature XX chain: Emergence of an effective temperature
The zero-temperature XX chain is studied with emphasis on the properties of a
block of spins inside the chain. We investigate the quantum fluctuations
resulting from the entanglement of the block with the rest of the chain using
analytical as well as numerical (density matrix renormalization group) methods.
It is found that the rest of the chain acts as a thermal environment and an
effective temperature can be introduced to describe the fluctuations. We show
that the effective temperature description is robust in the sense that several
independent definitions (through fluctuation dissipation theorem, comparing
with a finite temperature system) yield the same functional form in the limit
of large block size (). The effective temperature can also be shown
to satisfy the basic requirements on how it changes when two bodies of equal or
unequal temperatures are brought into contact.Comment: 19 pages, 7 figure
Dynamic scaling of fronts in the quantum XX chain
The dynamics of the transverse magnetization in the zero-temperature XX chain
is studied with emphasis on fronts emerging from steplike initial magnetization
profiles. The fronts move with fixed velocity and display a staircase like
internal structure whose dynamic scaling is explored both analytically and
numerically. The front region is found to spread with time sub-diffusively with
the height and the width of the staircase steps scaling as t^(-1/3) and t^1/3,
respectively. The areas under the steps are independent of time, thus the
magnetization relaxes in quantized "steps" of spin-flips.Comment: 4 pages, 3 eps figures, RevTe
What does a strongly excited 't Hooft-Polyakov magnetic monopole do?
The time evolution of strongly exited SU(2) Bogomolny-Prasad-Sommerfield
(BPS) magnetic monopoles in Minkowski spacetime is investigated by means of
numerical simulations based on the technique of conformal compactification and
on the use of hyperboloidal initial value problem. It is found that an
initially static monopole does not radiate the entire energy of the exciting
pulse toward future null infinity. Rather, a long-lasting quasi-stable
`breathing state' develops in the central region and certain expanding shell
structures -- built up by very high frequency oscillations -- are formed in the
far away region.Comment: 4 pages, 6 figure
Numerical investigation of the late-time Kerr tails
The late-time behavior of a scalar field on fixed Kerr background is examined
in a numerical framework incorporating the techniques of conformal
compactification and hyperbolic initial value formulation. The applied code is
1+(1+2) as it is based on the use of the spectral method in the angular
directions while in the time-radial section fourth order finite differencing,
along with the method of lines, is applied. The evolution of various types of
stationary and non-stationary pure multipole initial states are investigated.
The asymptotic decay rates are determined not only in the domain of outer
communication but along the event horizon and at future null infinity as well.
The decay rates are found to be different for stationary and non-stationary
initial data, and they also depend on the fall off properties of the initial
data toward future null infinity. The energy and angular momentum transfers are
found to show significantly different behavior in the initial phase of the time
evolution. The quasinormal ringing phase and the tail phase are also
investigated. In the tail phase, the decay exponents for the energy and angular
momentum losses at future null infinity are found to be smaller than at the
horizon which is in accordance with the behavior of the field itself and it
means that at late times the energy and angular momentum falling into the black
hole become negligible in comparison with the energy and angular momentum
radiated toward future null infinity. The energy and angular momentum balances
are used as additional verifications of the reliability of our numerical
method.Comment: 33 pages, 12 figure
Reaction-diffusion fronts with inhomogeneous initial conditions
Properties of reaction zones resulting from A+B -> C type reaction-diffusion
processes are investigated by analytical and numerical methods. The reagents A
and B are separated initially and, in addition, there is an initial macroscopic
inhomogeneity in the distribution of the B species. For simple two-dimensional
geometries, exact analytical results are presented for the time-evolution of
the geometric shape of the front. We also show using cellular automata
simulations that the fluctuations can be neglected both in the shape and in the
width of the front.Comment: 11 pages, 3 figures, submitted to J. Phys.
On the existence of Killing vector fields
In covariant metric theories of coupled gravity-matter systems the necessary
and sufficient conditions ensuring the existence of a Killing vector field are
investigated. It is shown that the symmetries of initial data sets are
preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra
Methadon maintenance treatment programs in Hungary: Treatment, Harm Reduction and Social Control
On the Noether charge form of the first law of black hole mechanics
The first law of black hole mechanics was derived by Wald in a general
covariant theory of gravity for stationary variations around a stationary black
hole. It is formulated in terms of Noether charges, and has many advantages. In
this paper several issues are discussed to strengthen the validity of the
Noether charge form of the first law. In particular, a gauge condition used in
the derivation is justified. After that, we justify the generalization to
non-stationary variations done by Iyer-Wald.Comment: Latex, 16 pages, arguments on gauge conditions and near-stationary
entropy are added, accepted for publication in Physical Review
- …