3,819 research outputs found
Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors
We consider source-free electromagnetic fields in spacetimes possessing a
non-null Killing vector field, . We assume further that the
electromagnetic field tensor, , is invariant under the action of the
isometry group induced by . It is proved that whenever the two
potentials associated with the electromagnetic field are functionally
independent the entire content of Maxwell's equations is equivalent to the
relation \n^aT_{ab}=0. Since this relation is implied by Einstein's equation
we argue that it is enough to solve merely Einstein's equation for these
electrovac spacetimes because the relevant equations of motion will be
satisfied automatically. It is also shown that for the exceptional case of
functionally related potentials \n^aT_{ab}=0 implies along with one of the
relevant equations of motion that the complementary equation concerning the
electromagnetic field is satisfied.Comment: 7 pages,PACS numbers: 04.20.Cv, 04.20.Me, 04.40.+
Stability of BTZ black strings
We study the dynamical stability of the BTZ black string against fermonic and
gravitational perturbations. The BTZ black string is not always stable against
these perturbations. There exist threshold values for related to the
compactification of the extra dimension for fermonic perturbation, scalar part
of the gravitational perturbation and the tensor perturbation, respectively.
Above the threshold values, perturbations are stable; while below these
thresholds, perturbations can be unstable. We find that this non-trivial
stability behavior qualitatively agrees with that predicted by a
thermodynamical argument, showing that the BTZ black string phase is not the
privileged stable phase.Comment: 9 pages, revised version to appear in Phys. Rev.
Regular phantom black holes
For self-gravitating, static, spherically symmetric, minimally coupled scalar
fields with arbitrary potentials and negative kinetic energy (favored by the
cosmological observations), we give a classification of possible regular
solutions to the field equations with flat, de Sitter and AdS asymptotic
behavior. Among the 16 presented classes of regular rsolutions are traversable
wormholes, Kantowski-Sachs (KS) cosmologies beginning and ending with de Sitter
stages, and asymptotically flat black holes (BHs). The Penrose diagram of a
regular BH is Schwarzschild-like, but the singularity at is replaced by a
de Sitter infinity, which gives a hypothetic BH explorer a chance to survive.
Such solutions also lead to the idea that our Universe could be created from a
phantom-dominated collapse in another universe, with KS expansion and
isotropization after crossing the horizon. Explicit examples of regular
solutions are built and discussed. Possible generalizations include -essence
type scalar fields (with a potential) and scalar-tensor theories of gravity.Comment: revtex4, 4 pages, no figure
Dirac Quantization of Parametrized Field Theory
Parametrized field theory (PFT) is free field theory on flat spacetime in a
diffeomorphism invariant disguise. It describes field evolution on arbitrary
foliations of the flat spacetime instead of only the usual flat ones, by
treating the `embedding variables' which describe the foliation as dynamical
variables to be varied in the action in addition to the scalar field. A formal
Dirac quantization turns the constraints of PFT into functional Schrodinger
equations which describe evolution of quantum states from an arbitrary Cauchy
slice to an infinitesimally nearby one.This formal Schrodinger picture- based
quantization is unitarily equivalent to the standard Heisenberg picture based
Fock quantization of the free scalar field if scalar field evolution along
arbitrary foliations is unitarily implemented on the Fock space. Torre and
Varadarajan (TV) showed that for generic foliations emanating from a flat
initial slice in spacetimes of dimension greater than 2, evolution is not
unitarily implemented, thus implying an obstruction to Dirac quantization.
We construct a Dirac quantization of PFT,unitarily equivalent to the standard
Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are
powerful enough to super-cede the no- go implications of the TV results. The
key features of our quantization include an LQG type representation for the
embedding variables, embedding dependent Fock spaces for the scalar field, an
anomaly free representation of (a generalization of) the finite transformations
generated by the constraints and group averaging techniques. The difference
between 2 and higher dimensions is that in the latter, only finite gauge
transformations are defined in the quantum theory, not the infinitesimal ones.Comment: 33 page
Stabilization of Inverse Miniemulsions by Silyl-Protected Homopolymers
Inverse (water-in-oil) miniemulsions are an important method to encapsulate hydrophilic payloads such as oligonucleotides or peptides. However, the stabilization of inverse miniemulsions usually requires block copolymers that are difficult to synthesize and/or cannot be easily removed after transfer from a hydrophobic continuous phase to an aqueous continuous phase. We describe here a new strategy for the synthesis of a surfactant for inverse miniemulsions by radical addition–fragmentation chain transfer (RAFT) polymerization, which consists in a homopolymer with triisopropylsilyl protecting groups. The protecting groups ensure the efficient stabilization of the inverse (water-in-oil, w/o) miniemulsions. Nanocapsules can be formed and the protecting group can be subsequently cleaved for the re-dispersion of nanocapsules in an aqueous medium with a minimal amount of additional surfactant
Twist and teleportation analogy of the black hole final state
Mathematical connection between the quantum teleportation, the most unique
feature of quantum information processing, and the black hole final state is
studied taking into account the non trivial spacetime geometry. We use the
twist operatation for the generalized entanglement measurement and the final
state boundary conditions to obtain transfer theorems for the black hole
evaporation. This would enable us to put together the universal quantum
teleportation and the black hole evaporation in the unified mathematical
footing. For a renormalized post selected final state of outgoing Hawking
radiation, we found that the measure of mixedness is preserved only in the
special case of final-state boundary condition in the micro-canonical form,
which resmebles perfect teleportation channel.Comment: version_
A non-autonomous stochastic discrete time system with uniform disturbances
The main objective of this article is to present Bayesian optimal control
over a class of non-autonomous linear stochastic discrete time systems with
disturbances belonging to a family of the one parameter uniform distributions.
It is proved that the Bayes control for the Pareto priors is the solution of a
linear system of algebraic equations. For the case that this linear system is
singular, we apply optimization techniques to gain the Bayesian optimal
control. These results are extended to generalized linear stochastic systems of
difference equations and provide the Bayesian optimal control for the case
where the coefficients of these type of systems are non-square matrices. The
paper extends the results of the authors developed for system with disturbances
belonging to the exponential family
The ``Nernst Theorem'' and Black Hole Thermodynamics
The Nernst formulation of the third law of ordinary thermodynamics (often
referred to as the ``Nernst theorem'') asserts that the entropy, , of a
system must go to zero (or a ``universal constant'') as its temperature, ,
goes to zero. This assertion is commonly considered to be a fundamental law of
thermodynamics. As such, it seems to spoil the otherwise perfect analogy
between the ordinary laws of thermodynamics and the laws of black hole
mechanics, since rotating black holes in general relativity do not satisfy the
analog of the ``Nernst theorem''. The main purpose of this paper is to attempt
to lay to rest the ``Nernst theorem'' as a law of thermodynamics. We consider a
boson (or fermion) ideal gas with its total angular momentum, , as an
additional state parameter, and we analyze the conditions on the single
particle density of states, , needed for the Nernst formulation
of the third law to hold. (Here, and denote the single particle
energy and angular momentum.) Although it is shown that the Nernst formulation
of the third law does indeed hold under a wide range of conditions, some simple
classes of examples of densities of states which violate the ``Nernst theorem''
are given. In particular, at zero temperature, a boson (or fermion) gas
confined to a circular string (whose energy is proportional to its length) not
only violates the ``Nernst theorem'' also but reproduces some other
thermodynamic properties of an extremal rotating black hole.Comment: 20 pages, plain LaTeX fil
Compactness of the space of causal curves
We prove that the space of causal curves between compact subsets of a
separable globally hyperbolic poset is itself compact in the Vietoris topology.
Although this result implies the usual result in general relativity, its proof
does not require the use of geometry or differentiable structure.Comment: 15 page
Adiabatic renormalization in theories with modified dispersion relations
We generalize the adiabatic renormalization to theories with dispersion
relations modified at energies higher than a new scale . We obtain
explicit expressions for the mean value of the stress tensor in the adiabatic
vacuum, up to the second adiabatic order. We show that for any dispersion
relation the divergences can be absorbed into the bare gravitational constants
of the theory. We also point out that, depending on the renormalization
prescription, the renormalized stress tensor may contain finite trans-Planckian
corrections even in the limit .Comment: Typos corrected; to appear in the Proceedings of IRGAC 06, Journal of
Physics
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