9,830 research outputs found
CN rings in full protoplanetary disks around young stars as probes of disk structure
Bright ring-like structure emission of the CN molecule has been observed in
protoplanetary disks. We investigate whether such structures are due to the
morphology of the disk itself or if they are instead an intrinsic feature of CN
emission. With the intention of using CN as a diagnostic, we also address to
which physical and chemical parameters CN is most sensitive. A set of disk
models were run for different stellar spectra, masses, and physical structures
via the 2D thermochemical code DALI. An updated chemical network that accounts
for the most relevant CN reactions was adopted. Ring-shaped emission is found
to be a common feature of all adopted models; the highest abundance is found in
the upper outer regions of the disk, and the column density peaks at 30-100 AU
for T Tauri stars with standard accretion rates. Higher mass disks generally
show brighter CN. Higher UV fields, such as those appropriate for T Tauri stars
with high accretion rates or for Herbig Ae stars or for higher disk flaring,
generally result in brighter and larger rings. These trends are due to the main
formation paths of CN, which all start with vibrationally excited H2*
molecules, that are produced through far ultraviolet (FUV) pumping of H2. The
model results compare well with observed disk-integrated CN fluxes and the
observed location of the CN ring for the TW Hya disk. CN rings are produced
naturally in protoplanetary disks and do not require a specific underlying disk
structure such as a dust cavity or gap. The strong link between FUV flux and CN
emission can provide critical information regarding the vertical structure of
the disk and the distribution of dust grains which affects the UV penetration,
and could help to break some degeneracies in the SED fitting. In contrast with
C2H or c-C3H2, the CN flux is not very sensitive to carbon and oxygen
depletion.Comment: New version of paper, correcting too high H2 excitation rates and
consequently too high CN column densities. Qualitative conclusions of the
paper remain unchanged. Quantitatively, the CN column densities are an order
of magnitude lower whereas fluxes decrease by a factor of 3-4. Rings are
larger by up to a factor of 2. 13 pages, 19 figures, accepted for publication
in A&
Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime
Building on a pair of earlier papers, I investigate the various point-wise
and averaged energy conditions for the quantum stress-energy tensor
corresponding to a conformally-coupled massless scalar field in the in the
(1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors
are analytically known, I can get exact results for the Hartle--Hawking,
Boulware, and Unruh vacua. This exactly solvable model serves as a useful
sanity check on my (3+1)-dimensional investigations wherein I had to resort to
a mixture of analytic approximations and numerical techniques. Key results in
(1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the
Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC
is violated everywhere in the spacetime (for any quantum state, not just the
standard vacuum states).Comment: 7 pages, ReV_Te
The causal structure of spacetime is a parameterized Randers geometry
There is a by now well-established isomorphism between stationary
4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries -
these Randers geometries being a particular case of the more general class of
3-dimensional Finsler geometries. We point out that in stably causal
spacetimes, by using the (time-dependent) ADM decomposition, this result can be
extended to general non-stationary spacetimes - the causal structure (conformal
structure) of the full spacetime is completely encoded in a parameterized
(time-dependent) class of Randers spaces, which can then be used to define a
Fermat principle, and also to reconstruct the null cones and causal structure.Comment: 8 page
From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture
The recent interest in ``time machines'' has been largely fueled by the
apparent ease with which such systems may be formed in general relativity,
given relatively benign initial conditions such as the existence of traversable
wormholes or of infinite cosmic strings. This rather disturbing state of
affairs has led Hawking to formulate his Chronology Protection Conjecture,
whereby the formation of ``time machines'' is forbidden. This paper will use
several simple examples to argue that the universe appears to exhibit a
``defense in depth'' strategy in this regard. For appropriate parameter regimes
Casimir effects, wormhole disruption effects, and gravitational back reaction
effects all contribute to the fight against time travel. Particular attention
is paid to the role of the quantum gravity cutoff. For the class of model
problems considered it is shown that the gravitational back reaction becomes
large before the Planck scale quantum gravity cutoff is reached, thus
supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision
Area products for stationary black hole horizons
Area products for multi-horizon stationary black holes often have intriguing
properties, and are often (though not always) independent of the mass of the
black hole itself (depending only on various charges, angular momenta, and
moduli). Such products are often formulated in terms of the areas of inner
(Cauchy) horizons and outer (event) horizons, and sometimes include the effects
of unphysical "virtual" horizons. But the conjectured mass-independence
sometimes fails. Specifically, for the Schwarzschild-de Sitter [Kottler] black
hole in (3+1) dimensions it is shown by explicit exact calculation that the
product of event horizon area and cosmological horizon area is not mass
independent. (Including the effect of the third "virtual" horizon does not
improve the situation.) Similarly, in the Reissner-Nordstrom-anti-de Sitter
black hole in (3+1) dimensions the product of inner (Cauchy) horizon area and
event horizon area is calculated (perturbatively), and is shown to be not mass
independent. That is, the mass-independence of the product of physical horizon
areas is not generic. In spherical symmetry, whenever the quasi-local mass m(r)
is a Laurent polynomial in aerial radius, r=sqrt{A/4\pi}, there are
significantly more complicated mass-independent quantities, the elementary
symmetric polynomials built up from the complete set of horizon radii (physical
and virtual). Sometimes it is possible to eliminate the unphysical virtual
horizons, constructing combinations of physical horizon areas that are mass
independent, but they tend to be considerably more complicated than the simple
products and related constructions currently being mooted in the literature.Comment: V1: 16 pages; V2: 9 pages (now formatted in PRD style). Minor change
in title. Extra introduction, background, discussion. Several additional
references; other references updated. Minor typos fixed. This version
accepted for publication in PRD; V3: Minor typos fixed. Published versio
Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum
Building on a series of earlier papers [gr-qc/9604007, gr-qc/9604008,
gr-qc/9604009], I investigate the various point-wise and averaged energy
conditions in the Unruh vacuum. I consider the quantum stress-energy tensor
corresponding to a conformally coupled massless scalar field, work in the
test-field limit, restrict attention to the Schwarzschild geometry, and invoke
a mixture of analytical and numerical techniques. I construct a semi-analytic
model for the stress-energy tensor that globally reproduces all known numerical
results to within 0.8%, and satisfies all known analytic features of the
stress-energy tensor. I show that in the Unruh vacuum (1) all standard
point-wise energy conditions are violated throughout the exterior region--all
the way from spatial infinity down to the event horizon, and (2) the averaged
null energy condition is violated on all outgoing radial null geodesics. In a
pair of appendices I indicate general strategy for constructing semi-analytic
models for the stress-energy tensor in the Hartle-Hawking and Boulware states,
and show that the Page approximation is in a certain sense the minimal ansatz
compatible with general properties of the stress-energy in the Hartle-Hawking
state.Comment: 40 pages; plain LaTeX; uses epsf.sty (ten encapsulated postscript
figures); two tables (table and tabular environments). Should successfully
compile under both LaTeX 209 and the 209 compatibility mode of LaTeX2
Is Quantum Spacetime Foam Unstable?
A very simple wormhole geometry is considered as a model of a mode of
topological fluctutation in Planck-scale spacetime foam. Quantum dynamics of
the hole reduces to quantum mechanics of one variable, throat radius, and
admits a WKB analysis. The hole is quantum-mechanically unstable: It has no
bound states. Wormhole wave functions must eventually leak to large radii. This
suggests that stability considerations along these lines may place strong
constraints on the nature and even the existence of spacetime foam.Comment: 15 page
Unconventional string-like singularities in flat spacetime
The conical singularity in flat spacetime is mostly known as a model of the
cosmic string or the wedge disclination in solids. Its another, equally
important, function is to be a representative of quasiregular singularities.
From all these of views it seems interesting to find out whether there exist
other similar singularities. To specify what "similar" means I introduce the
notion of the string-like singularity, which is, roughly speaking, an
absolutely mild singularity concentrated on a curve or on a 2-surface S
(depending on whether the space is three- of four-dimensional). A few such
singularities are already known: the aforementioned conical singularity, two
its Lorentzian versions, the "spinning string", the "screw dislocation", and
Tod's spacetime. In all these spacetimes S is a straight line (or a plane) and
one may wonder if this is an inherent property of the string-like
singularities. The aim of this paper is to construct string-like singularities
with less trivial S. These include flat spacetimes in which S is a spiral, or
even a loop. If such singularities exist in nature (in particular, as an
approximation to gravitational field of strings) their cosmological and
astrophysical manifestations must differ drastically from those of the
conventional cosmic strings. Likewise, being realized as topological defects in
crystals such loops and spirals will probably also have rather unusual
properties.Comment: Draft. References and comments are welcome. v2. Section 3 is intact,
the rest is made briefer and clearer. A couple of references are added. v3.
Insignificant correstions. The published versio
Effective refractive index tensor for weak field gravity
Gravitational lensing in a weak but otherwise arbitrary gravitational field
can be described in terms of a 3 x 3 tensor, the "effective refractive index".
If the sources generating the gravitational field all have small internal
fluxes, stresses, and pressures, then this tensor is automatically isotropic
and the "effective refractive index" is simply a scalar that can be determined
in terms of a classic result involving the Newtonian gravitational potential.
In contrast if anisotropic stresses are ever important then the gravitational
field acts similarly to an anisotropic crystal. We derive simple formulae for
the refractive index tensor, and indicate some situations in which this will be
important.Comment: V1: 8 pages, no figures, uses iopart.cls. V2: 13 pages, no figures.
Significant additions and clarifications. This version to appear in Classical
and Quantum Gravit
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