5,746 research outputs found
A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories
We present a general method for the analysis of the stability of static,
spherically symmetric solutions to spherically symmetric perturbations in an
arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves
fixing the gauge and solving the linearized gravitational field equations to
eliminate the metric perturbation variable in terms of the matter variables. In
a wide class of cases--which include f(R) gravity, the Einstein-aether theory
of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining
perturbation equations for the matter fields are second order in time. We show
how the symplectic current arising from the original Lagrangian gives rise to a
symmetric bilinear form on the variables of the reduced theory. If this
bilinear form is positive definite, it provides an inner product that puts the
equations of motion of the reduced theory into a self-adjoint form. A
variational principle can then be written down immediately, from which
stability can be tested readily. We illustrate our method in the case of
Einstein's equation with perfect fluid matter, thereby re-deriving, in a
systematic manner, Chandrasekhar's variational principle for radial
oscillations of spherically symmetric stars. In a subsequent paper, we will
apply our analysis to f(R) gravity, the Einstein-aether theory, and
Bekenstein's TeVeS theory.Comment: 13 pages; submitted to Phys. Rev. D. v2: changed formatting, added
conclusion, corrected sign convention
Stability of spherically symmetric solutions in modified theories of gravity
In recent years, a number of alternative theories of gravity have been
proposed as possible resolutions of certain cosmological problems or as toy
models for possible but heretofore unobserved effects. However, the
implications of such theories for the stability of structures such as stars
have not been fully investigated. We use our "generalized variational
principle", described in a previous work, to analyze the stability of static
spherically symmetric solutions to spherically symmetric perturbations in three
such alternative theories: Carroll et al.'s f(R) gravity, Jacobson &
Mattingly's "Einstein-aether theory", and Bekenstein's TeVeS. We find that in
the presence of matter, f(R) gravity is highly unstable; that the stability
conditions for spherically symmetric curved vacuum Einstein-aether backgrounds
are the same as those for linearized stability about flat spacetime, with one
exceptional case; and that the "kinetic terms" of vacuum TeVeS are indefinite
in a curved background, leading to an instability.Comment: ReVTex; 20 pages, 3 figures. v2: references added, submitted to PRD;
v3: expanded discussion of TeVeS; v4: minor typos corrected (version to
appear in PRD
Just how long can you live in a black hole and what can be done about it?
We study the problem of how long a journey within a black hole can last.
Based on our observations, we make two conjectures. First, for observers that
have entered a black hole from an asymptotic region, we conjecture that the
length of their journey within is bounded by a multiple of the future
asymptotic ``size'' of the black hole, provided the spacetime is globally
hyperbolic and satisfies the dominant-energy and non-negative-pressures
conditions. Second, for spacetimes with Cauchy surfaces (or an
appropriate generalization thereof) and satisfying the dominant energy and
non-negative-pressures conditions, we conjecture that the length of a journey
anywhere within a black hole is again bounded, although here the bound requires
a knowledge of the initial data for the gravitational field on a Cauchy
surface. We prove these conjectures in the spherically symmetric case. We also
prove that there is an upper bound on the lifetimes of observers lying ``deep
within'' a black hole, provided the spacetime satisfies the
timelike-convergence condition and possesses a maximal Cauchy surface. Further,
we investigate whether one can increase the lifetime of an observer that has
entered a black hole, e.g., by throwing additional matter into the hole.
Lastly, in an appendix, we prove that the surface area of the event horizon
of a black hole in a spherically symmetric spacetime with ADM mass
is always bounded by , provided
that future null infinity is complete and the spacetime is globally hyperbolic
and satisfies the dominant-energy condition.Comment: 20 pages, REVTeX 3.0, 6 figures included, self-unpackin
Gauge Invariant Effective Stress-Energy Tensors for Gravitational Waves
It is shown that if a generalized definition of gauge invariance is used,
gauge invariant effective stress-energy tensors for gravitational waves and
other gravitational perturbations can be defined in a much larger variety of
circumstances than has previously been possible. In particular it is no longer
necessary to average the stress-energy tensor over a region of spacetime which
is larger in scale than the wavelengths of the waves and it is no longer
necessary to restrict attention to high frequency gravitational waves.Comment: 11 pages, RevTe
The future of Genesis science
Solar abundances are important to planetary science since the prevalent model assumes that the composition of the solar photosphere is that of the solar nebula from which planetary materials formed. Thus, solar abundances are a baseline for planetary science. Previously, solar abundances have only been available through spectroscopy or by proxy (CI). The Genesis spacecraft collected and returned samples of the solar wind for laboratory analyses. Elemental and isotopic abundances in solar wind from Genesis samples have been successfully measured despite the crash of the re‐entry capsule. Here we present science rationales for a set of 12 important (and feasible postcrash) Science and Measurement Objectives as goals for the future (Table 1). We also review progress in Genesis sample analyses since the last major review (Burnett 2013). Considerable progress has been made toward understanding elemental fractionation during the extraction of the solar wind from the photosphere, a necessary step in determining true solar abundances from solar wind composition. The suitability of Genesis collectors for specific analyses is also assessed. Thus far, the prevalent model remains viable despite large isotopic variations in a number of volatile elements, but its validity and limitations can be further checked by several Objectives
The solar oxygen-isotopic composition: Predictions and implications for solar nebula processes
The outer layers of the Sun are thought to preserve the average isotopic and chemical composition of the solar system. The solar O-isotopic composition is essentially unmeasured, though models based on variations in meteoritic materials yield several predictions. These predictions are reviewed and possible variations on these predictions are explored. In particular, the two-component mixing model of Clayton and Mayeda (1984) (slightly revised here) predicts solar compositions to lie along an extension of the calcium-aluminum-rich inclusion (CAI) ^(16)O line between (δ^(18)O, δ^(17)O) = (16.4, 11.4)%0 and (12.3, 7.5)%0. Consideration of data from ordinary chondrites suggests that the range of predicted solar composition should extend to slightly lower δ^(18)O values. The predicted solar composition is critically sensitive to the solid/gas ratio in the meteorite-forming region, which is often considered to be significantly enriched over solar composition. A factor of two solid/gas enrichment raises the predicted solar (δ^(18)O, δ^(17)O) values along an extension of the CAI ^(16)O line to (33, 28)%0. The model is also sensitive to the nebular O gas phase. If conversion of most of the gaseous O from CO to H_2O occurred at relatively low temperatures and was incomplete at the time of CM aqueous alteration, the predicted nebular gas composition (and hence the solar composition) would be isotopically heavier along a slope 1/2 line. The likelihood of having a single solid nebular O component is discussed. A distribution of initial solid compositions along the CAI ^(16)O line (rather than simply as an end-member) would not significantly change the predictions above in at least one scenario. Even considering these variations within the mixing model, the predicted range of solar compositions is distinct from that expected if the meteoritic variations are due to non-mass-dependent fractionation. Thus, a measurement of the solar O composition to a precision of several permil would clearly distinguish between these theories and should clarify a number of other important issues regarding solar system formation
The Cosmic Censor Forbids Naked Topology
For any asymptotically flat spacetime with a suitable causal structure
obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying
conditions guaranteeing focusing of complete null geodesics, we prove that
active topological censorship holds. We do not assume global hyperbolicity, and
therefore make no use of Cauchy surfaces and their topology. Instead, we
replace this with two underlying assumptions concerning the causal structure:
that no compact set can signal to arbitrarily small neighbourhoods of spatial
infinity (``-avoidance''), and that no future incomplete null geodesic is
visible from future null infinity. We show that these and the focusing
condition together imply that the domain of outer communications is simply
connected. Furthermore, we prove lemmas which have as a consequence that if a
future incomplete null geodesic were visible from infinity, then given our
-avoidance assumption, it would also be visible from points of spacetime
that can communicate with infinity, and so would signify a true naked
singularity.Comment: To appear in CQG, this improved version contains minor revisions to
incorporate referee's suggestions. Two revised references. Plain TeX, 12
page
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