Installation drag considerations as related to turboprop and turbofan engines

Some of the specific areas associated with straight jet and turboprop engine installations are outlined where drag reduction and, thus, improved aircraft system performance is obtained. Specific areas constitute air intake sizing for general aviation aircraft, exhaust duct geometries and cooling system arrangements for propeller powered aircraft

Two-way digital driver/receiver uses one set of lines

Two-way /bilateral/ digital driver/receiver system using MOS circuits was designed for a multiprocess computer having several subsystems at relatively close locations. The system requires only a single set of communication lines between subsystems, thus achieving lower cost with increased reliability

Study of small turbofan engines applicable to general-aviation aircraft

The applicability of small turbofan engines to general aviation aircraft is discussed. The engine and engine/airplane performance, weight, size, and cost interrelationships are examined. The effects of specific engine noise constraints are evaluated. The factors inhibiting the use of turbofan engines in general aviation aircraft are identified

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

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 ${\Bbb R}^3$ 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 $A$ of the event horizon of a black hole in a spherically symmetric spacetime with ADM mass $M_{\text{ADM}}$ is always bounded by $A \le 16\pi M_{\text{ADM}}^2$, 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

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 (``$i^0$-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 $i^0$-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

Local continuity laws on the phase space of Einstein equations with sources

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page