20,675 research outputs found
Time (in)dependence in general relativity
We clarify the conditions for Birkhoff's theorem, that is, time-independence
in general relativity. We work primarily at the linearized level where guidance
from electrodynamics is particularly useful. As a bonus, we also derive the
equivalence principle. The basic time-independent solutions due to
Schwarzschild and Kerr provide concrete illustrations of the theorem. Only
familiarity with Maxwell's equations and tensor analysis is required.Comment: Revised version of originally titled "Kinder Kerr", to appear in
American Journal of Physic
Some exact solutions of the Dirac equation
Exact analytic solutions are found to the Dirac equation for a combination of
Lorentz scalar and vector Coulombic potentials with additional non-Coulombic
parts. An appropriate linear combination of Lorentz scalar and vector
non-Coulombic potentials, with the scalar part dominating, can be chosen to
give exact analytic Dirac wave functions.Comment: 4 pages. No figures. Presented in Hadron 2000: International Workshop
on Hadron Physics, Caraguatatuba, SP, Brasil, April 200
Circular Symmetry in Topologically Massive Gravity
We re-derive, compactly, a TMG decoupling theorem: source-free TMG separates
into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal
Killing vector, here concretely for circular symmetry. We can then generalize
it to include matter, which is necessarily null.Comment: amplified published versio
Shortcuts to Spherically Symmetric Solutions: A Cautionary Note
Spherically symmetric solutions of generic gravitational models are
optimally, and legitimately, obtained by expressing the action in terms of the
two surviving metric components. This shortcut is not to be overdone, however:
a one-function ansatz invalidates it, as illustrated by the incorrect solutions
of [1].Comment: 2 pages. Amplified derivation, accepted for publication in Class
Quant Gra
No Bel-Robinson Tensor for Quadratic Curvature Theories
We attempt to generalize the familiar covariantly conserved Bel-Robinson
tensor B_{mnab} ~ R R of GR and its recent topologically massive third
derivative order counterpart B ~ RDR, to quadratic curvature actions. Two very
different models of current interest are examined: fourth order D=3 "new
massive", and second order D>4 Lanczos-Lovelock, gravity. On dimensional
grounds, the candidates here become B ~ DRDR+RRR. For the D=3 model, there
indeed exist conserved B ~ dRdR in the linearized limit. However, despite a
plethora of available cubic terms, B cannot be extended to the full theory. The
D>4 models are not even linearizable about flat space, since their field
equations are quadratic in curvature; they also have no viable B, a fact that
persists even if one includes cosmological or Einstein terms to allow
linearization about the resulting dS vacua. These results are an unexpected, if
hardly unique, example of linearization instability.Comment: published versio
V/STOL maneuverability and control
Maneuverability and control of V/STOL aircraft in powered-lift flight is studied with specific considerations of maneuvering in forward flight. A review of maneuverability for representative operational mission tasks is presented and covers takeoff, transition, hover, and landing flight phases. Maneuverability is described in terms of the ability to rotate and translate the aircraft and is specified in terms of angular and translational accelerations imposed on the aircraft. Characteristics of representative configurations are reviewed, including experience from past programs and expectations for future designs. The review of control covers the characteristics inherent in the basic airframe and propulsion system and the behavior associated with ontrol augmentation systems. Demands for augmented stability and control response to meet certain mission operational requirements are discussed. Experience from ground-based simulation and flight experiments that illustrates the impact of augmented stability and control on aircraft design is related by example
Birkhoff for Lovelock Redux
We show succinctly that all metric theories with second order field equations
obey Birkhoff's theorem: their spherically symmetric solutions are static.Comment: Submitted to CQ
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