DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

Rayleigh distribution
θ=−˙ρ/ρ, whereρ is the density of the points
being followed.) θ can also be defined in terms
of the local velocity field u µ : θ =u µ
;µ , the
divergence is taken using the 4-velocity and 4metric.
The “;” is the metric covariant derivative.
Similarly the shear,σij is the 3-tensor defining
non-spherical motion
σij = uα;β +uβ;α − 1
3 gαβθ
P α
iPβ j
and P β
i is a projection into the 3-space associated
with the central particle. The quantity a α
is the acceleration of the velocity u α :a α =
u α ;β uβ .
Finally
ωij = uα,β −uβ,α
P α
i P β
j
is the rotation 3-tensor. The appearance of the
Ricci tensor Rαβ in the Raychaudhuri equation
can be related via Einstein’s equations to the
gravitational focusing power of matter. It can
be seen that θ and σij act to decrease the expansion,
ωij acts to increase it. See summation
convention.
Rayleigh distribution A probability density
function. It has non-zero skewness and describes
the distribution of certain non-negative
parameters (such as wave height in deep water).
Rayleigh–Jeans approximation An approximation
to Planck’s blackbody equation for
monochromatic specific intensity at long wavelengths.
For long wavelengths, we can make the
approximation hν