DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

effective pressure
independent theory but part of some nonabelian
unified (Grand Unification) theory in which the
asymptotic freedom (or finiteness) takes place.
At the energies comparable to the Planck energy
the local quantum field theory should be
(presumably) abandoned and instead one has to
consider a more fundamental string or superstring
theory. See effective charge.
effective pressure The pressure term of effective
stress in a porous medium. If p is
the total pressure, the effective pressure is defined
as p ′ =p−αpf , where pf is the pore
fluid pressure. The parameter α is defined as
α= 1 − K/Ks, where K and Ks are the bulk
moduli of the matrix frame and the solid grains
that constitute the matrix. In most practical
cases,Ks ≫K andα= 1. See effective stress.
effective stress In a porous medium, the pressure
term of the total stress σij is partially sustained
by the pore fluid. The stress tensor with
the effect of pore fluid subtracted is called the
effective stress. It is the effective stress that determines
the deformation and failure of the solid
component of the porous medium. The effective
stress is defined as
σ ′
ij =σij −αpfδij
wherepf is the pore fluid pressure. The parameter
α is defined as α = 1 − K/Ks, where K
andKs are the bulk moduli of the matrix frame
and the solid grains that constitute the matrix.
In most practical cases, Ks ≫K andα= 1.
effective temperature The effective temperature
of a blackbody is that temperature which
characterizes the energy flux (total power output)
at the surface of an object. The energy per
second emitted by an object at a given frequency
over a unit area is called the surface flux. It
is found by integrating the blackbody equation
over all solid angles and all frequencies. The
surface integral gives
Fν = Bν(ν,T) cosθdφdθ=πBν(ν,T)
in units of erg cm −2 s −1 Hz −1 , where θ is the
angle between the normal to the surface and the
path of an emitted photon, φ is the azimuthal
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angle, andBν is the Planck blackbody intensity
in units of erg s −1 cm −2 Hz −1 sr −1 . The total
energy emitted per second per unit area is the
surface flux (above) integrated over all frequen-
cies:
F= πBν(ν,T)dν= 2π5k4 15h3c 4
3T eff =σT4 eff
whereσ is the Stefan–Boltzmann constant. The
total energy flux of a blackbody is related to its
luminosity by,
F=L/4πr 2 =σT 4
eff .
In astronomy, one computes the effective temperatureofastar(orthesum)fromitsluminosity
by this formula. The effective temperature then,
is the characteristic temperature that relates a
star’s total output power to its size.
effluent Something that is discharged; commonlyusedtorefertothedischargefromasewer
or factory outfall lying in a river or coastal waters.
eigenray The integral curve of a principal
direction of the Killing bivector ∇[aKb]. By
the Killing equation, the symmetrized derivative
of the Killing vector K vanishes. In a spinorial
notation, the null eigendirection is given
by the solution αA of the eigenvalue problem
φ AB αB =λα A where φ AB is the spinor representation
of the Killing bivector. See Killing
vector.
eigenvalue An allowed value of the constant
a in the equation Au = au, where A is an operator
acting on a function u (which is called an
eigenfunction). Also called characteristic value.
eikonal approximation The approximation
to a wave equation which assumes the wave
function is of the form exp[iωt + ikx] where
ω and k are large. This replaces the second order
derivatives of the wave function by terms
proportional to the square of ω or of k.
einstein One mole of photons (6.023 × 10 23
photons).
Einstein–Cartan gravity An important particular
case of gravity with torsion. The action