DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

the mass measured outside the string of the particle
which is the current carrier. Then the fields
acquire a nonvanishing probability to jump off
the string and into a free particle state. There exists
then a maximum current, which in the case
of fermionic carriers of mass and charge qm is
given byJmax = qm/2π, beyond which the current
will fall drastically, showing saturation. See
Carter–Peter model, phase frequency threshold,
Witten conducting string.
current screening (cosmic string) Conducting
cosmic strings moving at a supersonic velocityv
in a plasma of densityρ induce a magnetic
shock since the charged particles in the plasma
cannot penetrate in regions too close to the string
core. The distancers from the string core to the
shock is given by
rs = J
cv √ ρ ,
with c the velocity of light and J the current
flowingalongthestring. Atdistanceslargerthan
rs, the plasma therefore does not see the current
on the string, so that it is said to be screened.
See conducting string.
current sheet A non-propagating boundary
between two plasmas with the magnetic field
tangential to the boundary, i.e., a tangential discontinuity
without any flow. Current sheets are
thought to exist in the solar corona with thicknesses
much smaller than typical coronal length
scales. Current sheets are required to separate
magnetic fields of opposite polarity. Examples
are the heliospheric current sheet separating the
two hemispheres of opposing polarity in the interplanetary
magnetic field, the tail current separating
the northern and southern part of the magnetosphere’s
tail, or the tips of helmet streamers.
The large current densities inherent to current
sheets may have an important role in heating the
corona, producing solar flares and prominence
formation. Current sheets are topological regions
which are most suitable for reconnection
to occur. See reconnection.
curvature A geometrical tensor describing
how much a given space differs from the flat
spaceofthesamenumberofdimensions. Calculationally
the components of the curvature ten-
© 2001 by CRC Press LLC
curved space-time
sor (the Riemann tensor) involve the connection
coefficients and their first derivatives, and the
structure coefficients describing the behavior of
the basis used (simple example: spherical coordinates,
where the structure coefficients vanish
vs. unit vectors parallel to the spherical coordinate
lines, structure constants nonzero). In Einstein’s
theory of gravity (general relativity), the
curvature is an expression of the gravitational
field. Flat space (zero curvature) is described
by special relativity. The components of the
curvature can be measured by repeated experiments
involving the acceleration of separation
of geodesics moving in various planes. That this
involves relative acceleration shows that the effects
of the curvature-tensor are a second-order
derivation from flatness. See connection, structure
coefficients.
curvature invariant Invariant functions of
the curvature tensor. There exist two types:
1. Polynomial invariants. In general relativity,
the Ricci scalar R is pointwise determined
by the matter distribution. Two
quadratic and two cubic invariants exist.
An example of these is the Kretschmann
scalarI=RabcdR abcd .
2. Ratios of various tensor functions of the
curvature tensor of like type.
See Riemann tensor.
curvature tensor See Riemann tensor.
curve A1− 1 mapping from the real numbers
to a space; for instance, the mapping from
the real numbers Z to the four-space given
in Minkowski coordinates: {Z} : {Z −→
X α (Z),α = 0 , 1 , 2 , 3 , }. It is expedient
to consider continuous and differentiable mappings
(hence curves) of this type.
curved space-time A general term for the
pseudo-Riemannian manifold with a non-zero
curvature metric. This is a concept that proves
very useful for the construction of quantum field
theory in curved space-time and especially in the
models of induced gravity. Any theory of gravity
should have two basic components: equations
for the matter fields and particles and equations
for the gravity itself. In quantum (and