DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

Kelvin (Thompson) circulation theorem
Kelvin (Thompson) circulation theorem In
a perfect fluid, the circulation of the velocity of
a fluid element is constant as the element moves
along flow lines.
Keplerian map In planetary dynamics, an
approximate but fast method to solve for the orbital
evolution of a small body such as a comet
in the solar system under the influence of the
planetary perturbations. One assumes that planetary
perturbations become significant only duringtheshortdurationaroundperihelionpassage,
and the orbit changes either by systematic, or in
some cases approximately random, small jumps
from one Keplerian orbit to another, as the small
body passes perihelion.
Kepler shear The velocity difference between
particles in adjacent Keplerian orbits
about a central massive body.
Kepler’s laws Observations of the motion of
planets due to Johannes Kepler.
1. All planets move in elliptical orbits, with
the sun at one focus of the ellipse.
2. The line connecting the sun and the planet
sweeps out equal areas in equal times.
3. The square of the period T of orbit of a
planet is proportional to the cube semimajor axis
a of its orbit:
T 2 =ka 3
where the proportionality factor k is the same
for all planets.
Kepler’s supernova (SN1604, 3C358) A
supernova that occurred in 1604 and was first
observed by Kepler on October 17 of that year.
Kepler reported that the star was initially as
bright as Mars, then brightened and surpassed
Jupiter within a few days, suggesting a peak
brightness of magnitude −2.25. It plateaued
at this brightness as it was lost in twilight of
November 1604. It reappeared in January 1605,
and Kepler found it still brighter than Antares
(m = 1). It remained visible until March 1606,
a naked-eye visibility of 18 months. From its
light curve, it was almost certainly type I supernova.
A remnant is now found at Right Ascension:
17 h 27 ′ 42 ′′ and Declination: −21 ◦ 27 ′ . It
is now observable as a remnant of about 3 arcmin
diameter, consisting of faint filaments in
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the optical, but as a shell in the radio and in
X-ray. The distance is approximately 4.4 kpc.
Kerr black hole (1963) A rotating black
hole, i.e., a black hole with angular momentum
associated to its spinning motion. The spin axis
of the Kerr black hole breaks the spherical symmetry
of a nonrotating (Schwarzschild) black
hole, and identifies a preferential orientation in
the space-time. In the vicinity of the hole, below
a limiting distance called the static radius,
the rotation of the hole forces every observer to
orbit the black hole in the same direction as the
black hole rotates. Inside the static radius is the
event horizon (the true surface of the black hole).
These two surfaces delimit the ergosphere of the
Kerr black hole, a region from which a particle
can in principle escape, extracting some of the
rotational kinetic energy of the black hole. On
theoretical grounds it is expected that gravitational
collapse of massive stars or star systems
will create spinning Kerr black holes, and the escape
of particles from the ergosphere, may play
an important role as the power source and collimation
mechanism of jets observed in radio
galaxies and quasars. See quasar.
Kerr metric (1963) The metric
ds 2 =
2Mr
− 1 −
r2 +a2 cos2
du+a sin
θ
2 θdφ
+ 2 du+a sin 2
θdφ dr+a sin 2
θdφ
+ r 2 +a 2 cos 2
θ dθ 2 + sin 2 θdφ 2
discovered by R.P. Kerr and representing the
gravitationalfieldofarotatingKerrblackholeof
massM and angular momentumaM, when the
condition a2 ≤M2 holds. When the condition
is not met, the space-time singularity at r= 0
and θ = π 2
2
is “naked”, giving rise to global
causality violation. Uniqueness theorems have
been proven that (at least with a topology of a
two-sphere of the event horizon) there are no
other stationary vacuum black hole metrics, assuming
general relativity is the correct theory of
gravity. See cosmic censorship.
Kerr–Newman metric The unique asymptotically
flat general relativistic metric describ-