DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

global topological defect
Antarctic circumpolar current, the North Atlantic
Deep Water spreads into the Indian and
Pacific basins, along with the Antarctic Bottom
Water. Compensating the deep outflow, warm
surface water flows back into the North Atlantic.
Because of a large temperature difference between
the surface (10 ◦ C) and deep (0 ◦ C) waters,
this overturning circulation transports a huge
amount of heat into the North Atlantic, making
winter much warmer in northern Europe than at
the same latitudes in North America.
global topological defect Topological defects
that may be important in early universe
cosmology, formed from the breakdown of a
rigid (or global) symmetry that does not have
“compensating” gauge fields associated to it.
Long-range interactions between the defects in
the network and energy stored in gradients of
the field cannot be compensated far away from
the defect; in general, these constitute divergentenergy
configurations. A cutoff for the energy is
physically given by other relevant scales of the
problem under study, such as the mean distance
between two arbitrary defects in the network, or
the characteristic size of the loop (in the case of
cosmic string loops), for example.
globular cluster A dense spherical cluster
of stars of Population II, typically of low mass
(≈ 0.5M⊙). Diameter of order 100 pc; containing
up to 10 5 stars. Globular clusters are a
component of the halo of the galaxy.
GMT See Universal Time (UT or UT1).
gnomon A vertical rod whose shadow in sunlight
is studied to measure the angular position
of the sun.
Goddard, Robert H. Rocket engineer
(1882–1945). Designed the liquid-propellant
rocket.
Goldberg–Sachs theorem (1962) A vacuum
spacetime in general relativity is algebraically
special if and only if it contains a shearfree
geodesic null congruence. See congruence,
Petrov types.
Goldstone boson See Goldstone model.
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Goldstone model A quantum field model of
a scalar field with a nonlinear self-interaction
(Goldstone, 1961). A theory in which the symmetry
of the Lagrangian is not shared by the
ground state (the vacuum, i.e., the lowest energy)
solution. The Lagrangian density reads
L=(∂µφ) ∗ (∂ µ φ)−V(φ)
with φ a complex scalar field ( ∗ means complex
conjugate) and the symmetry breaking potential
V(φ) has the “Mexican hat” form V =
1
4 λ(φ∗ φ−η 2 ) 2 , withλ andη positive constants.
L is invariant under the global transformation
φ → e i φ, with a constant in spacetime.
This model has a local potential maximum at
φ= 0 and the minima occur when the absolute
value of φ equals η. Hence, the minima can be
expressed asφ=ηe iθ and the phaseθ can take
any of the equivalent values between zero and
2π. Once one of these phases is chosen (and we
have, say, φvac =ηe iθvac as our vacuum state)
the original symmetry possessed by the model
is lost (broken). To see this, the original U(1)
transformationφ→e i φ will now changeθvac
by θ vac +: the model is no longer invariant
under the original symmetry.
By further analyzing this model in the vicinity
of the new vacuum state, one deduces that
the original Lagrangian can be written in terms
of massive and massless scalar fields, plus other
uninteresting interaction terms. It is the particle
associated with this massless field (whose degree
of freedom is related to motion around the
equal energy circle of minima of the potential
V ) that became known as the Goldstone boson.
In cosmology, global strings may arise from
configurations of the Goldstone field; these can
have important implications for the structure of
the universe. See Goldstone theorem, Higgs
mechanism.
Goldstone theorem Any spontaneous breaking
of a continuous symmetry leads to the existence
of a massless particle. This theorem shows
that when the Lagrangian of the theory is invariant
under a group of symmetries G, but the
ground state is only invariant under a subgroup
H , there will be a number of massless (Goldstone)
particles equal to the dimension of the
quotient space M ∼ G/H , and hence equal to