104 Cosmological Models
toward the future steepen. When the star has shrunk to the size of the Schwartzschild
radius, the equatorial section has become a trapped surface, the future of all light rays
from it are directed towards the world line of the center of the star. For an outside
observer the event horizon then remains eternally of the same size, but an insider
would find that the trapped surface of the star is doomed to continue its collapse
toward the singularity at zero radius. The singularity has no future light cone and
cannot thus ever be observed (Figure 5.5).
Black holes are probably created naturally in the aging of stars. The collapse of an
isolated heavy star is, however, not the only route to the formation of a black hole, and
probably not even the most likely one. Binary stars are quite common, and a binary
system consisting of a neutron star and a red giant is a very likely route to a black hole.
The neutron star spirals in (see Figure 5.5), accretes matter from the red giant at a very
high rate, about 1푀⊙per year, photons are trapped in the flow, gravity and friction
heat the material in the accretion disc until it emits X-rays. When the temperature
rises above 1MeV neutrinos can carry off the thermal energy.
For example, Cyg X-1 is a black hole—a main-sequence star binary with a hole
mass of more than about 10푀⊙, probably the most massive black hole in a binary
observed in the Galaxy. The enormous gravitational pull of the hole tears material
from its companion star. This material then orbits the hole in a Saturnus-like accretion
disc before disappearing into the hole. Finally, the main-sequence star explodes and
becomes a neutron star, which will ultimately merge into the hole to form a heavier
black hole.
Neutron stars and stellar black holes have masses of the order of 10푀⊙, supermas-
sive black holes have 10^6 −^10 푀⊙. There could be as many as 10^8 stellar black holes in
our galaxy. Black holes weighing thousands or million times the Chandrasekhar limit
of 1. 44 푀⊙cannot have been produced in the collapse of a single star. How they have
been produced is currently not well understood. The most likely route is by accretion
and coalescence of intermediate mass black holes.
Massive black holes are seen at very high redshift. The discovery of 10^9 푀⊙black
holes at푧> 7 .0 is mysterious since it is unclear how such massive objects could have
formed and grown so quickly at early times.
Observations of Black Holes. Since black holes cannot be seen directly, one has to
infer their existence from indirect evidence. Within our galaxy one can measure the
orbits of neighboring individual stars. In this way one has deduced that the central
few parsecs of our galaxy evidently hosts a dense and luminous star cluster and a very
compact radio source Sgr A∗[10]. Its intrinsic size is aa most 10 light minutes which
makes it the most likely candidate of a possible central black hole. There is evidence
for little motion of the Sgr A∗itself from the size and motions of the central compact
radio source.
There are precise determinations of the elliptical orbits and the velocity vectors of
about 30 stars in the vicinity, all having one common focal point located at the Sgr A∗,
see Figure 5.6. All the acceleration vectors intersect at Sgr A∗, and the velocity vectors
do not decrease with decreasing distance to Sgr A∗, indicating that the stars move in