106 Cosmological Models
The accretion disks of black holes are typically truncated near the innermost
circular orbit of matter, and hence the main effect is the deformation of a ring the
size of this orbit bending near the black hole, rather than the effect of the event hori-
zon itself. There will then be a shadow which is essentially a lensed image of the
event horizon, and its shape is closely related to the closed orbit for photons around
the black hole. Since photons that circle the black hole slightly within the photon
orbit will end up inside the event horizon while photons just outside will escape
to infinity, there is a rather sharp boundary between bright and dark regions. The
shadow itself is thus indeed primarily a deficit of photons due to absorption by the
event horizon.
A spectral turn-over indicates that the region becomes optically thin and allows
us to see through to the event horizon. The shadow is in principle detectable with
present-day technology and would allow many fundamental tests of general relativity
and its alternatives.
Active galactic nuclei (AGN) furnish other indirect proof for black holes. AGN often
exhibit quasars which require enormously powerful engines, much more than super-
novae could furnish. It is now thought that every AGN is powered by a massive central
black hole accreting radiation, matter and vacuum energy. The supermassive black
hole Sgr A∗is, however very inactive, so there is no quasar associated with it.
Spectacular flashes of energies 1000–10000 larger than those of SNe (10^54 erg, or
the release of 1푀⊙in a few 0.1 s) are seen homogeneously distributed in the universe.
TheseGamma Ray Burstshave a duration of 10−^2 to 10^2 s. The very first one nearly
started a third World War when United States intelligence suspected that the Soviet
Union was testing a new arm above the Earth.
The GRBs are not ejected from black holes, rather they originate from the grav-
itational collapse of a neutron star to a black hole. One possible route for short
GRBs is that they originate from an initial binary system consisting of a compact
carbon–oxygen (CO) core star and a neutron star. The CO core explodes as a super-
nova, and part of its ejecta accretes onto the neutron star which reaches its critical
mass and collapses to a black hole. A new neutron star is then generated by the super-
nova as a remnant. The energy released in the GRB is energetically dominant to super-
novae, so it cannot originate in an SN. Long-duration GRBs are believed to be due to
a continued energy injection mechanism which powers the forward shock, giving rise
to an unusual and long-lasting afterglow.
If a neutron star and a black hole are gravitationally bound they can give rise to a
new process of merging, resulting in a gravitational collapse leading to a new black
hole with the emission of a GRB and possibly gravitational waves.
5.5 Extended Gravity Models
In Chapter 3.3 we derived the Einstein Equation (3.28) from the Einstein–Hilbert
action
푆=∫ d^4 푥