Black Holes

After a star has exhausted its nuclear fuel, it can no longer remain in equilibrium and
must ultimately undergo gravitational collapse. The star will end as a white dwarf
if the mass of the collapsing core is less than the famous Chandrashekhar limit of 1.4
solar masses. It will end as a neutron star if the core has a mass greater than the
Chandrashekhar limit and less than about 35 times the mass of the sun. It is often
believed that a core heavier than about 5 solar masses will end, not as a white dwarf
or as a neutron star, but as a black hole. However, this belief that a black hole will
necessarily form is not based on any firm theoretical evidence. An alternate possibility
allowed by the theory is that a naked singularity can form, and the purpose of the
present article is to review our current understanding of gravitational collapse and the
formation of black holes and naked singularities.
A black hole has been appropriately described by Chandrashekhar as the most
beautiful macroscopic object known to man. Only a few parameters suffice to describe
the most general black hole solution, and these objects have remarkable thermodynamic
properties. Further, excellent observational evidence for their existence has
developed over the years (Rees 1998). Thus, there can be no doubt about the reality of
black holes, and the gravitational collapse of very many sufficiently massive stars
must end in the formation of a black hole...

However, the following question is still very much open. If the collapsing core is
heavy enough to not end as a neutron star, does this guarantee that a black hole will
necessarily form? The answer to this question has to come from the general theory of
relativity, and unfortunately this remains an unsolved problem.
What we do know from general relativity about gravitational collapse is broadly
contained in the celebrated singularity theorems of Geroch, Hawking and Penrose. It
has been shown that under fairly general conditions, a sufficiently massive collapsing
object will undergo continual gravitational collapse, resulting in the formation of a gravitational singularity. The energy density of the collapsing matter, as well as the
curvature of spacetime, are expected to diverge at this singularity.
Is such a singularity necessarily surrounded by an invisible region of spacetime, i.e.
has a black hole formed? The singularity theorems do not imply so. The singularity
may or may not be visible to a far away observer. If the singularity is invisible to a far
away observer, we say the star has ended as a black hole. If it is visible, we say the
star has ended as a naked singularity. We need to have a better understanding of
general relativity in order to decide whether collapse always ends in a black hole or
whether naked singularities can sometimes form.
Given this situation, Penrose was led to ask (Penrose 1969) whether there might
exist a cosmic censor who forbids the existence of naked singularities, 'clothing each
one of them with a horizon’? Later, this led to the cosmic censorship hypothesis,
which in broad physical terms states that the generic singularities arising in the gravitational
collapse of physically reasonable matter are not naked. Till today, this
hypothesis remains unproven in general relativity, neither is it clear that the hypothesis
holds true in the theory. What is of course true is that the hypothesis forms the
working basis for all of black hole physics and astrophysics. If cosmic censorship
were to not hold, then some of the very massive stars will end as black holes, while
others could end as naked singularities. As we will argue in section 3, these two kinds
of objects have very different observational properties.
There are various very important reasons for investigating whether or not cosmic
censorship holds in classical general relativity. As we have mentioned above, the
hypothesis is vital for black hole astrophysics. Unfortunately this fact is rarely
appreciated by the astrophysics community. The hypothesis is also necessary for the
proof of the black hole area theorem. It is not clear what the status of this theorem
will be if the hypothesis were to not hold. If naked singularities do occur in classical
relativity, they represent a breakdown of predictability, because one could not predict
the evolution of spacetime beyond a naked singularity. Such singularities would then
provide pointers towards a modification of classical general relativity, so that a
suitable form of predictability is restored in the modified theory. Further, naked
singularities might be observable in nature, if they are allowed by general relativity.
Undoubtedly then, it is important to find out if the censorship hypothesis is valid.
We wish to make two further remarks. Firstly, while a great deal is known about the
properties of stationary black holes, we know very little about the process of black
hole formation. In fact we know as little about the formation of black holes as we do
about the formation of naked singularities. Secondly, it has sometimes been remarked
that a theory of quantum gravity is likely to get rid of the singularities of classical
general relativity, irrespective of whether these singularities are naked or covered.
Why then does it eventually matter whether or not cosmic censorship holds? The
answer to this legitimate objection is the following. A quantum gravity theory is
expected to smear out a classical singularity and replace it by a region of very high,
albeit finite, curvature. If the classical singularity is hidden behind a horizon (i.e. is a
black hole), this quantum smeared region remains invisible to an external observer.
However, if the classical singularity is naked, the smeared region of very high
curvature will be visible to far away observers, and the physical processes taking place
near this smeared region will be significantly different from those taking place outside
the horizon of ordinary astrophysical black holes. Hence, from such an experimental
standpoint, quantum gravity has little bearing on the question of cosmic censorship.
To put it differently, quantum gravity is not expected to restore the event horizon, if
the horizon is absent in the classical theory.
Since a theorem proving or disproving the hypothesis has not been found, attention
has shifted to studying model examples of gravitational collapse, to find out whether
the collapse ends in a black hole or a naked singularity. While specialised examples
such as have been studied are nowhere near a general proof, they are really all that we
have to go by, as of now. However, there does seem to be an underlying pattern in the
results that have been found in these examples, which gives some indication of the
general picture. It is interesting that all models studied to date admit both black hole
and naked singularity solutions, depending on the choice of initial data. In the next
section, we give a summary of what has been learnt from these examples and what
they probably tell us about cosmic censorship. In the third section we will address the
question of whether naked singularities might occur in nature, and if so, what they
would look like to an observer.