# Black Holes

Indirectly, we have been making reference to the idea of a black hole through the basic models used to describe the effects of general relativity. However, we have not really made any attempt to justify the thinking that lies behind this concept. So let us ask the most obvious question:

*What is a black hole? *

In 1783, an English geologist John Michell suggested that it would
be theoretically possible for gravity to be so strong that nothing,
not even light, could escape it pull. However, to generate the necessary
gravitational field, an object would have to be unimaginably dense.
At the time, the necessary conditions for what were initially called
‘*dark stars’* seemed physically impossible. Although the idea
was published by the French mathematician and philosopher, Pierre-Simon
Laplace, in two successive editions of an astronomy guide, it was eventually
dropped from the third edition. However, in 1916, the concept was revived
when the German astrophysicist Karl Schwarzschild computed the gravitational
fields of a star, using Einstein's new field equations. The solution
reduced the complexity of the field equations based on the assumption
that the gravitational object was perfectly spherical, uncharged and
non-rotating. His calculations then yielded a solution that seems to
suggest what has become known as a *‘singularity’*. While scientists
theorized that a singularity could lie at the centre of a black hole,
the term ‘*black hole’* was not introduced until the 1971 and normally
attributed to the physicist John Wheeler.

The `*Schwarzschild metric*`
is essentially a generalization of the geometric and causal structure
of spacetime around a gravitational body. In general terms, this metric
defines a measure between 2 points in spacetime that accounts for the
curvature caused by gravity. The coordinates used by the metric can
generally be thought of in terms of spherical coordinates with an extra
time coordinate [t]. In many examples, the complexity of the spatial
coordinates can be reduced to the radial distance [r] from the singularity;
although the practical problem of how the
*coordinate radius [r]* is measured needs to be considered.
However, when [r] becomes increasingly small, the metric starts to suggest
some very puzzling results, which subsequently led to the definition
of the event horizon, which implies that the curvature of spacetime
would become infinite. Equally puzzling is the region within the event
horizon, which suggests that anything, including light, would be obliged
to fall towards the singularity and ultimately be crushed as the tidal
forces grow without limit. As such, this region becomes effectively
isolated from the rest of the universe, although the Gullstrand-Painlevé
coordinates suggest that there is nothing intrinsically wrong with the
curvature of spacetime in that region. This region is defined by its
event horizon, because any event, which takes place within this region,
is forever hidden to anyone outside the event horizon. The Schwarzschild
metric allows the radius of the event horizon, from the singularity,
for a given mass [M] to be calculated. However, initially, nobody worried
too much about these implications because there was, at that time, no
‘*real’* object thought to be dense enough to have a Schwarzschild
radius [Rs] that existed outside the radius occupied by its mass [M].
As a consequence, black holes were not really taken serious until 1939,
when Oppenheimer and Snyder considered the possibility that stars, a
few times more massive than the sun, might collapse under the force
of gravity during the end-stage of their life cycle. This process will
be discussed further, but for now, the assumption being followed is
that once a certain stage is reached, there is no known process that
can prevent the collapse of matter towards the singularity.

As such, a black hole might be described as a very simple object
having only three properties: mass, spin and electrical charge; although
due to the way black holes are thought to form, their electrical charge
may be zero. It is highlighted that the nature of energy-matter
within a black hole is essential unknown, partly because it is hidden
from the exterior universe, and partly because the matter would, in
theory, continue to collapse until it has infinite density and zero
volume. However, while mathematics of relativity might be capable of
defining a point singularity, it contradicts another accepted axiom
of science, i.e. quantum physics, and to-date the primary evidence is
still based on the indirect observation that some very small volumes
of space have incredibly high gravitational fields. However, this has
not prevented astronomers from forwarding many objects they think to
be black holes. The evidence typically being based on deduction relating
to the gravitational effects on other objects, which may also emit X-rays,
assumed to be generated by the phenomenal acceleration of in-falling
matter. However, it should be noted that this initial description of
a black holes is entirely based on general relativity and does not include
the probable effects of quantum mechanics, or even the role of
electromagnetism is space - see
*Plasma Model*. Therefore, almost everything
written about black holes in this discussion should be considered as
speculation, albeit speculation supported by generally accepted mathematical
conjecture. So while the existence of black holes is now often taken
for granted, it is still important to understand where the limits of
inference should be applied in this entire discussion.