Black Holes

1Indirectly, 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.