The Singularity Problem, and The Universe

Black holes are arguably the most fascinating and mysterious objects in the known universe. Our fascination is heightened by the recent imaging, for the first time, of the event horizon of a galactic supermassive black hole. This was a monumental feat of ingenuity and engineering on the part of contemporary astronomers, mathematicians, computer programmers, and physicists. And it was, equally, a monumental achievement of the human mind, dating back to the work of Albert Einstein in the early days of the twentieth century. As first recognized by German physicist Karl Schwarzschild in 1916, Einstein’s general theory of relativity predicts the existence of a particularly strange phenomenon occurring inside the radius of any celestial object whose mass becomes equal to rc2/2G. It was soon apparent that an object satisfying the Schwarzschild metric should not allow anything, including light, to escape from within this “horizon” radius.


Singularity problem
Stranger still, it eventually became apparent that such an object had no obvious means of stabilizing itself at any given radius of gravitational collapse, no matter how small! Effectively, an empty black "hole" would be created inside the Schwarzschild radius, with the exception of an infinitely small and infinitely dense "singularity" at the hole's geometric center. This was a strange prediction of general relativity that even Einstein could not accept. After all, what could "infinitely small" and "infinitely dense" even mean?! Infinity may be an acceptable concept to a mathematician, but physicists tend to abhor the idea of real objects with infinite properties. Accordingly, we would prefer to invoke real or imagined principles of quantum physics in order to avoid the conundrum presented by an infinite singularity. This has become the primary inspiration for developing theories of quantum gravity collectively known as loop quantum gravity. It is also a primary motivation for the intrinsically beautiful, although somewhat abstract, hyperdimensional and mathematically complex collection of string theories. Unfortunately, there is not, as of yet, a fully coherent and provable theory of quantum gravity upon which we can hope to understand the inner workings of a black hole, to say nothing of the gravitational conditions at the inception of the universe. This singularity problem is just one of the many puzzling things about black holes and the very early universe, some of which are addressed in this book.

Universe
In the 1960s, English mathematical physicists Roger Penrose and Stephen Hawking cleverly extended the black hole singularity problem to our expanding universe. They proved that a backward time extrapolation of the expansion should inevitably lead to the same problem implied at the geometric center of a Schwarzschild black hole. Thus, allowing for the time symmetry of general relativity, the implication of their work [1][2][3] was that our universe has this feature, and perhaps others, in common with a nonrotating, electrically neutral, black hole. Whether the universe could be a time-reversed black hole-like object (sometimes referred to as a "white hole") has been a subject of vigorous debate over the last 50 years [4][5][6][7][8][9][10][11].
When one rearranges the Schwarzschild formula, it is readily apparent that the M/r ratio (the ratio of the gravitational mass to Schwarzschild's horizon radius) of an equilibrated, nonrotating, electrically neutral black hole must equal c 2 /2G. This ratio (approximately 6.73 × 10 26 kg/m in metric units) is effectively a constant of nature incorporating two of the most fundamental constants of nature, Maxwell's speed of light and Newton's gravitational constant. Furthermore, one could make a strong argument that this mathematical relationship is a reliable signature of a black hole or black hole-like object.
One of the features surprisingly in common between Schwarzschild black holes and the observable universe has been documented fairly recently and has been a subject of great interest to myself and others. A series of astronomical observations since the early 1990s [12][13][14][15] allow one to calculate a reasonably accurate M/r ratio value for the observable universe. If so inclined, the interested reader can skip the foundational references indicated and simply look up the relevant numbers on the Wikipedia link entitled "observable universe." The mass M of the observable universe is now estimated to be 1.5 × 10 53 kg, and the radius r of the observable universe is now estimated to be 4.4 × 10 26 m. One can readily see that this implies a current M/r ratio value for the observable universe of approximately 3.4 × 10 26 kg/m. Consequently, the M/r ratio values for an equilibrated Schwarzschild black hole and the expanding observable universe are of the same order of magnitude. One should let that sink in.

A useful model
The above calculation made from recently published observations was unavailable to an earlier generation of physicists. This new result, in combination with the timesymmetric properties of general relativity enshrined within Hawking's singularity theorem, provides an excellent starting point for exploring the heuristic cosmology model of the universe I present in this book. It is believed to be the first cosmology model of its kind, namely, that which solely incorporates in its assumptions reasonable speculations about black hole time reversal. Thus, Hawking's singularity theorem is the founding principle of this model which I call flat space cosmology.
So far, this model appears to be quite accurate with respect to correlations between its embedded predictions at any particular point in cosmic time and a variety of astronomical observations. It is my hope that the reader will begin with this chapter and be inspired to study the model further. The competing "concordance model" incorporating inflationary cosmology may not be the last word after all!

A sense of wonder
As the reader delves further into this book, it is also my hope that he or she will have a sense of wonder for how far we have come in understanding black holes and the rules governing the expansion of our universe. That so much of our universe is actually comprehensible was a wonder to even Albert Einstein. However, as the new ideas presented in this book clearly show, there are still many creative avenues for further exploration.

Author details
Eugene Terry Tatum Independent Researcher, Bowling Green, Kentucky, USA *Address all correspondence to: ett@twc.com © 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.