In a recent short post, I briefly discussed the fact that what is nowadays referred to as the Schwarzschild metric often identified as the black hole metric actually differed from the exact solution to Einstein’s equations published by Karl Schwarzschild in January 1916.

Indeed, the original Schwarzschild solution was devoid of singularity except at the origin of coordinates. This is in stark contrast with what we call the Schwarzschild metric today which contains a singularity (terms in the metric that blow up) at the famous Schwarzschild radius (which is not located at the “origin”) supposed to represent the event horizon of an object called a black hole.

This mismatch between the contemporary black hole metric named after Schwarzschild’s and the actual original metric published by Schwarzschild compelled me to query in my previous post if the latter would ever have come-up with the model of a black hole: a region of space where space-time swap their roles after having crossed a singularity of the metric.

To find the full metric generated by an extended massive body such as a star, Schwarzschild actually used two steps: in a first publication in January 1916 he found a static solution in an empty space surrounding a point mass at the origin. In a second publication in February 1916 he found a static solution inside a uniformly distributed mass in a sphere (as a side note, these publications were unaccessible to an English reading audience until the 1990s). The full solution is then obtained by “stitching” the two solutions in a specific way so as to ensure mathematical consistency.

The question is then the following: does the traditional model of static blackholes, as it is taught and told all over the world, do justice to the mathematical rigour geometers of the early 20th century such as Schwarzschild were displaying?

Some mathematicians and physicists think that no, current black hole theories lack mathematical rigour, which then completely undermines the metaphysics of such objects.

I have recently come across a series of two Youtube videos by a French physicist called Jean-Pierre Petit on the mathematics and history of black holes. The first video is 1h20min long and destined to a lay audience. The second video is targeting a more expert audience and aims at convincing them with good old mathematical equations and reasoning, it is 5h20min long.

Irrespective of whether I endorse the conclusions of Jean-Pierre Petit or not, his videos appeared to me as incredibly informative in the sense that I think that anyone taking an interest in the subject should be aware of the well documented historical and mathematical mishaps which have reportedly paved the development of black hole theory. If anything, a proponent of black hole models should be aware of these historical and mathematical critics to arm themselves with thoughtful counterarguments instead of brushing them off as heresy.

Because these videos are in French, I have undertaken the task of providing English subtitles for them. I found that not all parts of the scientific and colloquial terms used in French in the original videos allow for a perfect translation in English. But I do hope that my subtitles will capture the essence of it.

I have finished the subtitles for the 1st video of 1h20min in length during my Easter break (the 5h20min one is going to take much much longer to work on and will have to wait a bit). In the mean time the 1h20min can be watched below or directly on youtube. I hope you will enjoy :).

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