Mistakes in Mathematical Formalism of the Stephen Hawking's Doctoral Thesis

We present to the international scientific community a series of misprint and some mathematical mistake found in Stephen Hawking's doctoral thesis. These errors have been found as a result of my translation work into Spanish of the aforementioned thesis. As it is of public knowledge, the thesis of Hawking has been released to the public by the University of Cambridge and we have used it to translate it into Spanish and simultaneously edit all its equations in LATEX format, which were written by hand by its author during of Cambridge whose names do not appear in the thesis. As director of the thesis was the astrophysicist Dr. D. W. Sciama1.


Introduction
We present to the international scientific community a series of misprint and some mathematical mistake found in Stephen Hawking's doctoral thesis.These errors have been found as a result of my translation work into Spanish of the aforementioned thesis.As it is of public knowledge, the thesis of Hawking has been released to the public by the University of Cambridge and we have used it to translate it into Spanish and simultaneously edit all its equations in LATEX format, which were written by hand by its author during of Cambridge whose names do not appear in the thesis.As director of the thesis was the astrophysicist Dr. D. W. Sciama1 .
As a result of this work and to my surprise, we have been able to find:

•
Several typographical errors that, however, can be seen as spelling mistakes • Some errors associated with the mathematical formalism used by Hawking in his doctoral thesis.

Spelling Mistakes
Hawking's thesis was typed and we understand that this work was carried out by his first wife.Table 1 summarizes the errata that were identified in this sense and that correspond basically to spelling mistakes.

Pg 17
In the Hoyle-Narlikar field equations, Hawking's original presents an error in this equation, namely the term 2 (m (a)  ;i m (b)   ;k ) appears without closing its second parenthesis.In fact, LATEX would not allow to write it that way (Figure 1).

Pg 31
Hawking writes Rab=R p o bp instead of: Rab=R p a bp is doing an operation of contraction of indices and instead of a a place what looks like a o or a zero (Figure 3).

Pg 32
Hawking writes Clearly introduce a α where a a should go (Figure 4).

Pg 46
Hawking writes ha(,/q) rbs u r ∇ s and it is not concretely understood what kind of covariant or contravariant tensor operation it wants to express (Figure 5).

Pg 65
In equation 3.54 of the original an addition symbol is repeated twice: ( ) 6).

Mistakes in Mathematical Formalism of the Stephen Hawking's Doctoral Thesis
Horacio Useche Losada*

Pg 70
On page 70, equation 4.10, Hawking seems to assign an exponent to the last of the components in this group of equations but it is illegible and it is also a component that is annulled (Figure 7).

Pg 70
On page 70, Hawking writes the set of components as ψ (something)S where the word "something" denotes an illegible symbol that could be something like ψ √S , or similarly ψ +S , o ψ -S , which does not make much sense if the components are null (Figure 8).

Pg 76
Hawking writes: forgetting to close a parenthesis, note the (Figure 9).

Pg 96
Hawking says: \When the six parameters a, b, c, d are given... "but it is evident that there are only four parameters to which it refers (Figure 12).

Pg 120
Hawking seems to have forgotten here the symbol to insert, which we believe is σ but in its original, page 120, a blank space simply appears (Figure 13).
Because it is one of the most important contribution of Hawking to science, we hope that the University of Cambridge will correct these problems and publish a refined edition of this important scientific work [9][10][11][12][13][14][15][16][17][18].

Figure 1 :
Figure 1: Page 17, he did not close a parenthesis.

Figure 2 :
Figure 2: Page 28, again, he did not close a parenthesis.

Figure 9 :
Figure 9: Page 76, another parenthesis that does not close.

Figure 12 :
Figure 12: Page 96, wrong reference to number of parameters.

Figure 13 :
Figure 13: Page 120, forgot to quote a numeric variable value.

Table 1 :
Department of Applied Mathematics, Surcolombiana University in Neiva, Huila, Colombia Spelling mistakes in the Hawking's thesis.