The post is divided into two parts. The first part deals with the gender citation gap in Einstein studies and history and philosophy of general relativity. The second part outlines my comments on the paper that does not cite and discusses my work.

**Gender Citation Gap in Einstein Studies **

The value of an academic paper is often determined by the number of times other scholars mention that paper in their own papers. In fact, men get cited more than women. See here.

The other day I saw this tweet dealing with the survival of the “fittest” (i.e. white men):

Pretty soon it became clear to me that the good ole boys club in my field (Einstein studies etc.) neither cited nor discussed my books and papers. Yeah, the good ole boys still do not cite and discuss my papers and books. I wonder whether they cite Muslim scholars and non-white scholars?

The Gray test is the propensity for not citing and mentioning women and non-white scholars. So when we talk about white males not citing us, people say silence is golden. To be a woman in the academy you have to be silent and accept that men ignore your existence and that they have a propensity to cite and mention other white men. I wish I was making a mountain out of a molehill but unfortunately, I’m not.

I’m really tired and I want to let go of the dream that I will be an academic for the rest of my life. The watershed moment for a woman scholar comes when she sees this. Three male scholars published a paper on gravitational waves a month ago in *Nature* (which has the highest impact factor):

In this paper, Blum, A., Lalli, R. and Renn J (2018). “Gravitational waves and the long relativity revolution.” *Nature Astronomy* 2, 534-543, the authors write (on page 535):

“Einstein never published on the problem of gravitational waves again and most probably maintained the view that one could obtain plane gravitational waves only through the linearized equations.^{14 }”

Note 14 sends the reader to the following reference: A. Einstein, *The Meaning of Relativity*, 1953:

It makes my skin crawl to read this because a year ago, I wrote an email to one of the authors of this paper, Jürgen Renn, in which I told him that Einstein’s mathematical derivation of gravitational waves from 1916 and 1918 (that plane gravitational waves are obtained from the linearized Einstein’s field equations) has a central role in Einstein’s book, *The Meaning of Relativity*. Here is the text straight from the horse’s mouth:

This is the email:

Dear Jürgen,

I have seen in google the preface or introduction of your book with Gutfreund: “The Formative Years….”. In this book you have written the following in the introduction (attached):

“Chapter 6 addresses one of the key themes of modern general relativity: gravitational waves. […]. This is the only major topic debated during the formative years that has no trace in *The Meaning of Relativity*. Had we restricted our commentaries to the contents of Einstein’s book, there would be no reason to mention gravitational waves; […]”.

*The Meaning of Relativity*of 1922 and

__gravitational waves do have trace in__. Actually, the mathematical derivation given in the gravitational waves paper of 1918

*The Meaning of Relativity*__has a central role__in

*The Meaning of Relativity*of 1922 (the first printed book and also in later versions, even in the fifth one). I have demonstrated it in a book on Einstein which I have published lately. According to the printed version, it appears that Einstein’s interest in this topic had not faded away completely by the time he delivered the Princeton lectures.

I will explain it briefly: in 1916 Einstein made a mistake and he rejected de Sitter’s metric (see attached image 2). Subsequently, in 1918 Einstein accepted de Sitter’s metric and in *The Meaning of Relativity* of 1922, he reproduced the mathematical derivation he had given in his gravitational waves paper of 1918 (see attached image which includes only part of the derivation 1 and 2). The 1918 gravitational-waves-paper derivation and de Sitter’s metric have a central role in this book and using the latter and Huygens principle Einstein obtained the deflection of light and several other predictions he had already obtained in his review article of 1916 by following a different path.

Kind regards,

Gali

Wendy Laura Belcher, please note that Jürgen Renn did not pass the Gray test because he did not mention my name in the above paper. I don’t think people in my field care about your Gray test. I’m getting gray hair from these men not passing the Gray test. I put my foot down about significant matters and the Gray test **is** a significant matter. I want to scream at the top of my lungs but I know it won’t even wake the dead. I could not mention this incidence before for ethical reasons. My hands were tied. Actually, I was between the rock and the hard place because I was an r. How would you operate in this situation? The golden rule is: men can come and sweep you off. Therefore, if I am not for myself, who will be for me? Anyway, people should learn that the truth always comes out.

**My General Comments on The Paper:**

The linearized Einstein’s field equations (where we ignore all nonlinear contributions) are valid for weak gravitational fields. The metric is described as the Minkowski flat space-time, plus some small perturbation. The perturbation of the metric can propagate

as a plane gravitational wave in the vacuum. In 1916 and 1918, Einstein demonstrated that within the linearized theory the weak-field (transverse) gravitational waves carry energy. He then found a formula called the quadrupole formula that describes the rate of energy loss due to the emission of gravitational waves from a binary system. Far from the binary sources of gravitational radiation, the gravitational field is very weak. Thus, solutions from the linearized theory should coincide with solutions from the full non-linearized theory.

In an analogy to electrodynamics where accelerated charges emit electromagnetic waves, Einstein concluded that gravitational waves propagate at the speed of light and that plane gravitational waves travel with the velocity of light *c* in the Minkowski flat space-time.

In 1936 Einstein and his assistant Nathan Rosen believed that in the full non-linearized theory exact gravitational waves could not be described without introducing singularities into the components of the metric describing the wave. However, Howard Percy Robertson suggested to Einstein a transformation from space-time, suitable for representing plane gravitational waves, to cylindrical coordinates. The problematic singularity was then located at the origin of the cylindrical axis and the material source of the cylindrical waves at the origin represented the singularity. Einstein and Rosen were, therefore, able to describe exact cylindrical gravitational waves.

In 1937 Rosen came to the conclusion that there were no exact plane-waves. However, in the 1950s Hermann Bondi and Felix Pirani showed: “Unfortunately, plane gravitational waves do not exhibit their planeness in so clear a way as plane electromagnetic waves do, and the published plane-wave solutions have received some criticism. We have therefore thought it necessary to discuss plane-wave metrics in detail in this paper, and to investigate their physical properties more thoroughly than hitherto”.

They thus defined an exact plane gravitational wave in the full nonlinear theory and concluded that plane gravitational waves carry energy (this is a simplified explanation).

Authors of the paper:

argue (page 539):

And the nitty-gritty of the paper (page 541):

And:

However, it seems to me that the shoe does not fit because the gravitational waves detected by the LIGO team were weak-field gravitational waves. These gravitational waves were so weak that they were treated as if they were gravitational plane waves from Einstein’s 1918 linearized theory (see the paper, The Mathematical Theory of Gravitational Waves by several authors). Practically, therefore, LIGO verified Einstein’s prediction of 1918.