Story about machines generating energy with parallel universes, endangering ours

I suppose I read this story in a book in the nineties but I have no memory of actually reading it or the cover, I just remember a lot of the plot.

Scientists find out they are being contacted by the inhabitants of some other universe. I believe this happens by one element being exchanged with another (I remember wolfram was involved because I had never heard that word before) and messages somehow added. This leads to earth building some sort of machine together with the other universe (it is the description of this machine that I really would like to read again) that somehow generates energy on both sides. Only later do the people on earth realize, that it also slowly changes some of natures constants, threatening, I believe, the sun.

The book also had detailed descriptions of everyday life in both universes. I remember some sport played in the lower gravity of the moon and the aliens having three distinctive sexes.

Answer

Almost certainly Asimov's The Gods Themselves.

The plot description on wikipedia gives most of the detail.

The book is in 3 parts.

Part 1, "Against Stupidity...", deals with the discovery:

Radiochemist Frederick Hallam discovers that a container's contents have been altered. He initially accuses a colleague of tampering with his sample, but eventually finds that the sample, originally tungsten, has been transformed into plutonium 186—an isotope that cannot occur naturally in our universe. As this is investigated, Hallam gets the credit for suggesting that the matter has been exchanged by beings in a parallel universe; this leads to the development of a cheap, clean, and apparently endless source of energy: the "Electron Pump"

Part 2, "...The Gods Themselves...", deals with the aliens:

The inhabitants are divided into dominant "hard ones" and subject "soft ones". The latter have three sexes with fixed roles for each sex:

Part 3, "...Contend In Vain?", is set on the moon:

Lunar society is diverging radically from that of Earth. The lower gravity has produced people with a very different physique. Their food supply is manufactured and distasteful to inhabitants of Earth. They enjoy low-gravity sports that would be impossible on Earth, such as an acrobatic game like "tag" performed in a huge cylinder.