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In our universe, in order for a cloud of gas to collapse into a star it needs to release heat energy in the form of radiation, so that it can cool down enough to collapse into a star.

I read what Greg Egan said about the Riemannian Universe on his website https://www.gregegan.net/ORTHOGONAL/ORTHOGONAL.html and also read the Orthogonal series. Both discuss how the main difference between the Riemannian Universe and our universe is that there are four fundamentally similar dimensions instead of three space like dimensions and one time like dimension, and the minus sign in the equation for the spacetime interval is replaced by a plus sign.

In the Riemannian Universe photons would have rest mass and releasing photons would cause a body to heat up instead of cool down because kinetic energy is opposite of total energy, and releasing photons would lower the total energy of an object, and so increase the kinetic energy energy of the particles making up that object. I don't remember either the website or the book going into detail on how star formation would work in the Riemannian Universe and having a cloud of gas radiate away energy wouldn't work for getting it to collapse into a star as radiating would cause the gas to get hotter.

How might star formation work in the Universe described in the Orthogonal Series? Also what might cause stars to shine in this type of universe?

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    $\begingroup$ I'm not sure that you'll get an answer in line with the physics tag, on account of the universes being counterfactual. Just a suggestion, but you might want to swap that tag for the science-fantasy one. $\endgroup$ – Measure of despare. Jul 4 at 4:39
  • $\begingroup$ People interested in getting into the alternate physics of this universe might want to look at the series of pages starting at gregegan.net/ORTHOGONAL/00/PM.html (more links at the top of the page) $\endgroup$ – Hypnosifl Jul 4 at 4:57
  • $\begingroup$ I think it would be better if you could summarize the key aspects of this orthogonal physics in the question itself. $\endgroup$ – L.Dutch Jul 4 at 5:10
  • $\begingroup$ "releasing photons would lower the total energy of an object" is what happens in our world $\endgroup$ – L.Dutch Jul 4 at 6:37
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    $\begingroup$ L.Dutch I am aware that releasing photons also lowers the total energy of an object in our universe. However the implications of lowering the total energy of an object is different in our universe from the universe described in the orthogonal series as in our universe it makes an object cooler, while in the universe described in the orthogonal series it makes an object hotter. That's why I mentioned it. $\endgroup$ – Anders Gustafson Jul 4 at 14:48
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Well, for one thing, stars don't form in the Orthogonal universe. Stars and planets both are all primordial chunks of solid matter broken off of the "cosmic egg". Stars are just the ones that happen to have been set on fire--and the fact that that can happen to any planet is kinda the central driving conflict of the series!

However, if we want to imagine a. different universe with the same metric in which stars can condense from gas, there is really only one mechanism I can think of: gravothermal collapse and evaporative cooling. Basically, as particles interact gravitationally, they will develop a thermal velocity distribution. Because gravitationally bound systems have a negative heat capacity, if the cloud does not have a uniform temperature, it is possible to encounter an instability the hotter part of the cloud will transfer energy to the colder portion, becoming hotter and more compact in the process, until the colder portion completely disperses.

Additionally, given a thermal velocity distribution, some particles will happen to have a thermal velocity above escape velocity from the cloud, thus evaporating and cooling it. However, this takes an incredibly long time. You can get an idea of how long by noting that our has existed for insufficient time for dark matter to collapse into star-sized blobs through evaporative cooling. It can, however, induce the initial temperature discrepancy between surface and core regions to trigger a gravothermal collapse.

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