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To my understanding, the curvature of spacetime is determined by the stress-energy tensor. I was wondering if we could calculate some of those components using radiation.

Is it possible that objects that possess immense electromagnetic radiation, for example, will follow with a strong gravitational pull? Does radiation occupy physical space?

Just had a thought experiment where I visualize spacetime like water that engulfs any solid object and doesn't go through it. But in my visualization, the actual spacetime didn't touch the solid object since the solid object occupies more space than its physicality. It engulfs the radiation and interacts with it. Just thoughts :).

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In general relativity, any source of energy/momentum/pressure will affect the curvature of spacetime. A well-known toy example for this is the Reissner-Nordström metric, which models a black hole with a mass and an electric charge; the resulting electric field has enough energy, pressure, and so forth to affect the curvature of spacetime.

As another example, in the early universe (shortly after the Big Bang) the stress-energy tensor was dominated by the effects of "radiation". There's a bit of a subtlety here because in a cosmological sense "radiation" means any particles that travel at or near the speed of light, including neutrinos and very-high-energy massive particles like electrons or protons. But at least for some portion of the Universe's early evolution, a substantial fraction of this "radiation" was in fact electromagnetic radiation; and a Universe dominated by radiation expands differently from a Universe dominated by "cold" matter (either conventional or "dark") or by dark energy.

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  • $\begingroup$ I am just wondering about the collision of the background/spacetime(cold) with the oscillating electromagnetic field(hot) which should result in an event maybe gravitational waves. Why can't we claim that the curve of spacetime is the emergence of spacetime interacting with an electromagnetic field and more like space is occupied with radiation? If we go into quantum real and ask the question what is the actual interaction of object A in environment B and maybe the result is actually nothing special, we test the same theory in a large finite number of interacting fields that become dense. $\endgroup$
    – Ray Luxembourg
    Commented Jun 29, 2023 at 14:21
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I didn't understand your thought experiment, otherwise yes, radiation has a gravitational pull.

Is it possible that objects that possess immense electromagnetic radiation, for example, will follow with a strong gravitational pull? 

Yes, radiation is part of the energy momentum tensor for the EM field and thus it enters the Einstein equations, affecting space time curvature. You can also create, in theory, black holes only using light if you concentrate enough of it in a point, see Kugelblitz

Does radiation occupy physical space? Yes it does. You can send a radiation pulse and the pulse will have a certain dimension, occupying space. Also laser light has a definite dimensionality and the beam has a certain radius depending on you laser.

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  • $\begingroup$ I am just wondering about the collision of the background/spacetime(cold) with the oscillating electromagnetic field(hot) which should result in an event maybe gravitational waves. Why can't we claim that the curve of spacetime is the emergence of spacetime interacting with an electromagnetic field and more like space is occupied with radiation? If we go into quantum real and ask the question what is the actual interaction of object A in environment B and maybe the result is actually nothing special, we test the same theory in a large finite number of interacting fields that become dense. $\endgroup$
    – Ray Luxembourg
    Commented Jun 29, 2023 at 14:20
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    $\begingroup$ "The collision of cold spacetime with hot radiation" has literally no meaning. Spacetime has no temperature in GR and do not collide with radiation. Radiation is embedded into the spacetime structure. Spacetime curvature emerges from interactions with radiation but also with every other form of energy density. The last part about quantum mechanics i didn't understand what you meant $\endgroup$
    – LolloBoldo
    Commented Jun 29, 2023 at 16:34
  • $\begingroup$ Spacetime has no temperature - this is miss leading statement that can be understood in different ways. Energy lives inside spacetime and energy has a temperature difference between nothing and something. To say that there is absolutely no interaction with the background is wrong. GR is not a constant and it is there until another Einstein comes into our world and changes our paradigm with big respect of course. It is most likely that these interactions are taken into account by different medium or variable that includes this. $\endgroup$
    – Ray Luxembourg
    Commented Jul 13, 2023 at 13:01

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