I have a question, can we make space curved with only light? I'd be happy if you could help me edit the tags.
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3$\begingroup$ Related. $\endgroup$– J.G.Commented Oct 16, 2022 at 7:13
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1$\begingroup$ Related: physics.stackexchange.com/q/22876/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Oct 16, 2022 at 11:48
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$\begingroup$ See this answer for a universe filled only with photons physics.stackexchange.com/a/570320/226902 $\endgroup$– QuilloCommented Oct 17, 2022 at 18:38
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1 Answer
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No, it is not possible. Warped spacetime is caused by physical objects with rest mass. The stress-energy tensor ${\rm{T}}_{\mu}^{\nu}$ for electromagnetc waves is traceless, i.e. it describes objects with zero rest mass. From Einstein field equation it follows that the trace of Ricci curvature, $\rm{R}\equiv \rm{R}_{\mu}^{\mu}$, is then zero: \begin{equation}\label{einstein} {\rm{R}}_{\mu}^{~\nu}-\frac{1}{2}{\rm{R}}_{\lambda}^{~\lambda}~\delta_{\mu}^{\nu}=\kappa~{\rm{T}}_{\mu}^{~\nu},~~~\rm{R}-2~\rm{R}=\kappa~{\rm{T}}_{\mu}^{~\mu}=0. \end{equation} As in the case of Schwarzschlid vacuum solution it does not mean that spacetime is flat. The light is excitation of electromagnetic field which in turn is caused by charged particles possessing rest mass (source of warping).
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After reading some comments I have to admit that my answer could be controversial or even incorrect. Most physicists would say: ‘anything’ that has nonzero stress-energy bends spacetime. This includes light. However, the stress-energy tensor is GR is not simply a source of gravity as the charges and currents are in EM theory. It describes merely matter properties (energy density, stresses and their fluxes) that affect spacetime and vice versa, it represents a kind of interface between them, see Dennis Lehmkuhl General Relativity as a Hybrid theory: The Genesis of Einstein's work on the problem of motion. Furthermore, although light has momentum and energy it has no rest mass. In contrary to matter light does not take up space and is non-localizable. Only if absorbed or emitted the light quanta show their particles properties. In-between they have no defined trajectory. An atom that emits light diminish its rest mass by $\Delta m=h\nu/c^2$. Due to Einstein field equations this process has to be accompanied by emission of gravitational wave at the same time. That is what I understand under light warping spacetime.
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6$\begingroup$ This answer is incorrect. The Ricci scalar is not the only relevant parameter for determining curvature. (See en.wikipedia.org/wiki/Curvature_invariant_(general_relativity) )There are many examples of curved spacetime from light or other massless radiation, for example en.wikipedia.org/wiki/Pp-wave_spacetime $\endgroup$– DaleCommented Oct 16, 2022 at 15:11
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1$\begingroup$ That is new for me. I will delete my answer but I would like you to leave your comment or just write the correct answer, if possible. $\endgroup$– JanGCommented Oct 16, 2022 at 16:34
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$\begingroup$ One comment more: I did not assert that Ricci scalar zero means no warped spacetime. The link to Pp-wave spacetime as example for curved spacetime from massless radiation is for me not quite instructive. The cornerstone of GR is the equivalence principle saying that gravitational and inertial mass are equal. How to formulate it in regard to massless entities? $\endgroup$– JanGCommented Oct 16, 2022 at 17:51
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1$\begingroup$ @Dale your short answer to the question under consideration is then yes. I will try to understand it, especially the examples, thanks! $\endgroup$– JanGCommented Oct 17, 2022 at 18:06
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1$\begingroup$ @Lemon a Kugelblitz of 20 cm diameter being a black hole would have the mass 2.2466e+25 kg or equivalently the energy 2.2466e+41 Joule. $\endgroup$– JanGCommented Oct 19, 2022 at 15:38