2

I have a question, can we make space curved with only light? I'd be happy if you could help me edit the tags.

Qmechanic
  • 201,751
user365891
  • 43

1 Answers1

0

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).

Addendum

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.

JanG
  • 1,831
  • 6
    This answer is incorrect. The Ricci scalar is not the only relevant parameter for determining curvature. (See https://en.wikipedia.org/wiki/Curvature_invariant_(general_relativity) )There are many examples of curved spacetime from light or other massless radiation, for example https://en.wikipedia.org/wiki/Pp-wave_spacetime – Dale Oct 16 '22 at 15:11
  • 1
    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. – JanG Oct 16 '22 at 16:34
  • 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? – JanG Oct 16 '22 at 17:51
  • @JanGogolin well what do you mean by gravitational mass? Can you point to specific definition within GR framework for such a thing? The equivalence principle in that formulation is made within newtonian framework and what is meant is mostly that all bodies falls with the same acceleration no matter their constitution. It is not meant that inertial mass is source of gravity. – Umaxo Oct 16 '22 at 20:36
  • It is a common knowledge that relativistic bullets with a large kinetic energy and negligible mass don’t bend spacetime due to the Poincare Principle of Relativity or equivalently, because the contribution to the stress-energy tensor by the kinetic energy is exactly cancelled out by tine opposite contribution by the momentum (gravitomagnetism). Photons are ultimate relativistic bullets, so light viewed as a beam of photons does not bend spacetime. However, light as a classical wave contributes to the stress-energy tensor differently (as Dale pointed out). Only Quantum Gravity can resolve this. – safesphere Oct 16 '22 at 20:48
  • @Umaxo I did not tell that inertial mass is source of gravity but that it equals the gravitational mass. The last one is the mass $M$ staying in the expression for Schwarzschild radius $r_{S}=2GM/c^2$. Of course, you are right about original EP. Its modern formulation can be found in Nikola Paunkovic and Marko Vojinovic paper entitled ‘Equivalence Principle in Classical and Quantum Gravity’ (https://arxiv.org/abs/2210.00133v1). – JanG Oct 17 '22 at 15:07
  • @JanGogolin a new answer is not necessary. Both the G Smith and the user4552 answers to the duplicate question are valid. There are many spacetimes with massless classical radiation (e.g. light) that have non-zero curvature: pp wave spacetimes mentioned above, the Bonnor beam, Vaidya null dust solutions, Robinson-Trautman null dusts, etc. Regarding the equivalence principle, that is only a local principle. Globally, the corner stone is the Einstein Field Equation. The manifold structure guarantees that the equivalence principle holds for all of the above spacetimes – Dale Oct 17 '22 at 17:26
  • 1
    @Dale your short answer to the question under consideration is then yes. I will try to understand it, especially the examples, thanks! – JanG Oct 17 '22 at 18:06
  • but when I read the concept of Kugeblitz on Wikipedia, they define it as follows

    "In theoretical physics, kugelblitz (German for "lightning ball") is a concentration of heat, light (here emphatic) or radiation so intense that its energy forms the horizon. of events and got stuck there: according to general relativity and the mass-energy analogy.[1] More simply, a kugelblitz is a black hole formed from radiation instead of matter." Can it warp space?@JanGogolin

     – user365891 Oct 18 '22 at 14:47
  • @Lemon I am afraid they have written nonsense. To get black hole you have to compress your energy $E$ into a ball of Schwarzschild radius $r_{S}=2G/c^4 E$. – JanG Oct 19 '22 at 15:10
  • 1
    @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. – JanG Oct 19 '22 at 15:38