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I know mass bends the space around it and I also remember matter can be converted into energy and vice versa, so my question is: can energy interact with space in a similar fashion as matter does?

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Yes, the source of the gravitational field in general relativity is the stress-energy tensor The $00$ component is the total energy density

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    $\begingroup$ Can you provide a layman explanation of what is stress energy tensor, I tried searching however they are mostly written in jargon thanks. $\endgroup$
    – user6760
    Mar 16 '15 at 7:31
  • $\begingroup$ Since the word tensor in tbe name already takes it out of the layman realm, I don't think so. But someone may have a good heuristic. $\endgroup$ Mar 16 '15 at 9:27
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    $\begingroup$ @user6760: The stress-energy tensor is simply a set of 16 numbers that describe the various forms of energies in space, whether it be in the form of matter, flux of matter, shear stress, pressure, etc. All give rise to a change in the space(time) in which this energy is distributed. $\endgroup$
    – pela
    Mar 16 '15 at 11:27

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