I want to know if in general relativity we calculate the curvature of space time taking into account the energy due to an electromagnetic field.
Yes-just solve Einstein's equations with the energy-momentum tensor of the electromagnetic field as RHS, along with Maxwell's equations, of course.
In general relativity the gravitational attraction exists between masses as well as the radiation (electromagnetic) energy. This is why the light ray deflects around the sun. Then there is the gravitational redshift phenomenon which ulters the frequency of the light ray and therefore the period of the wave. Then you have the time dilation phenomenon. But in all these calculations, gravitational constant G is used and not the Coulomb constant. So the effect on the curvature of the space time is very small.
Recently I proposed the following article in which I have argued that Coulomb constant k is capable of curving the space time just like the gravitational constant G. This kind of curvature of space time occur near the nucleus of an atom.
https://www.researchgate.net/publication/319291737_Hydrogen_spectra_using_Einstein%27s_field_equations
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Yes-just solve Einstein's equations with the energy-momentum tensor of the electromagnetic field as RHS, along with Maxwell's equations, of course.
I think that it is mass-energy that distorts space-time so a first approximation is just to use the effect of the mass density equivalent to the energy density of the electromagnetic wave.
Einstein's equation takes into account the energy-momentum tensor regardless of its origin. So, yes, you have to consider energy-momentum tensor of EM field while solving Einstein's field equation.
Dear E.Arrieta,
"Does the energy of an electromagnetic field curves space-time"
I do not agree that the energy of an electromagnetic field curves the space-time.. The main reason is that Einstein himself did not agree with this.
In fact, the electromagnetic field should be incorporated in a minkowski structure of an accelerating inertial frame where the amount of acceleration is equals to the amount of accleration of a chared particle.
Regards
Ramesh Chandra
Yes in as in Newtonian gravity mass (scalar) is considered as source and gravitational field (vector) as effect; in General relativity the source is energy-momentum (tensor) and effect is space time curvature (which can be quantified by Riemann curvature tensor, Ricci curvature tensor, Ricci scalar ...). So, energy of electromagnetic field curves space time. But how to measure such a curvature of space-time, that is another interesting question.
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