For fairly naive explanation, The big problem of treating gravity as EM is due to the variation of geometry of space time because of which there is no gauge fixing term for gravitational fields in general like we have in QED.

Further complications arise if we take string theory into the picture where gravitons (quanta of gravity waves ) are explicitly in the closed string spectrum whereas EM waves are basically flowing currents of open strings these EM waves carry the string charges that couple to something called Kalb Ramond field and end point of the strings are electrical charges coupled to EM waves aka Maxwell fields now if we try to go with same logic for closed string then the current flow is a loop as it has no D brane and it has no end point so interaction of gravitons is nothing like that of EM waves and we may have to think over the topological or geometrical changes.

Even further E fields lorentz transform to B but not gravitons.

One may treat gravitational potential as 5th component of EM potentia tensor but the 5th dimension is compactified in our universe as we all know so at the end we wouldn’t be able to observe the gravity wave flow contradicts the fact that we already have.

So in that sense gravity can’t be decomposed into 2 components like EM fields

Sydney Ernest Grimm with respect,

If gravity needed a medium or a field to propagate then how come we are able to study the influence of so call dark matter on expansion of universe even though EM waves don’t interact with the said dark matter?

And as far as I know yes gravity is not a fundamental field but is considered as an entropic force field as a massless object has more number of states with respect to its massless counterpart like for massless uni directional moving massless fermion we have 2 states but for massive fermions we have 3 states.

And yes the EM forces and gravity forces do superimpose but it doesn’t necessarily mean that gravity can be decomposed into E and B fields respectively.Or better yet we don’t have so called grandunification still so if gravity can be decomposed into E and M fields then where would be the problem?

And as you mentioned in your answer there is one vector field one scalar field and one topological field it can be shown via string Theory as follows

open string carries string charge interacting with background fields (Kalb Ramond field) and as these string charges are flowing along the string they flow towards D branes and on these D branes they assume the nature of maxwell field(vector field) a massless scalar field lies perpendicular to the plane of the D branes (scalar field) and it not necessary that only open strings exist there is a possibility of closed strings whose one of the first excited states are gravitons (quanta of gravity) the point I want to make that apart from tachyons the spectrum of closed strings states and open string states are never same so in that sense one cannot decompose gravity into EM waves rather closed strings have to decay into 2 open strings first and at that point the open string doesn‘t represent gravitons but polarized photons or some other particle in the open string spectrum (not necessarily photons)and end points of that string represent electric charges interacting with maxwell field and the maxwell field on D branes carry string charges which interact with the Kalb Ramond field.

Please do correct me if I m wrong somewhere.

Sydney Ernest Grimm thank you for your explanation,

I have been looking at the work of Kaluza and Klein and they did propose a theory where 5th dimensions in the metric gmn ie gm5 represent maxwell field and I have used the similar idea when I gave the answer at 1st to make a remark in a sense in which gravity could not be deco into EM waves your idea of matter concentration and free energy concentration is quite intriguing but as far as I have been able to realize I can combinly put matter and free energy in Tmn and use Einstein’s equation to solve it and then I don’t think that I need to consider matter and free energy concentration seperately and as we know Einstein’s equation is a Tensor equation so it must be true for a vector field and the topological field simultaneously as far I know

In fact I was reading an article were the inconsistency of eintein’s negligence of gravity in Tmn was treated as one of the major drawback of GR but I think that it is much like treating with virtual particles in QED where we integrate it out by summing or integrating over all momenta of virtual particle that appear in loop diagrams and then work in on shell criteria as virtual particle at the end get annhilated but the problem with gravity is it is always there and is working just like virtual particle fluctuations in GR which we want to remove and have a fine tuning in some sense.

In fact we do that in EFT were some degrees of freedom are integrated out due to their irrelevant scales and gravity feels just like that to me in GR sure there are EM ,vaccum fluctuations but gravity is no less of a devil that is why we do not have global energy conservation in GR and we are able to have predictions regarding geometry in GR or have solutions for linearized gravity but i don’t think any one has solved Einstein’s equation fully generalized and high precision but have rather local solutions (in general)using say birkoff’s theorem to make further predictions.

And bending of EM waves is due to gravity and as EM waves have energy in some Lorentz frame they are massive and hence they can interact via gravitation and

please help and explain how there are 33 dimensions in string theory I used normal ordering and concept of Lorentz invariance and I get 26 and I know there are 10 in super string theory

Thank you for such a wonderful discussion and response and Please do correct me if I m wrong somewhere.