This is not mainstream physics. There are some people who (without having a stated theory that I know of) insist that Gravity, Electricity, and Magnetism are related. Some point to symmetry in Maxwell's Equations as a potential indication of this (intuitive) connection. Is it possible that there are "Maxwell-like" equations that relate Electricity and Magnetism directly to Gravity? All forms of electromagnetic energy do interact with gravity. Are there any physicists who are working on this sort of theory?
I know two (non-mainstream) distinct ways.
A particular physics viewpoint that 'is not mainstream' do not cast in itself a ban, at least it should not be so. To a physicist minded person there are no taboos. To be mainstream means that, in the present, the main focus of the mindforce is concentrated in the exploration of certain labyrinths that once were hidden behind a closed door. Other doors were closed without further exploration and a sign was placed at the entrance: Dead End. Some solitary minds pursue the difficult job of digging other labyrints. If they succeed they will be our heros. The only quality that is required is honesty, IMO, as is posted at the entrance of this site.
from the Discussion section:
Linked with this paper Polarizable vacuum analysis of electric and magnetic fields by Xing-Hao Ye, 2009
The other approach that I'm aware is explored in Douglas Pinnow book 'Our Resonant Universe' it follows after the steps of Kaluza-Klein, Goedecke and Haus (and Maxwell ;-) and ...
You can have a glimpse of the model and explore further starting from here.
I'm used to see two arguments against the possibility of unification of EM and gravity: