From Osher Doctorow

Nikodem J. Poplawski of Indiana U. in "A unified, purely affine theory
of gravitation and electromagnetism," arXiv: 0705.0351 v1 [gr-qc] 2
May 2007, 5 pages (2 columns per page) shows that Maxwell's equations
w sources arise naturally in the unified framework and that the
Einstein and Lorentz equations arise if mass has electromagnetic
origin.

Poplawski has 19 papers in arXiv (if only 14 show up, try to select
Physics, Dynamics, Mathematics, although all the papers are
technically in the Physics section according to the labels) from 2005
through 2007.

The paper is also interesting for comparing 3 types of theories:

1) Purely affine (Einstein-Eddington) formulation of gravitation
2) Metric-affine (Palatini) formulation of gravitation
3) Purely metric (Einstein-Hilbert) formulation of gravitation

All 3 are dynamically equivalent if we restrict the cases (2) and (3)
to Lagrangians that are linear in the cuvature tensor. The 3
respectively derive the field equations by:

4) varying action with respect to connection
5) varying action with respect to both metric and connection regarded
as independent
6) varying action with respect to metric

Osher Doctorow