The Yilmaz theory of gravitation is an attempt by Huseyin Yilmaz (1924–2013; Turkish: Hüseyin Yılmaz) and his coworkers to formulate a classical field theory of gravitation which is similar to general relativity in weak-field conditions, but in which event horizons cannot appear.
Yilmaz's work has been criticized on the grounds that: It is well known that attempts to quantize general relativity along the same lines which lead from Maxwell's classical field theory of electromagnetism to quantum electrodynamics fail, and that it has proven very difficult to construct a theory of quantum gravity which goes over to general relativity in an appropriate limit.
However Yilmaz has claimed that his theory is "compatible with quantum mechanics".
In his theory, Yilmaz wishes to retain the left hand side of the Einstein field equation (namely the Einstein tensor, which is well-defined for any Lorentzian manifold, independent of general relativity) but to modify the right hand side, the stress–energy tensor, by adding a kind of gravitational contribution, namely the scalar field.
According to Yilmaz's critics, this additional term is not well-defined, and cannot be made well defined due to issues with covariance.