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:

• his proposed field equation is ill-defined
• event horizons can occur in weak field situations according to the general theory of relativity, in the case of a supermassive black hole
• the theory is consistent only with either a completely empty universe or a negative energy vacuum^[1]

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". He suggests that it might be an alternative to superstring theory.

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. According to Yilmaz's critics, this additional term is not well-defined, and cannot be made well defined.^{[citation needed]}

No astronomers have tested his ideas, although some have tested competitors of general relativity; see Category:Tests of general relativity.

• Yilmaz, H. (1992). "Toward a field theory of gravitation". Nuovo Cimento B. 107 (8): 941–960. Bibcode:1992NCimB.107..941Y. doi:10.1007/BF02899296. S2CID 120702676.
• Misner, C. W. (1999). "Yilmaz Cancels Newton". Nuovo Cimento B. 114 (9): 1079–1085. arXiv:gr-qc/9504050. Bibcode:1999NCimB.114.1079M. In this paper, Charles Misner argues that Yilmaz's field equation is ill-defined.
• Alley, C.O.; Aschan, P. K.; Yilmaz, H. (1995). "Refutation of C. W. Misner's claims in his article "Yilmaz Cancels Newton"". arXiv:gr-qc/9506082.
• Fackerell, E. D. (2006). "Remarks on the Yilmaz and Alley papers". School of Mathematics and Statistics F07, University of Sydney. Archived from the original on 2004-09-20. In this preprint, Edward Fackerell criticizes several claims by Yilmaz concerning gtr
• Alley, C. O.; Yilmaz, H. (2000). "Response to Fackerell's Article". arXiv:gr-qc/0008040.
• Misner, C.; Thorne, K. S.; Wheeler, J. A. (1973). Gravitation. W. H. Freeman. ISBN 0-7167-0344-0. See section 20.4 for nonlocal nature of gravitational field energy, and all of chapter 20 for relation between integration, Bianchi identities, and 'conservation laws' in curved spacetimes.

• One page in the websiteRelativity on the World Wide Web (archived link) lists some apparent misstatements by Yilmaz concerning the general theory of relativity, similar to those discussed by Fackerell.