The Yilmaz theory of gravitation is an attempt by Huseyin Yilmaz (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 various grounds, including the claims 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
Yilmaz disputes these criticisms. He claims that his critics have misunderstood him, but it has been suggested that his papers are too murky in crucial places to admit a single clear interpretation.
It is well known that naive 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. Yilmaz has claimed that, in contrast, his theory is in some sense 'compatible with quantum mechanics'. He suggests that it might be an alternative to superstring theory.
To understand one of the most basic criticisms of Yilmaz's work, one needs to be familiar with
- the statement of the Einstein field equation,
- the distinction between coordinate dependent and coordinate independent quantities,
- facts concerning integration in curved spacetimes,
- facts concerning gravitational energy-momentum pseudotensors in general relativity.
With this background in hand, one can say that Yilmaz apparently wishes to keep 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.
No astronomers have tested his ideas, although some have tested competitors of general relativity; see Category:Tests of general relativity.
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