LF, TTERE AL lgUOVO CIMENTO VOL. 13, N. 16 16 Agosto 1975

A Bimetr ic Theory o f Gravitation.

N. ROSEN

Depar tment o/ Physics , Teehnion- Israe l Ins t i tu te o] Technology - Hai]a

(ricevuto il 26 Maggio 1975)

This is in reference to a letter by YILMAZ that appeared some time ago in this journal (1) in connection with my work on a bimetric theory of gravitation (3). At the time ] decided not to reply to the letter because I dislike becoming involved in con- troversies. However, several friends have urged me to write a reply in order to clear up misunderstandings that might have been caused by that letter, and I have finally decided to write some remarks.

Thc main purpose of the letter by YILMAZ appears to be to show that the theory which I proposed is inconsistent, and in order to do this he attributes to me the co-ordinate condition

(4) ~(~g~) = 0 .

I find this most surprising. For in my paper (2), although I mentioned the possibility of a condition equivalent to the above, I clearly pointed out with the help of eqs. (54), (58), (59), p. 443, that in general this condition would give an inconsistency and cannot be used (except in certain special cases). That being the case, one cannot help wondering why YILMAZ wrote his letter, unless he did this without having read my paper thoroughly.

In his letter YILlVIAZ claims to have obtained general solutions of the field equa- tions of the bimetric theory and that these arc the same as the solutions in his theory of gravitation (references in (1)). I t is not my purpose here to pass judgment either on his procedure for obtaining solutions or on his theory of gravitation.

However, I should like to point out that the bimetrie theory of gravitation (s) is a consistent theory which gives agreement with all the observations carried out up to now, to the same accuracy as the general theory of relativity. I t has been investi- gated by the group of THORNE at Caltech and found to be viable. I t differs from general relativity in that it gives a considerably larger maximum mass (about 5.6 times as large

(1) H. YILM~Z: Lett. Nuovo Cimento, 10, 201 (1974). (~) N. I~OSE~': Gen. Rev. Gray., 4, 435 (1973). (8) N. ROSE,C: Leit. Nuovo Cimento, 8, 889 (1973); Ann. o] Phys., 84, 455 (1974).

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614 •. ROS~X

for a certain equation of state) for a cold neutron star (4), and it does not appear to predict the existence of black holes. I t also predicts different gravitational red-shifts and different propagation velocities for electromagnetic and gravitational radiation in a gravitat ional background field.

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I would like to thank Prof. A. PAPAPETROU for helpful discussions.

,(~) Submitted for publication.