Annnlen der Physik. 7. Folge, Band 47, Heft 8, 1990, S. 677-678 J. A. Barth, Lcipzig

Short Communieaiion

Antigravity and Maximal Acceleration

By CORRADO MASSA

Reggio Emilia, Italy

Antigravitation und maximale Beschleunigung

Attempts to unify gravitation with the other natural forces suggest [l] gravity is transmitted by a particle of nonzero rest mass m in addition to the usual maasless gravi- ton. If so, the gravitational potential V(r ) of a mass M contains a component of the Yukawa form and reads

V ( r ) = a ( W r ) + B(M/r) exp(-pr) , (1) where a, f i are (respectively) the coupling constant of the massless and of the massive graviton; = mc/ti is the inverse Compton wavelength of the massive graviton (c = the speed of

light, ti = the reduced Planck constant). At small distances, pr + 0 and V ( r ) 4 -GM/r where G = -(a + B) is the gravitational constant, measured locally (a- 6.67 10-8 cm3 g-1 s-%). Eq. (1) can be written as

V ( r ) = - (GM/r) (1 + b)-I [l + b exp(-pr)], b # 1.

The gravitational acceleration r = a = --dV/dr is

a = - (GM/r*) (1 + b)-l[ 1 + b( 1 + X) exp( -X)] , X = pr .

(3)

Any mass m, placed at rest at the distance r from M obeys the relativistic-qimntum constraint [ 21

la1 < 2 m0c3/h. (4)

The numerical value and the sign of b depend on the particular theory involved. Assume b > 0 and obtain from (5)

b < (1 - y+)[y? - (1 + X) exp(-X)]-l. (6)

678 Ann. Physik Leipzig 47 (1990) 8

As r 03, the constraint is obeyed only if b < - 1, in contrast with our assumption b > 0; therefore we must drop the assumption b > 0 and are forced to conclude b < 0 (if b # 0, of course).

I don’t investigate the case r + 0 because as r + 0 the quantum spread in the linear momentum of m,, tends to infinity and our zero-initial-speed assumption breaksdown.

A negative b means that gravity is a mixture of the ordinary attractive force, carried by the spin-2 graviton, and of a repulsive force (antigravity); thus our result b < 0 implies the massive graviton is a spin-s particle with 8 = an odd number, likely 1 (of course on scale larger than l/p the antigravity component is negligible and attraction dominates). It’s interesting to point out antigravity arises naturally in supergravity theories [3]. Notice also the assumptions b - -0.9 and 1/p- 1P cm (= a typical galactic size) explain the observed flat shape of the galactic rotation curves with no need of postulating the presence of dark matter.

References

[l] GIBBONS, G. W.; WHITINQ, B. F.: Nature, 291 (1981) 636. [2] CAIASIELLO, E. R.: Lett. Nuovo Cimento 41 (1984) 370, and references therein. [3] SHERK, J.: Phys. Lett. 88 B (1979) 266. [4] SANDERS, R. H. : Astron. Astrophye. 186 (1984) L 21.

Bei der Redaktion eingegangen am 2. Februar 1990.

Anschr. d. Verf.: CORRADO MASSA Via Fratelli Manfredi 66 1-42100 Reggio Emilia, Italy

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