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Antigravity and Maximal Acceleration.

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Annnlen der Physik. 7. Folge, Band 47, Heft 8, 1990, S. 677-678
J. A. Barth, Lcipzig
Short Communieaiion
Antigravity and Maximal Acceleration
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 graviton. If so, the gravitational potential V ( r )of a mass M contains a component of the
Yukawa form and reads
+ B(M/r)exp(-pr)
V ( r )= a ( W r )
a, fi 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).
B) is the gravitational
At small distances, p r + 0 and V ( r )4 -GM/r where G = -(a
constant, measured locally (a- 6.67 10-8 cm3 g-1 s-%). Eq. (1) can be written as
+ b)-I [l + b exp(-pr)],
V ( r )= -(GM/r) (1
# 1.
The gravitational acceleration r = a = --dV/dr is
a = -(GM/r*)(1
X =pr.
+ b)-l[ 1+ b( 1+ X) exp(-X)]
Any mass m, placed at rest at the distance r from M obeys the relativistic-qimntum
constraint [21
la1 < 2 m0c3/h.
The numerical value and the sign of b depend on the particular theory involved. Assume
b > 0 and obtain from (5)
+ X) exp(-X)]-l.
b < (1 - y+)[y? - (1
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- 1
Pcm (= a typical
galactic size) explain the observed flat shape of the galactic rotation curves with no need
of postulating the presence of dark matter.
[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.
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accelerating, antigravity, maximal
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