#### The fifth force implies no existance of blackholes?

Title: The fifth force implies no existance of blackholes?

We know by now that Newton's formula of gravitational potential on gravity, w=G*m(r)/r, (with singularity for star radius=r=0, m(r) is the mass of the star),

is modified by the presence of the "Fifth force" (or said anti-gravity effect) given from the formula of Fischbach E. 1986

(see even Rujula A.D. 1986, Cowsik R. 1990, Thomas J. 1989, formula without singularity).

The Fischbach's formula of the gravitational potential corrected is:

w=G*m(r)*(1-a*exp(-r/L))/r

where G is the universal gravitational constant, corrected by a=0.01:0.001, which is the intensity of the fifth force, called ipercharge,

that depends on the relative amount of neutrons upon number of protons, in range L=100:1000 meters, of mass m of the star on radius r.

The question of the title if the fifth force implies no existance of blackholes, is because there is no presence of singularity

in the gravitational potential corrected by Fischbach E.:

lim(r-->0)(1-a*exp(-r/L))/r=a/L. (theoreme of De Hospital for limits).

We know that in General Relativity the Einstein's Field Equations derived from the Newtons formula, (see Weinberg S. 1972 chapter 7.1.3 and 7.1.12),

have the presence of singularity for the radius of the star going to zero: r-->0, where the metric tensor A(r)=g(rr)=1/(1-2*G*m(r)/r),

(see Weinberg in chapter 11.1.11) gives the presence of blackholes with the Schwarzschild radius (1=2*G*m(R)/R).

But if we use the corrected gravitational potential of Fischbach E. 1986 without singularity, modifying the Einstein's Field Equations;

probably the new Einstein's Field Equations shall become without the presence of singularity; it is amazing;

giving a curvature that is bounded, with radius metric tensor A(r)=g(rr)<"curvature limit".

Infact, the metric tensor in radius r is g(rr)=1/[1-(1-a*exp(-r/L))2mG/r] for the Schwarzschild solution (see Weinberg 8.1.7 and 8.2.11);

and you can easily verify that it hasn't any singularity, (so g(rr) doesn't approach infinite value for any radius r, neither with Schwarzschild radius).

So blackholes do not exist for the presence of the fifth force?

But another question is the neutron stars with the fifth force: how are they phenomenologically? Do they exist? And how?

The new Einstein's Field Equations depending on the formula of Fischbach 1986, looks as:

R(ij) - 1/2 * g(ij) * R = {g(mn) * A(mn) + T(mn) * B(mn)} * T(ij) where the indices of tensors are i,j,m,n=1,2,3,4;

where T(ij) is the energy momentum tensor, and R(ij) is the Ricci tensor, and g(ij) is the metric tensor. A(mn) and B(mn) are to be found.

Bibliography:

Cowsik R. et al. 1990: Phy.Rev. Lett.64:337

Fischbach E. et al. 1986: Phy.Rev.Lett.57:3

Rujula A.D. 1986: Phy.Lett.180:213.

Thomas J. 1989: Phy.Rev.Lett.63:1963

Weinberg S. 1972 "Gravitation and Cosmology" Wiley.

Good Research. Bye.