Authors
Johnny Iannello
Abstract
If we consider the “Fifth force” as an external force of the classical newtonian gravitational field introduced in the Theory of General Relativity, we will obtain the new modified Einstiens’ field equations.
We unify the "Fifth Force" with the "Gravitational Force" applying the Theory of General Relativity. The result is that probably the "new modified Einstein's field equations" will not present any kind of singularity with the presence of the "Fifth Force". Peculiar phenomenologies on stars and galaxies nucleus, the expansion or not of the universe can be fairly treated with the new modified Einstein's field equations.
It is well known that General Theory of Relativity is a geometric theory of gravitation and the curvature of spacetime is related to the energy and momentum. This relation is specified by Einstein’s equations. The experimental tests are numerous and, therefore, it is impossible to question its validity but this does not prevent us from proposing new ideas. In this work, we want to introduce the Fifth Force, not considering the universal gravitational constant. In this way we obtain modified field equations. The aim of the paper is to observe that, if we introduce this fifth force, the principle of the equivalence is violated and, probably, there are never singularities in the metric when we solve the field equations.
Maybe the Schwarzschild radius for a symmetrical static spherical star doesn’t compare: to be proved with “computational mathematics”.
Throughout the paper, the symbols refer to the textbook of Weinberg , considering even the speed of light as c=1.
Image 1 Introduction
What is the fifth force?
If we consider two nucleons of mass m1 and m2, they will exert a gravitational potential energy of the following form ([5]-[8], formula of Gibbons and Fischbach without singularity):
⦁ U12 = -G m1 m2 (1+ e- r1,2 )/ r1,2
where G is the universal gravitational constant (G=6.673*10-11 Nm2/kg2), corrected by =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 per nucleon, in range
-1 =100:1000 meters, ( if can be a positive or a negative quantity).
The property of this phenomenological formula (1) in confront of Newton’s gravity law is that it hasn’t any *singularity.
Material and methods
The geodetic equation inserting the fifth force.
We follow the same calculations of Chapter 3.2 Weinberg 1972, to find the geodesic equation adding the fifth force: considering it as an “external force”, acting upon the gravitational field. We need to find this type of geodesic equation to modify the Einstein field equation, acting with metric tensor, goo.
The Newtonian limit with the fifth force to find the metric tensor of time goo.
We want to find the dependency of the metric tensor goo upon the potential of the gravitational field and the potential of the fifth force 5. This shall be useful to obtain the Einstein’s field equations with the fifth force, following the same calculations of Chapter 3.4 Weinberg 1972, but violating the principle of equivalence.
Considering (-8G) = (-8G/c4 for velocity of light, c=1), not a constant, but a scalar function, we obtain the new Einstein’s field equations modified by the presence of the fifth force.
Results
Black holes do not exist!
Discussion
In this paper we have obtained a modified Einstein’s field equations by introducing the fifth force of Gibbons-Fischbach. We invite to look for numerical solutions in the case of a static field with spherical symmetry. It would be interesting to understand if there are *singularities or not.
The system (41), must be resolved with “computational mathematics”, to verify if there are present or not *singularities in the metric tensors gij.
It is well known that in the standard Schwarzschild space-time there is a *singularity in the metric and it would be interesting if our approach leads to a *singularity-free metric or not. Indeed, this would have consequences about the existence of black holes.
We think that it’s possible to arrive, in another way, to a complete compact Einstein’s field equation, (33), about its second member with the energy-momentum tensor, introducing the “fifth force” in General Relativity, by using another approach, instead of using “Newtonian limit”: the theorems, properties and methods of the “Continuum Mechanics Theory” (because the formula (1) of Gibbons and Fischbach has “elastic” properties as a stretching and squeezing spring holding two masses, that is a repulsive and an attractive gravitational force). And after we can apply the “Principle of Minimum Action”, trying to find the opportune Langragian of this “elastic” continuum ensemble of celestial masses, (considering the universe as a many body, n-body system).
Nevertheless it’s necessary and it must be verified the orbitals of the planets and stars, for the consistency of the new modified Einstein’s field equations (33), found by introducing the fifth force in the general relativity theory.
Title: BLACK HOLES DO NOT EXIST.
OTHER LOGICAL MATHEMATICAL DEMONSTRATION THAT BLACK HOLES DO NOT EXIST USING WEINBERG STEVE BOOK. (for who knows physics).
1) Black holes do not exist?
2) No. Black holes do not exist.
1) Why? Show the demonstration. 2)This is the demonstration.
2) Get the book of author Steven Weinberg, “Gravitation and Cosmology” 1972, at chapter 8.2 and follow the wrong logic of Schwarzschild.
So it says at chapter 8.2 page 179, that “the field equations for empty space are”
Rμν=0.
But if it’s an empty space it means that the mass of any astrophysical object is zero, (for example stars which mass is zero M=0); so even the gravitational potential φ=-GM/r = 0, (see (3.4.4), Weinberg book, where r is the radius of the star); and so even the energy-momentum tensor is zero, Tij=0(see chapter 2.8 and 5.3 and formula (5.3.4), Weinberg book).
So when in the book of Weinberg says on page 180 writing about the formula: rB(r)=r+constant1 (8.2.9) where B(r) = gtt is the time metric tensor: “To fix the constant1 of integration we recall that at great distances from a central mass M…” that for hypothesis of empty space the mass is zero M=0, the gravitational potential is zero, φ= - GM/r = 0 implies B=1 and so constant1=0 and so even the radius metric tensor A=grr. That means curvature with flat space when Rμν=0. So the formula of Schwarzschild is wrong: B(R)=[1-2MG/r] (see wrong logic and formula (8.2.10), Weinberg book). And this means, even that it’s failed the use of Schwarzwild radius R that satisfies a singularity as 2MG/R =1. So black holes horizon doesn’t exist. Further considerations in future papers will be made introducing the “fifth force” of GibbonsG.W.-Fischbach.E 1986, in the theory of general relativity together with the energy-momentum tensor Tij.
So if we found that the metric tensors B=1 and A=1 for any radius r in empty space, that means that black holes do not exist even for radius r going to 0, r-->0.
So stars do not become black holes. And black holes do not exist in the universe.
Further details
WARNING: INTERNATIONAL SAFETY FLIGHT RULES for students of POLITICAL SCIENCE UNIVERSITY:
Every life must be respected. The automated flight on the moon, without astronauts, is helpful to improve the expansion of the humanity, just trying to plant on the moon right vegetables and proper fruits on its artificial ground and artificial climate that permits the plants to grow. Every life must be respected. The automated spacecraft or flying object that goes on the moon must take off or start flying only from the center of the oceans, NOT over lands, to crash on people. The trajectories of the automated flying object that goes on the moon, must be away from countries, to not crash hurting families or any people, and to not crash down hurting persons, when landing on the water of the center of the ocean (with the parachute?). Goodluck in your administration and politics!
WARNING_ALERT:
About weight and falling: “The heavy and big fruits or vegetables as water-melons and pumpkins grow on the plane earth
for our security; but little and light fruits as apples grow on the trees, so falling down aren’t dangerous to our or everyone lifes life”.
--------------------------------------------------------------------------------------------------------------------
“Mathematics” or “math and geometry” subjects” is a bad evil that must be handled very carefully, on human societies that uses it as a tool (like a hammer); to be used carefully and not to use it as an arm. For example, (statistics or not statistics, economy or not economy), see what "mathematics" caused on human societies. For example, a lot of accidents in the societies with projects: projects of cars that crash over people, airplanes that fall over families, buildings with heavy stoney or rocky roofs that can fall over people, nuclear reactors that can explode over families, etc.
Title: BLACK HOLES DO NOT EXIST.
OTHER LOGICAL MATHEMATICAL DEMONSTRATION THAT BLACK HOLES DO NOT EXIST USING WEINBERG STEVE BOOK. (for who knows physics).
1) Black holes do not exist?
2) No. Black holes do not exist.
1) Why? Show the demonstration. 2)This is the demonstration.
2) Get the book of author Steven Weinberg, “Gravitation and Cosmology” 1972, at chapter 8.2 and follow the wrong logic of Schwarzschild.
So it says at chapter 8.2 page 179, that “the field equations for empty space are”
Rμν=0.
But if it’s an empty space it means that the mass of any astrophysical object is zero, (for example stars which mass is zero M=0); so even the gravitational potential φ=-GM/r = 0, (see (3.4.4), Weinberg book, where r is the radius of the star); and so even the energy-momentum tensor is zero, Tij=0(see chapter 2.8 and 5.3 and formula (5.3.4), Weinberg book).
So when in the book of Weinberg says on page 180 writing about the formula: rB(r)=r+constant1 (8.2.9) where B(r) = gtt is the time metric tensor: “To fix the constant1 of integration we recall that at great distances from a central mass M…” that for hypothesis of empty space the mass is zero M=0, the gravitational potential is zero, φ= - GM/r = 0 implies B=1 and so constant1=0 and so even the radius metric tensor A=grr. That means curvature with flat space when Rμν=0. So the formula of Schwarzschild is wrong: B(R)=[1-2MG/r] (see wrong logic and formula (8.2.10), Weinberg book). And this means, even that it’s failed the use of Schwarzwild radius R that satisfies a singularity as 2MG/R =1. So black holes horizon doesn’t exist. Further considerations in future papers will be made introducing the “fifth force” of GibbonsG.W.-Fischbach.E 1986, in the theory of general relativity together with the energy-momentum tensor Tij.
So if we found that the metric tensors B=1 and A=1 for any radius r in empty space, that means that black holes do not exist even for radius r going to 0, r-->0.
So stars do not become black holes. And black holes do not exist in the universe.
In superconductivity experiments with the so called superfluid experiments, approaching to temperatures of 0.3Kelvin, it's easy to see the effects of the fifth force.
References
1. Bertolami O., Bohmer C. G., Harko T. and Lobo F. S. M., Phys. Rev. D 75, 104016 (2007)
2. Will C. M., Living Rev. Rel. 17, 4, (2014).
3. Licata I., Corda C., Benedetto E., Grav. Cosm. 22, 1, 48 (2016)
4. Cowsik R. et al. 1990: Phy.Rev. Lett.64:337
5. Fischbach E. et al. 1986: Phy.Rev.Lett.57:3
6. Gibbons G.W. et al. 1981 : Nature.291 :636
7. Rujula A.D. 1986: Phy.Lett.180:213.
8. Thomas J. 1989: Phy.Rev.Lett.63:1963
9. Weinberg Steven 1972 "Gravitation and Cosmology" Edition: Wiley.
10. Membrado M. et al. 1990 : The Astrophysical Journal. 348 :212
11. Spiegel Murray R. 1975: collana Schaum „Analisi vettoriale“, Edition: Etas Libri.
12. Wolfgang Rindler 2006 “Relativity”, Edition: Oxford.
13. Ashok Das 2011 “Lectures on Gravitation” Edition: World Scientific.
14. Misner C.W., Thorne, Wheeler 1973: “Gravitation” Edition: Freeman and Company
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Johnny Iannello Sunday, 05 February 2023 - 14:58 UTC
Who wants to learn more astrophysics about stars evolution and the statement of the Universe we live in.