Ben-Amots: Relativistic exponential gravitation and exponential potential of electric charge

ABSTRACT: We present theories of gravitation and electric potentials with exponential dependence on the reciprocal distance. In the context of this kind of electric potential we investigate the dynamics of a relativistic electron interacting with a proton.

SUMMARY: We investigated two new gravitation theories with variable rest mass. We find that both give results very close to general relativity for known weak gravitational fields but both suggested theories do not exhibit "black holes." In order to verify which theory fits reality, analysis of existing NEA/NEO observational data is suggested.
An exponential electric potential similar to the exponential gravitation potential presently discussed is used for investigating the orbits of an electron around a proton. A new set of hydrogen electron orbitals inner to the Bohr orbitals and very close to the proton is found.

59 references:
Milne, E.A., "Rational electrodynamics: V. The neutron and nuclear dynamics," Phil. Mag., v. 34(7), 246-258 (1943). See pp. 246-250.
Milne, E.A., "Kinematic Relativity" Clarendon Press, Oxford, UK, pp. 203-210, 214-220 in (1951) edition.
( -- First edition was in 1948).
Schiff, L.I., "Motion of a gyroscope according to Einstein's theory of gravitation," Proc. Nat. Acad. Sci., v. 46, pp. 871-82 (1960)
and more 56 references.

KEYWORDS: Exponential potential, sub-Bohr orbital, Variable rest mass

REVIEWER: Anonymous.

REVIEW: I have enjoyed reading the article in the Found. of Phys. It is a very interesting, important and well written work with a lot of examples. I like this paper.

ERRATA IN PAPER:

Third line after Equation (14) should read: that (14) is consistent...

Line 12 in the page after Equation (26) should read: 1.00000000 as necessary...

Equation (7) should be deleted as following:

The paragaph that includes Equation (7) should read:
"Vankov [5-7, 16] and also Ben-Amots [22] further extend (6) to electric charge."

The paragraph before Equation (9) should read:
"We derived the pseudo line element (8) corresponding to (6) using a procedure similar to that of Weinberg..."

The line before Equation (10) should read:
"line element corresponding to (6). We calculate the ..."

The line before Equation (14) should read:
"Introducing the coefficient 2 we get the "line element" corresponding to (6):"

The second line after Equation (14) should read:
"Coleman has also shown [24] that (14) is..."

The fifth line after Equation (14) should read:
"We argue [22] that the variable mass (6) implies that the gravitational field exhibits ..."

COMMENT: Lectured 14.6.2006 in IARD2006 Conference.

CITED BY:
Majernik, Vladimir (1934-2017)
"An alternative to classical naked singularity and black hole,"
Phys. Essays, v. 22, pp. 413-419 (2009)
https://doi.org/10.4006/1.3187148

Tsang, Ling Man,
"Some static spherical classical solutions including the cosmological term,"
Canadian J. Pure Appl. Sci., v. 4, No. 1, pp. 1073-1079 (2010)
See p. 1078
The author name is erroneously cited as Amots instead the correct family name
Ben-Amots

Walker, Colin,
"Calculation of gravitational potential by the method of multiple redshifts,"
(2010),
http://sites.google.com/site/revisingnewton

Walker, Colin,
"Newtonian potential and the Einstein equivalence principle,"
Foundational Questions Context (2012),
http://www.fqxi.org/data/essay-contest-files/Walker_shells.pdf

Cited by
Teruel, Gines R. Perez,
"On the movement of a particle in a gravitational field in the context of the special theory of relativity,"
academia.edu (2015)
http://academia.edu

Cited by
Teruel, Gines R. Perez,
"On the variation of the mass in a gravitational field and Mach s Principle,"
viXra (2014)
https://www.vixra.org/pdf/1412.0226v3.pdf

Cited by
Teruel, Gines R. Perez,
"Non-linear energy conservation theorem in the framework of Special Relativity"
European Journal of Physics, v. 36, 045009 (2015)
arXiv (2015)
http://www.arxiv.org/pdf/1505.0481v1.pdf

Cited by
Majernik, Vladimir (1934-2017)
"The Lenz-Sommerfeld approach to general relativity with variable masses"
Researchgate.net (2015)

Cited by
Boonserm, P., Ngampitipan, T., Simpson, A., Visser, M.,
"The exponential metric represents a traversable wormhole"
(May 2018)
arXiv:1805.03781v3 [gr-qc] (May 2018)
"exponential metric represents a traversable wormhole"
Phys. Rev. D, (October 2018)
DOI:10.1103/PhysRevD.98.084048

Cited by
Simpson, Alex
"Traversable Wormholes, Regular Black Holes, and Black-Bounces"
(2019)
M.Sc. thesis
Victoria University of Wellington, New zealand
School of Mathematics and Statistics
and the same also in:
https://arXiv.org/pdf/2103.14055.pdf (4.2021)

Cited by
Turimov, B., Turaev, Y., Ahmedov, B., Stuchlik, Z.,
"Circular motion of test particle around wormhole represented by exponential metric,"
Phys. Dark Universe 100946, (4 January 2022)

Cited by
Partha Pratim Nath & Debojit Sarma
"Generalized form of exponential wormhole metric,"
arXiv:2301.09334v1 (23 January 2023)

Cited by
Tuhina Manna, & Farook Rahaman, & Tanmoy Chowdhury
Strong Lensing in the Exponential wormhole spacetimes
SSRN Electronic Journal (February 2023)
DOI: 10.2139/ssrn.4349260

Cited by
Tuhina Manna, & Farook Rahaman, & Tanmoy Chowdhury
Strong Lensing in the Exponential wormhole spacetimes
SSRN Electronic Journal (February 2023)
DOI: 10.2139/ssrn.4349260

Cited by
Partha Pratim Nath and Debojit Sarma
Study of exponential wormhole metric in $f(R)$ gravity
Physica Scripta, V. 99, No. 4 (March 2024)
arXiv:2307.04237 (July 2023)

Cited by
S.H. Mazharimousavi
Vacuum traversable wormhole
arXiv:2309.02874 (September 2023)

Cited by
Mazharimousavi, S.H.
Axially symmetric exponential metric
Physics of the Dark Universe
v. 43, 101412 (February 2024)

Cited by
Changjun Gao; Jianhui Qiu
From the Janis-Newman-Winicour naked singularities to Einstein-Maxwell phantom wormholes
Universe
10(8):328 (August 2024)
Preprint, Researchgate (July 2024)

Cited by
Partha Pratim Nath and Debojit Sarma
A new class of traversable wormhole metrics
The European Physical Journal C
84(10) (October 2024)
0OI: 10.1140/epjc/s10052-024-13401-5

Cited by
Faizuddin A., Jaydeep G., Bouzenada A.
Positive energy density in topologically charged exponential wormholes and Regge-Wheeler potential
The European Physical Journal C
85(1):110
(January 2025)
DOI: 10.1140/epjc/s10052-025-13819-5

Cited by
Partha Pratim Nath and Debojit Sarma
Exponential wormhole, its quasinormal modes, and study in logarithmic f(R) gravity
Annals Phys. 479 (2025) 170067
(May 14, 2025)
DOI: 10.1016/j.aop.2025.170067

AUTHOR'S COMMENTS (not included in the paper): The present paper was submitted a few months after the conference of June 2006 to the editor of the proceedings. As usual, the editor passed it to the reviewers and waited for their comments and my corrections. He did the same for all the other papers of the proceedings. Only after the editor gathered all the corrected papers, he submitted all of them together to the journal. The journal printed the papers with the date of submission to the journal, 3rd January 2007. This is a normal process for conference papers. I was accused in 2020 by an author of another paper published in 2006 that my paper submitted in 2007 did not refer to his paper of 2006. However, his paper was submitted in December 2006, a few days before the editor submitted my paper to the journal, and a few months after I submitted this paper to the editor. Therefore, I could not know about his paper on time. Furthermore, there is no obligation to refer to all the papers. Also, the reason for not referring to a paper is mostly not finding it in a survey. It is recommended to refer to the important first papers on the subject. The important first authors of the relevant papers were Milne (1938, 1943), Yilmaz (1958), Coleman (1971), and six others, whom my paper refers to 14 of their papers, but these predecessors were not referred by the accuser author, who ignored all the predecessors in order to claim that his paper of 2006 was the first one. Apparently he did not make any survey, which led him to believe that he was the first one. Anyway, my present paper includes much more relevant continuation derivations than all the references, and other not referred papers, either later or earlier. The most important issue is a new derivation in the present paper of a new set of sub-Bohr orbitals of the electron around a proton. The second important issue in my paper is another brand new derivation of other equations that leads to yet another solution without a black hole. No predecessor exists for both these original issues in my paper.

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