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 TITLE: Relativistic exponential gravitation and exponential potential of electric charge
 AUTHOR: Ben-Amots, N.
 SOURCE: Foundations of Physics, v. 37, No. 4-5 , pp. 773-787 ( May 2007).
Fulltext from journal: doi:10.1007/s10701-007-9112-1
 
 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, V.
"An alternative to classical naked singularity and black hole,"
Phys. Essays, v. 22, pp. 413-419 (2009)

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,"
viXra (2014)
http://www.vixra.org/pdf/1412.0226v7.pdf
http://www.rxiv.org/pdf/1412.0226v7.pdf

Cited by
Teruel, Gines R. Perez,
"On the variation of the mass in a gravitational field and Mach’s Principle,"
viXra (2014)
http://www.vixra.org/pdf/1412.0226v3.pdf
http://www.rxiv.org/pdf/1412.0226v1.pdf

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

Cited by
Vladimir Majernik (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

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