A scalar field gravitational analog of the Reissner-Nordstrom solution is investigated. The nonlinear Newtonian model has an upper-limit of charge for a central mass, which agrees with the general relativistic condition required for the existence of the black hole horizon. The maximum limit for accumulation by bombardment of charged particles is found. The aim is to investigate the resulting physics after severing the effects of curvature from the effects of energy-mass equivalence.

1.
P. C.
Peters
, “
Where is the energy stored in a gravitational field?
,”
Am. J. Phys.
49
,
564
569
(
1981
).
2.
J. H.
Young
, “
A charge contribution to (pseudo-) Newtonian gravity
,”
Am. J. Phys.
59
,
565
567
(
1991
).
3.
D.
Lovelock
, “
The four-dimensionality of space and the einstein tensor
,”
J. Math Phys.
13
(
6
),
874
876
(
1972
).
4.
J.
Franklin
, “
Self-consistent, self-coupled scalar gravity
,”
Am. J. Phys.
83
,
332
337
(
2015
).
5.
D. J.
Cross
, “
The relativistic gamma factor from Newtonian mechanics and Einstein's equivalence of mass and energy
,”
Am. J. Phys.
84
,
385
387
(
2016
).
6.
R.
Wald
, “
Gedanken experiments to destroy a black hole
,”
Ann. Phys.
82
,
548
556
(
1974
).
7.
V. E.
Hubeny
, “
Overcharging a black hole and cosmic censorship
,”
Phys. Rev. D
59
,
064013
(
1999
).
8.
S.
Isoyama
,
N.
Sago
, and
T.
Tanaka
, “
Cosmic censorship in overcharging a Reissner-Nordstróm black hole via charged particle absorption
,”
Phys. Rev. D
84
,
124024
(
2011
).
9.
J. D.
Jackson
,
Classical Electrodynamics
(
Wiley
,
New York
,
1998
).
10.
C.
Misner
,
K.
Thorne
, and
J.
Wheeler
,
Gravitation
(
Freeman
,
New York
,
1973
).
11.
H.
Levine
,
E. J.
Moniz
, and
D. H.
Sharp
, “
Motion of extended charges in classical electrodynamics
,”
Am. J. Phys.
45
,
75
78
(
1977
).
12.
S.
Hod
, “
Universal charge-mass relation: From black holes to atomic nuclei
,”
Phys. Lett. B
693
,
339
342
(
2010
).
13.
M. R. R.
Good
,
P. R.
Anderson
, and
C. R.
Evans
, “
Mirror reflections of a black hole
,”
Phys. Rev. D
94
,
065010
(
2016
).
14.
M. R. R.
Good
, “
On spin-statistics and bogoliubov transformations in flat spacetime with acceleration conditions
,”
Int. J. Mod. Phys. A
28
,
1350008
(
2013
).
15.
M. R. R.
Good
,
K.
Yelshibekov
, and
Y. C.
Ong
, “
On horizonless temperature with an accelerating mirror
,”
JHEP
1703
,
1
32
(
2017
).
16.
J.
Linsley
, “
Evidence for a primary cosmic-ray particle with energy 1020 eV
,”
Phys. Rev. Lett.
10
(
4
),
146
148
(
1963
).
17.
N.
Shaham
and
T.
Piran
, “
Implications of the penetration depth of ultrahigh-energy cosmic rays on physics at 100 TeV
,”
Phys. Rev. Lett.
110
,
021101
(
2013
).
18.
A.
Einstein
, “
Zur theorie des statschen gravitationsfeldes
,”
Ann. Phys. (Leipzig)
343
,
443
458
(
1912
);
A.
Einstein
,
The Collected Papers of Albert Einstein
, translated by Anna Beck (
Princeton U.P.
,
Princeton
,
1996
), Vol.
4
, pp.
107
120
.
19.
P. G. O.
Freund
and
Y.
Nambu
, “
Scalar field coupled to the trace of the energy-momentum tensor
,”
Phys. Rev.
174
,
1741
1743
(
1968
).
20.
M.
Sereno
, “
Weak field limit of Reissner-Nordstrom black hole lensing
,”
Phys. Rev. D
69
,
023002
(
2004
).
21.
J.
Sorce
and
R.
Wald
, “
Gedanken experiments to destroy a black hole II: Kerr-Newman black holes cannot be over-charged or over-spun
,”
Phys. Rev. D
96
(
10
),
104014
(
2017
).
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.