TY - JOUR
TI - The Relation between General Relativity's Metrics and Special
Relativity's Gravitational Scalar Generalized Potentials and Case
Studies on the Schwarzschild Metric, Teleparallel Gravity, and Newtonian
Potential
AU - Vossos, Spyridon
AU - Vossos, Elias
AU - Massouros, Christos G.
JO - Particle & Particle Systems Characterization
PY - 2021
VL - 4
TODO - 4
SP - 536-576
PB - MDPI
SN - 0934-0866, 1521-4117
TODO - 10.3390/particles4040039
TODO - Einstein's Equivalence Principle; gravitational deflection of light;
gravitational red shift; kinematics and dynamics of the solar system;
linear spacetime transformation; Lorentz metric; precession of Mercury's
perihelion; Newtonian gravitational potential; non-Riemannian metric;
Shapiro time delay; Schwarzschild metric; Teleparallel Gravity;
variable-speed wave
TODO - This paper shows that gravitational results of general relativity (GR)
can be reached by using special relativity (SR) via a SR Lagrangian that
derives from the corresponding GR time dilation and vice versa. It also
presents a new SR gravitational central scalar generalized potential
V=V(r,r.,phi.), where r is the distance from the center of gravity and
r.,phi. are the radial and angular velocity, respectively. This is
associated with the Schwarzschild GR time dilation from where a SR
scalar generalized potential is obtained, which is exactly equivalent to
the Schwarzschild metric. Thus, the Precession of Mercury's Perihelion,
the Gravitational Deflection of Light, the Shapiro time delay, the
Gravitational Red Shift, etc., are explained with the use of SR only.
The techniques used in this paper can be applied to any GR spacetime
metric, Teleparallel Gravity, etc., in order to obtain the corresponding
SR gravitational scalar generalized potential and vice versa. Thus, the
case study of Newtonian Gravitational Potential according to SR leads to
the corresponding non-Riemannian metric of GR. Finally, it is shown that
the mainstream consideration of the Gravitational Red Shift contains two
approximations, which are valid in weak gravitational fields only.
ER -