A Possible Exact Solution for the Newtonian Constant of Gravity
Yanpeng Li *
The 2nd Institute of Electronic Science, School of Electrical Science and Engineering, National University of Defense Technology, Changsha, 410073, China.
*Author to whom correspondence should be addressed.
Abstract
Compared with our knowledge of other fundamental constants, the exact value of the Newtonian
constant of gravity (G) has long been enigmatic, and there is currently no ocially accredited
exact solution for G. Dierent from the widely adopted experimental approach and unlike other
theoretical ways in resolving the value of G, by applying to the eld equation of general relativity
two newly developed tensor-based mathematical approaches (one is referred to as \eigen-modulus"
to show the converging ability of a tensor, the other is called \the law of tensorial determination"
to evaluate indeterminate forms involving tensors), we provide a possible exact solution to G that
only relates to the electrical permittivity (ϵ0) and magnetic permeability (μ0) of free space, and
is the corresponding
mass density with constant value, with η = 1 (kg·m
−3). This research casts doubt on the prevailing
hypothesis that G is an independent constant. Our nding may place the theory of gravity and
many related researches on a more objective and quantitative footing. The result not only aects
the theory of gravity but also plays a key role in maintaining theories of classical mechanics,
cosmology, general relativity and astrophysics.
Keywords: Exact solution, tensor analysis, eigenvalue, eigen-modulus, Einstein tensor, energy-momentum tensor, Newtonian constant of gravity