Abstract
Let the coordinate system xi of flat space-time to absorb a second rank tensor field Φij of the flat space-time deforming into a Riemannian space-time, namely, the tensor field Φuv is regarded as a metric tensor with respect to the coordinate system xu. After done this, xu is not the coordinate system of flat space-time anymore, but is the coordinate system of the new Riemannian space-time. The inverse operation also can be done. According to these notions, the concepts of the absorption operation and the desorption operation are proposed. These notions are actually compatible with Einstein’s equivalence principle. By using these concepts, the relationships of the Riemannian space-time, the de Donder conditions and the gravitational field in flat space-time are analyzed and elaborated. The essential significance of the de Donder conditions (the harmonic conditions or gauge) is to desorb the tensor field of gravitation from the Riemannian space-time to the Minkowski space-time with the Cartesian coordinates. Einstein equations with de Donder conditions can be solved in flat space-time. Base on Fock’s works, the equations of gravitational field in flat space-time are obtained, and the tensor expression of the energy-momentum of gravitational field is found. They all satisfy the global Lorentz covariance.
Highlights
General Relativity (GR) is widely accepted wherewith its graceful structures and elegance of its concepts, giving a description of gravitational phenomena in agreement with observation, it is rather disconcerting to note that the theory appears strikingly different from the present particle theory
Why is the structural form of Einstein equations correct even if it is obtained from the geometric interpretation that people feel uncomfortable? What relationship between the gravitational field and the Riemannian space-time is exactly? Can we find a way to hold the structural form of Einstein equations, abandon the purely geometric interpretation of gravitation and make the equations global Lorentz invariance? Or can we regard Einstein equations as the equations of gravitation in flat space-time?
We have answered why the structural form of Einstein equations is correct even if it is obtained from the geometric interpretation that people feel uncomfortable
Summary
General Relativity (GR) is widely accepted wherewith its graceful structures and elegance of its concepts, giving a description of gravitational phenomena in agreement with observation, it is rather disconcerting to note that the theory appears strikingly different from the present particle theory. The notions of energy and momentum play an important role in physics, while there is no widely accepted way to localize the energy and momentum of the gravitational field itself [2] Facing those disharmonies, a number of authors have discussed the utility of introducing the metric of flat background space-time into GR [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. Can we find a way to hold the structural form of Einstein equations, abandon the purely geometric interpretation of gravitation and make the equations global Lorentz invariance? The significance of the coordinates and the essence of the gravitational red-shift will be analyzed and elaborated
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