Abstract
In the general theory of relativity, the fundamental metric tensor plays a special role, which has its physical basis in the peculiar aspects of gravitation. The fundamental property of gravitational fields provides the possibility of establishing an analogy between the motion in a gravitational field and the motion in any external field considered as a noninertial system of reference. Thus, the properties of the motion in a noninertial frame are the same as those in an inertial system in the presence of a gravitational field. In other words, a noninertial frame of reference is equivalent to a certain gravitational field. This is known as the principle of equivalence. From the mathematical viewpoint, the same special role can be played by the small deformation strain tensor, which describes the geometrical properties of any region deformed because of the effect of some external agent. It can be proved that, from that tensor, all the mathematical structures needed in the general theory of relativity can be constructed.
Highlights
Within the theoretical frame of classical fluid dynamics, the effect of applied forces to any continuous medium is studied
When the deformation is the result of a process of hydrostatic or volumetric compression or expansion, the small deformation strain tensor is reduced to the sum of the elements of its principal diagonal, that is, its trace
In order to get the physical significance of the fundamental tensor fields uμυ and gμυ, let us consider a region of space-time in which the gravitational field vanishes
Summary
Within the theoretical frame of classical fluid dynamics, the effect of applied forces to any continuous medium is studied. Under the action of applied forces, the region occupied by the continuous medium exhibits deformations to some extent, that is to say, the region changes in shape and volume. Those deformations can be described mathematically by the small deformation strain tensor. When the deformation is the result of a process of hydrostatic or volumetric compression or expansion, the small deformation strain tensor is reduced to the sum of the elements of its principal diagonal, that is, its trace This trace is likewise in this case, the fractional change of the volume element of the region occupied by the continuous medium. That characteristic property of the matter is contained in that tensor [1]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
