Introducing Tensors to physics students

Physical Review D, 2015

We study Weitzenböck's torsion and discuss its properties. Specifically, we calculate the measured components of Weitzenböck's torsion tensor for a frame field adapted to static observers in a Fermi normal coordinate system that we establish along the world line of an arbitrary accelerated observer in general relativity. A similar calculation is carried out in the standard Schwarzschild-like coordinates for static observers in the exterior Kerr spacetime; we then compare our results with the corresponding curvature components. Our work supports the contention that in the extended general relativistic framework involving both the Levi-Civita and Weitzenböck connections, curvature and torsion provide complementary representations of the gravitational field.

In most sciences one generation tears down what another has built and what one has established another undoes. In Mathematics alone each generation builds a new story to the old structure. – HERMAN HANKEL

Scalars are those quantities which can be defined by a single number. It just tells you how much of something there is. For example, if someone says that the temperature is 32 C o then it means that something is 32 units hotter on a temperature scale or if you say something is moving at a speed of 45 km/h then it means that the object is covering 45 km in an hour, regardless of its direction. Other examples of scalar quantities are, energy, work done, electrical resistance etc. A scalar quantity is only represented by a letter or a symbol.