Towards a Theory of Spacetime Theories by Dennis Lehmkuhl Gregor Schiemann & Erhard Scholz

Author:Dennis Lehmkuhl, Gregor Schiemann & Erhard Scholz
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(14)

This is the new type of Einstein elevator. In GR, the Einstein elevator was described by a holonomic reference frame with . Then, in the Riemann spacetime of GR, one could introduce Riemannian normal coordinates. Here, in the gauge theoretical approach, the constraint of holonomicity is dropped and this new degree of freedom, which expresses itself in a rotational acceleration, admits to introduce normal frames. The equivalence principle can then be applied in this new context. For new developments of this notion, see Nester [34] and Giglio and Rodrigues [35].

As soon as we require in a metric-affine space integrability of length and angle measurements, we have to postulate6 . Then we arrive at a Riemann–Cartan space (RC-space), which was mentioned in the context of the gauging of the Poincaré group in Sec. 3. In such a space, if we choose orthonormal frames, the connection becomes antisymmetric; then we have the potentials as gravitational variables. Again normal frames like in (14) can be found

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