Pound-Rebka experiment and torsion in the Schwarzschild spacetime

Details Pound-Rebka experiment and torsion in the Schwarzschild spacetime Pound-Rebka experiment and torsion in the Schwarzschild spacetime

2009-03-14

arxiv.org/abs/0903.2565v2

Phys. Rev. D 80, 044036 (2009)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, two figures, one typo fixed, one paragraph added in section 5

Scientific paper

10.1103/PhysRevD.80.044036

We develop some ideas discussed by E. Schucking [arXiv:0803.4128] concerning the geometry of the gravitational field. First, we address the concept according to which the gravitational acceleration is a manifestation of the spacetime torsion, not of the curvature tensor. It is possible to show that there are situations in which the geodesic acceleration of a particle may acquire arbitrary values, whereas the curvature tensor approaches zero. We conclude that the spacetime curvature does not affect the geodesic acceleration. Then we consider the the Pound-Rebka experiment, which relates the time interval $\Delta \tau_1$ of two light signals emitted at a position $r_1$, to the time interval $\Delta \tau_2$ of the signals received at a position $r_2$, in a Schwarzschild type gravitational field. The experiment is determined by four spacetime events. The infinitesimal vectors formed by these events do not form a parallelogram in the (t,r) plane. The failure in the closure of the parallelogram implies that the spacetime has torsion. We find the explicit form of the torsion tensor that explains the nonclosure of the parallelogram.

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