Vibrating Systems in Schwarzschild Spacetime: Towards a New Test of General Relativity?

Astronomy and Astrophysics – Astronomy

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Changing the shape of a free falling body in a gravitational field can induce a change in its motion. Such effects are well known and have been proposed in space technology for propellentless propulsion. In Newtonian physics, two-body systems (two spacecrafts connected by a tether) orbiting a central mass have been studied. Once-per-orbit modulations of the tether length may be used to change the orbit of the system.
In the present communication, we consider the problem in the framework of general relativity. More precisely, we will study the free fall of an oscillating two body systems, whereby we will focus on a radial free fall towards a central body and on a circular orbit around a central body. We will show that in general relativity, there are new effects that are not present in Newtonian physics.
Starting from the work by Guéron and Mosna [1], we will show that it is possible to slow down or to accelerate a radially free falling body. Further properties of this effect will be discussed [2].
In the circular case, we will show that the vibrating system changes its orbit according to a purely relativistic deviation [3]. This deviation increases with the distance to the central body and thus might be observed in low gravity fields in the Solar System. This can lead to a new test of general relativity. Promising systems to measure this effect are small systems with a high vibrational frequency. As a simple but realistic example, we will present simulations based on molecular vibrations.
[1] E.Guéron and R.A.Mosna, "The relativistic glider", PRD7(2007)081501
[2] L.Bergamin, P.Delva, A.Hees, "Vibrating systems in Schwarzschild spacetime: I-The radial fall", submitted to PRD, gr-qc/0901.2298
[3] L.Bergamin, P.Delva, A.Hees, "Vibrating systems in Schwarzschild spacetime: II-The quasi-circular orbit", submitted to PRD, gr-qc/0901.2306

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