Interferometers...: Testing Relativistic Gravity in Space by David P. Landau, Kurt Binder

By David P. Landau, Kurt Binder

Complaints of a gathering on Gyros, Clocks, Interferometers...: checking out common Relativity in house, held in undesirable Honnef from August 21-27, 1999. issues coated contain the Lense-Thirring impact, the detection of gravitational waves, trying out the equivalence precept, electromagnetic box and gravity, and clocks and rods in gravitational fields.

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1. In the neighborhood of that central particle there are two other point particles equipped with a mirror. At first, the central point particle emits a flash of light which hits the auxilary point particles. These auxilary point particles reflect this flash of u light in such a way that it again meets the central point particle and, in addition, the other auxilary particle positioned appropriately behind the cenl1 l2 tral particle. Then the auxilarty particles again reflect the flash of light so that it again meets the central particle and the other auxilary particle, and auxilary particle auxilary particle central particle so on, see Fig.

For a stationary gravitational field this means g(x) = g(x1 , x2 , x3 ) and, if the The Lense–Thirring Effect 41 ∗ gravitational field possesses an additional axial symmetry, then g(x) = g(x1 , x3 ), where x0 plays the role of the time coordinate and x2 the role of the angle ϕ. Therefore ds2 = gµν (x1 , x3 )dxµ dxν . If we choose x1 = ρ and x3 = ϑ, then ∗ ds2 = g00 (ρ, ϑ) dt2 + 2g0i (ρ, ϑ) dt dxi + gij (ρ, ϑ) dxi dxj . (56) We call a gravitational field static if the rotation of the time–like Killing congruence vanishes (cf.

F. W. ): LNP 562, pp. 31–51, 2001. c Springer-Verlag Berlin Heidelberg 2001 32 C. L¨ ammerzahl and G. Neugebauer ν with the Christoffel symbol { µσ } := 12 g νρ (∂µ gρσ + ∂σ gρµ − ∂ρ gµσ ). We do not assume any normalization condition of the 4–velocity. Light rays with tangents l obey the same equation of motion (1), but with the additional condition g(l, l) = 0. – In addition, we will assume Einstein’s field equations. 2 Rotation In order to define the notion of rotation, we use the so–called zig–zag construction, or the bouncing photon, as introduced by Pirani [1].

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