Gravitational clock compass and the detection of gravitational waves

Abstract

We present an alternative derivation of the gravitational clock compass and show how such a device can be used for the detection of gravitational waves. Explicit compass setups are constructed in special types of space-times, namely for exact plane gravitational waves and for waves moving radially relative to an observer.

Extended gravitational clock compass: new exact solutions and simulations

“…where (n) C is the value of the function given by (3) evaluated at the position (n) y α and the velocity (n) v α . In order to determine the linear acceleration we use 3 pairs of clocks at opposite positions, namely ( (1) y α , (7) y α ), ( (2) y α , (8) y α ) and ( (3) y α , (9) y α ). This yields a set of equations which can be used to solve for a α leading, in terms of the C's, to…”

“…If we set the velocities of the clocks to zero, we obtain a 1 = 1 4y 11 (1) C − (7) C , a 2 = 1 4y 22 (2) C − (8) C ,…”

“…This is achieved by considering pairs of clocks located along each axis and choosing velocities with opposite direction, perpendicular to their position vectors. Hence, the initial conditions for the 6 clocks are chosen as follows: the first 3 are located at (1) y α , (2) y α , and (3) y α as defined in (7), with velocities perpendicular to each position vector, i.e. we choose (1)…”

“…. , 6) in (7), with all distances set to equal values, i.e. y 11 = y 22 = y 33 = y 41 = y 42 = y 52 = y 52 = y 61 = y 63 = y.…”

“…This method has been developed in [1,5] and can be viewed as complementary to the use of deviation equations [6] and swarms of test bodies. An alternative derivation of the clock compass and its use in the context of exact gravitational wave spacetimes can be found in [7].…”