Relativistic experiments in the space–time of an earth-fixed rotating observer in the weak-field slow-rotation Kerr background

We use the weak field and slow rotation limit of the Kerr metric for the space–time around the Earth. Then, by applying rotational transformations to it, we investigate some relativistic experiments such as the Lense–Thirring effect and the Sagnac effect around the Earth in the frame of an Earth-Fixed rotating observer. We calculate the general relativistic corrections and separate the contribution of the corrections due to the mass and angular momentum of the Earth from the contribution of the corrections due to the coordinate transformation of the rotating observer. We also compare the order of magnitude of correction terms. We compare the results with the situation where the Schwarzschild metric is used to evaluate these experiments around the Earth.