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We propose a covariant definition of standing gravitational waves in general relativity. 1 The same year the problem of gravitational standing waves was investigated by Sir Hermann Bondi in his last paper on general relativity [2]. Standing waves appear naturally in some quasistationary approximations in binary black holes inspirals -an approach introduced by Detweiler [3] and pursued by Price [4] and others [5][6][7][8][9][10].

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The theory of Schwarzschild timelike geodesics is revisited. Basing on a result by Weierstrass and Biermann, we derive a formula describing all non radial, time-like trajectories in terms of Weierstrass elliptic functions. Quite remarkably, a single formula works for an entire geodesic trajectory, even if it passes through turning points. Using this formula, we derive expressions for the proper and coordinate time along the geodesic.