Abstract
It is proved that accelerating nondiffracting gravitational Airy wave-packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non-accelerating nondiffracting gravitational wave-packets.
Highlights
Nondiffracting wave-packets are known solutions to Schrödinger equation [1,2] and Maxwell equations [3,4], and several experimental studies have been dedicated to them [3,4,5,6,7,8,9,10,11]
In Ref. [12] it is established that the usual dispersion relation for massless fields kμkμ = 0 is valid only when the Bohm potential associated to the solution vanishes, but otherwise the modified right-hand side is exactly equal to the Bohm potential, which may be either positive or negative
Exact nondiffracting gravitational waves can be obtained from a modification of Ehlers– Kundt solution [36,37]
Summary
Nondiffracting wave-packets are known solutions to Schrödinger equation [1,2] and Maxwell equations [3,4], and several experimental studies have been dedicated to them [3,4,5,6,7,8,9,10,11]. The nondiffracting accelerating gravitational wavepacket is the real part of full solution (2). Structured nondiffracting gravitational Airy wavepackets with finite energy can be constructed using Gaussian beams [39,45,46]. The finite energy gravitational Airy wavepacket is given by. In red solid lines we display the evolution of the position of the maxima lobe, that moves in a curved trajectory, displaying its acceleration in such plane
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