Abstract
We study collective features of the scattering of gravitational waves on relic wormholes and normal matter objects. We derive and solve the GW energy transport equation and show that the scattered signal lies in the same frequency spectrum bands as the basic signal. The scattering forms long living tails which always accompany the basic signal and have a universal form. The scattering on normal matter objects forms tails which have always the retarded character, while wormholes lead to advanced tails as well. In addition, wormholes may produce considerably stronger effect when the total energy in tails detected on the Earth exceeds that in the incident direct wave. In both cases the retarding tails have a long living character when the mean amplitude behaves with time as hsim 1/sqrt{t+R/c}. For a single GW event the echo tails give only a tiny contribution to the mean amplitude. However such tails accumulate with events and form a stochastic GW background which may be observed by the contribution to the noise.
Highlights
To avoid misunderstanding we point out that the echoes generated by the scattering of GWs have much bigger timescales as compared to the near-horizon or other strong field effects discussed in [8,9,10]
We study collective features of the scattering of gravitational waves on relic wormholes and normal matter objects
The typical timescale for echoes in the case of near-horizon effects has the order δt ∼ M, where M is the mass of a compact object and some small parameter which determines the closeness of the object to a black hole, e.g., see details in [10]
Summary
To avoid misunderstanding we point out that the echoes generated by the scattering of GWs have much bigger timescales as compared to the near-horizon or other strong field effects discussed in [8,9,10]. In the case of scattering the typical value has the order δt ∼ s R/c, where R is the distance to the source, c is the speed of light, and, in general situation, a parameter s is not even small In this sense the detected echoes have no the direct relation to effects discussed in our paper. There is no any rigorous experimental evidence for the existence of exotic forms of matter, or for the presence of any modification of general relativity (we leave aside possible quantum corrections which work only in the quasi-classical region, e.g., at Planck scales) This means that the approximation of spherical throats should be very rough. Priate metric in [20,21]) and construct the map of geodesic lines at boundaries for a spherical wormhole
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