Tidal forces are gravitational waves. (arXiv:1912.00591v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Goswami_R/0/1/0/all/0/1">Rituparno Goswami</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Ellis_G/0/1/0/all/0/1">George F. R. Ellis</a>
In this paper we show in a covariant and gauge invariant way that in general
relativity, tidal forces are actually a hidden form of gravitational waves.
This must be so because gravitational effects cannot occur faster than the
speed of light. Any two body gravitating system, where the bodies are orbiting
around each other, may generate negligible gravitational waves, but it is via
these waves that non-negligible tidal forces (causing shape distortions) act on
these bodies. Although the tidal forces are caused by the electric part of the
Weyl tensor, we transparently show that some small time varying magnetic part
of the Weyl tensor with non zero curl must be present in the system that
mediates the tidal forces via gravitational wave type effects. The outcome is a
new test of whether gravitational effects propagate at the speed of light.
In this paper we show in a covariant and gauge invariant way that in general
relativity, tidal forces are actually a hidden form of gravitational waves.
This must be so because gravitational effects cannot occur faster than the
speed of light. Any two body gravitating system, where the bodies are orbiting
around each other, may generate negligible gravitational waves, but it is via
these waves that non-negligible tidal forces (causing shape distortions) act on
these bodies. Although the tidal forces are caused by the electric part of the
Weyl tensor, we transparently show that some small time varying magnetic part
of the Weyl tensor with non zero curl must be present in the system that
mediates the tidal forces via gravitational wave type effects. The outcome is a
new test of whether gravitational effects propagate at the speed of light.
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