arXiv:0906.1366gr-qc
Relativistic theory of tidal Love numbers
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Abstract
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
The article is mainly about an interesting chapter in the history of the metre <https://en.wikipedia.org/wiki/History_of_the_metre#Meridiona...> which effectively won versus the second/metre pendulum approach (which was fiddly to calibrate and keep true for any given environment…
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