Gravitational Waves as Anisotropy of Space

Abstract

A binary star system, which has a mutual orbiting rotational speed of ω_b, produces a time-dependent anisotropy of space at an observer. The equation of geodesic deviation shows that the resulting anisotropy of space gives rise to a gravitational force between two mirrors, which form an interferometer, and that force is proportional to ω_b² times the anisotropy of space. Because 2π⁄ω_b is of the order of days or years, the rigidity k⁄m_o of the interferometer, where k is the force constant of a nongravitational force that supports the mirrors and m_o is the reduced mass of the mirrors, is much larger than ω_b². The amplitude of the vibrational motion of the interferometer with frequency ω_b (in terms of its equilibrium length) is given by (ω_b²⁄(k⁄m₀)) times the anisotropy of space. On the other hand, if we rotate the interferometer with an angular speed of ω of 1 radian/s or more, we can make k⁄m_o<ω², in which case the factor (ω_b²⁄(k⁄m_o)) disappears, and the rotating interferometer will be useful as a detector of the gravitational waves due to binary star systems.