Abstract
We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a suitable boundary value problem. This puts on solid ground previous approximate calculations. We find consistency with previous results obtained from eikonal expansions at the level of accuracy accessible to current gravitational wave detectors.
Highlights
The geometric optics equations arise at first order in eikonal expansions, where one explicitly introduces a frequency parameter ω and an eikonal function ψ, seeking solutions possessing a series expansion of the amplitude in inverse powers of ω [13]. The validity of such high-frequency approximations in the considered context has been questioned in [14], and some previous attempts to obtain formulae applicable for all incidence angles of the gravitational wave have led to expressions which are undefined if the gravitational waves (GWs) propagates parallelly to one of the interferometer arms [15, 16]
We confirm that a calculation of the interference pattern based on eikonal expansions, and on geometric optics, is consistent with Maxwell equations within the model analysed here, and provides the key information needed for current experiments
If there exists a corresponding solution of the Maxwell equations, this solution is unique and independent of the coordinates by an identical argument
Summary
Interferometric gravitational wave detectors are the only instruments so far that have been able to directly detect gravitational waves (GWs). The geometric optics equations arise at first order in eikonal expansions, where one explicitly introduces a frequency parameter ω and an eikonal function ψ, seeking solutions possessing a series expansion of the amplitude in inverse powers of ω [13] The validity of such high-frequency approximations in the considered context has been questioned in [14], and some previous attempts to obtain formulae applicable for all incidence angles of the gravitational wave have led to expressions which are undefined if the GW propagates parallelly to one of the interferometer arms [15, 16]. We confirm that a calculation of the interference pattern based on eikonal expansions, and on geometric optics, is consistent with Maxwell equations within the model analysed here, and provides the key information needed for current experiments.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
