Research on gravitational waves from extreme mass ratio inspirals in an axisymmetric Finslerian extension of Schwarzschild spacetime

Abstract

We investigate gravitational waves from extreme mass ratio inspirals in an axisymmetric Finslerian extension of the Schwarzschild spacetime. Its angular component is described by a two-dimensional Randers space, with the Schwarzschild limit recovered at Finslerian parameter $ε= 0$. This structure breaks spherical symmetry, causing generic orbits to undergo orbital plane precession. Using multipolar radiation reaction and adiabatic orbital averaging, we derive the leading order Finslerian corrections to the energy, axial angular momentum, and total angular momentum fluxes. These corrections enter at Newtonian order and take different forms. We then incorporate these corrections into a higher-order Schwarzschild hybrid flux model to evolve the orbital elements and construct waveforms at mass quadrupole order using the numerical kludge method. The Finslerian corrections affect both the conservative orbital dynamics and the dissipative inspiral, producing cumulative phase shifts relative to the Schwarzschild waveform. For the representative source observed by LISA over one year with signal-to-noise ratio of 20, the noise weighted mismatch analysis shows that Finslerian waveforms with $|ε| \gtrsim 2 \times 10^{-6}$ are distinguishable from their Schwarzschild counterparts, with higher initial eccentricities further lowering the distinguishable value of $|ε|$. For a Schwarzschild injection, the Fisher matrix analysis yields a marginalized $1σ$ uncertainty of $σ_ε\simeq 1.26 \times 10^{-6}$. These results show the potential of space-based gravitational wave detectors to probe the axisymmetric Finslerian extension of the Schwarzschild spacetime.