Detecting the environment around the supermassive black holes and tests of general relativity are important applications of extreme-mass-ratio inspirals(EMRIs).There is still a challenge to efficiently describe variou...Detecting the environment around the supermassive black holes and tests of general relativity are important applications of extreme-mass-ratio inspirals(EMRIs).There is still a challenge to efficiently describe various“dirty”impacts on the inspirals,such as dark matter,gas,dipole radiation,and electromagnetic interaction.In this study,we find the inherent linearity of the asymptotic solution of the inhomogeneous Teukolsky equation.On the basis of this property,we completely decouple the factors of the perturber and the background spacetime in the energy fluxes and waveforms.With the new decoupling form,the waveforms of EMRIs with non-geodesic motion in Kerr spacetime can be conveniently calculated.This will help to resolve the environment(including gas,field,dark matter,electromagnetic interaction)around supermassive black holes and test general relativity.展开更多
Extreme-mass-ratio inspirals(EMRIs)are among the most important sources for future spaceborne gravitational wave detectors.In this kind of system,compact objects usually orbit around central supermassive black holes o...Extreme-mass-ratio inspirals(EMRIs)are among the most important sources for future spaceborne gravitational wave detectors.In this kind of system,compact objects usually orbit around central supermassive black holes on complicated trajectories.Usually,these trajectories are approximated as the geodesics of Kerr space-times,and orbital evolution is simulated with the help of the adiabatic approximation.However,this approach omits the influence of the compact object on its background.In this paper,using the effective one-body formalism,we analytically calculate the trajectory of a nonspinning compact object around a massive Kerr black hole in an equatorial eccentric orbit(omitting the orbital inclination)and express the fundamental orbital frequencies in explicit forms.Our formalism includes the first-order corrections for the mass ratio in the conservative orbital motion.Furthermore,we insert the mass-ratio-related terms into the first post-Newtonian energy fluxes.By calculating the gravitational waves using the Teukolsky equations,we quantitatively reveal the influence of the mass of the compact object on the data analysis.We find that the shrinking of geodesic motion by taking small objects as test particles may not be appropriate for the detection of EMRIs.展开更多
基金supported by the National Key R&D Program of China(Grant No.2021YFC2203002)the National Natural Science Foundation of China(Grant No.12173071)。
文摘Detecting the environment around the supermassive black holes and tests of general relativity are important applications of extreme-mass-ratio inspirals(EMRIs).There is still a challenge to efficiently describe various“dirty”impacts on the inspirals,such as dark matter,gas,dipole radiation,and electromagnetic interaction.In this study,we find the inherent linearity of the asymptotic solution of the inhomogeneous Teukolsky equation.On the basis of this property,we completely decouple the factors of the perturber and the background spacetime in the energy fluxes and waveforms.With the new decoupling form,the waveforms of EMRIs with non-geodesic motion in Kerr spacetime can be conveniently calculated.This will help to resolve the environment(including gas,field,dark matter,electromagnetic interaction)around supermassive black holes and test general relativity.
基金NSFC No.11773059supported by MEXT,the JSPS Leading-edge Research Infrastructure Program,JSPS Grantin-Aid for Specially Promoted Research 26000005,JSPS Grant-in-Aid for Scientific Research on Innovative Areas 2905:JP17H06358,JP17H06361,and JP17H06364,JSPS Core-to-Core Program A.Advanced Research Networks,JSPS Grant-in-Aid for Scientific Research(S)17H06133,the joint research program of the Institute for Cosmic Ray Research,the University of Tokyothe Key Research Program of Frontier Sciences,CAS,No.QYZDB-SSWSYS016。
文摘Extreme-mass-ratio inspirals(EMRIs)are among the most important sources for future spaceborne gravitational wave detectors.In this kind of system,compact objects usually orbit around central supermassive black holes on complicated trajectories.Usually,these trajectories are approximated as the geodesics of Kerr space-times,and orbital evolution is simulated with the help of the adiabatic approximation.However,this approach omits the influence of the compact object on its background.In this paper,using the effective one-body formalism,we analytically calculate the trajectory of a nonspinning compact object around a massive Kerr black hole in an equatorial eccentric orbit(omitting the orbital inclination)and express the fundamental orbital frequencies in explicit forms.Our formalism includes the first-order corrections for the mass ratio in the conservative orbital motion.Furthermore,we insert the mass-ratio-related terms into the first post-Newtonian energy fluxes.By calculating the gravitational waves using the Teukolsky equations,we quantitatively reveal the influence of the mass of the compact object on the data analysis.We find that the shrinking of geodesic motion by taking small objects as test particles may not be appropriate for the detection of EMRIs.
