Reduced one-body density matrix of Tonks-Girardeau gas at finite temperature

With thermal Bose–Fermi mapping method, we investigate the Tonks–Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increase in temperature, the Tonks gas distributes in wider region. The reduced one-body density matrix is diagonal dominant in the whole temperature region, and the off-diagonal elements shall vanish rapidly with the deviation from the diagonal part at high temperature.

Energy flux and waveforms by coalescing spinless binary system in effective one-body theory

We present a study on the energy radiation rate and waveforms of the gravitational wave generated by coalescing spinless binary systems up to the third post-Minkowskian approximation in the effective one-body theory.To derive an analytical expansion of the null tetrad components of the gravitational perturbed Weyl tensorΨ4in the effective spacetime,we utilize the method proposed by Sasaki et al.During this investigation,we discover more general integral formulas that provide a theoretical framework for computing the results in any order.Subsequently,we successfully compute the energy radiation rate and waveforms of the gravitational wave,which include the results of the Schwarzschild case and the correction terms resulting from the dimensionless parameters a2and a3in the effective metric.

Analytical effective one-body formalism for extreme-mass-ratio inspirals with eccentric orbits

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.

Gravitational-wave equation in effective one-body background for spinless binary

The effective one-body method provides a framework to apply the black hole perturbation theory to the binary system where two masses can be comparable.We study the gravitational-wave equation in the background of the effective one-body system for the spinless binary,which is in general available with the spherically symmetric background as well.We obtain the gauge conditions for the decoupled wave equation,and also give the solutions to the gauge conditions in terms of the metric perturbation for a special case,which extends the result by Jing et al.(Sci.China-Phys.Mech.Astron.65,260411(2022)).Finally we obtain the gravitational-wave equation which is the generalization of the Teukolsky equation.

New self-consistent effective one-body theory for spinless binaries based on the post-Minkowskian approximation

The effective one-body theories, introduced by Buonanno and Damour, are novel approaches to constructing a gravitational waveform template. By taking a gauge in which ψ_(1)^(B) and ψ_(3)^(B) vanish, we find a decoupled equation with separable variables for ψ_(4)^(B) in the effective metric obtained in the post-Minkowskian approximation. Furthermore, we set up a new self-consistent effective one-body theory for spinless binaries, which can be applicable to any post-Minkowskian orders. This theory not only releases the assumption that v/c should be a small quantity but also resolves the contradiction that the Hamiltonian, radiation-reaction force, and waveform are constructed from different physical models in the effective one-body theory with the post-Newtonian approximation. Compared with our previous theory [Sci. China-Phys. Mech. Astron. 65, 260411(2022)], the computational effort for the radiation-reaction force and waveform in this new theory will be tremendously reduced.

Teukolsky-like equations with various spins in spherically symmetric spacetime

We study wave equations with various spins on the background of a general spherically symmetric spacetime.We obtain the unified expression of the Teukolsky-like master equations and the corresponding radial equations with the general spins.We also discuss the gauge dependence in the gravitational-wave equations,which have appeared in previous studies.