We derive a fully analytic Keplerian-type parametrization solution to conservative motion of spinning binary in ADM gauge. This solution is able to describe three dimensional motion of binaries of arbitrary eccentricity, mass ratio and initial configuration of spin angular momentum up to the leading order of post-Newtonian(PN) approximation and a linear order in spin. Based on our results waveforms can be quickly computed with high accuracy.
We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two non-spinning compact objects moving in an eccentric orbit. The orbital elements of the parametrization are explicitly given in terms of the 3PN accurate conserved orbital energy and angular momentum in both Arnowitt, Deser, and Misner-type and harmonic coordinates. Our representation will be required to construct post-Newtonian accurate `ready to use' search templates for the detection of gravitational waves from compact binaries in inspiralling eccentric orbits. Due to…
The angular and the radial parts of the dynamics of the perturbed Kepler motion are separable in many important cases. In this paper we study the radial motion and its parametrizations. We develop in detail a generalized eccentric anomaly parametrization and a procedure of computing a generic class of integrals based on the residue theorem. We apply the formalism to determine various contributions to the luminosity of a compact binary.
We analyze the relativistic dynamical properties of Keplerian and non-Keplerian circular orbits in a general axisymmetric and stationary gravitational field, and discuss the implications for the stability of co- and counter-rotating accretion disks and tori surrounding a spinning black hole. Close to the horizon there are orbital peculiarities which can seem counterintuitive, but are elucidated by formulating the dynamics in terms of the orbital velocity actually measured by a local, zero-angular-momentum observer.
We derive fourth post-Newtonian (4PN) contributions to the Keplerian-type parametric solution associated with the conservative dynamics of eccentric, non-spinning compact binaries. The solution has been computed while ignoring certain zero-average, oscillatory terms arising due to 4PN tail effects. We provide explicit expressions for the parametric solution and various orbital elements in terms of the conserved energy, angular momentum and symmetric mass ratio. Canonical perturbation theory (along with the technique of Pade approximant) is used to incorporate the 4PN nonlocal-in-time tail effe…
We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third post-Newtonian accurate conservative orbital dynamics influenced by the leading order spin effects, namely the leading order spin-orbit interactions. The orbital elements of the representation are explicitly given in terms of the conserved orbital energy, angular momentum and a quantity that characterizes the leading order spin-orbit interactions in Arnowitt, Deser…
The construction of a generic parametrization of spinning geometries which can be matched continuously to the Kerr metric is an important open problem in General Relativity. Its resolution is more than of academic interest, as it allows to parametrize and quantify possible deviations from the no-hair theorem. Various approaches to the problem have been proposed, all with their own (severe) limitations. Here we discuss the metric recently proposed by Johannsen and Psaltis, showing that (i) the original metric describes only corrections that preserve the horizon area-mass relation of nonspinning…
We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was designed mainly for toroids around spin-less black holes. We integrate numerically axial stationary Einstein equations with self-gravitating disks around spinless or spinning black holes; that includes the first ever integration of the Keplerian selfgravitating tori. This construction can be used for the description of tight black hole-torus systems produced during coalescences of two neutron stars or mo…
A couple of dozen Earth-like planets orbiting M dwarfs have been discovered so far. Some of them have attracted interest because of their potential long-term habitability; such a possibility is currently vigorously debated in the literature. I show that post-Keplerian (pK) orbit precessions may impact the habitability of a fictitious telluric planet orbiting an oblate late-type M dwarf of spectral class M9V with $M_\star=0.08\,M_\odot$ at $a=0.02\,\mathrm{au}$, corresponding to an orbital period $P_\mathrm{b}\simeq 4\,\mathrm{d}$, inducing long-term variations of the planetary obliquity $\vare…
We present a recently developed prescription to obtain ready-to-use gravitational wave (GW) polarization states for spinning compact binaries on hyperbolic orbits. We include leading order spin-orbit interactions, invoking 1.5PN-accurate quasi-Keplerian parametrization for the radial part of the orbital dynamics. We also include radiation reaction effects on $h_+$ and $h_{\times}$ during the interaction. In the GW signals from spinning binaries there is evidence of the memory effect in both polarizations, in contrast to the non-spinning case, where only the cross polarizations exhibits non-van…
The secular evolution of a spinning, massive binary system in eccentric orbit is analyzed, expanding and generalizing our previous treatments of the Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin effects up to the 3/2 post-Newtonian order are considered, both in the equations of motion and in the radiative losses. The description of the orbit in terms of the true anomaly parametrization provides a simple averaging technique, based on the residue theorem, over eccentric orbits. The evolution equations of the angle variables characterizing the relative orientation of …
We review a recently proposed approach to construct gravitational wave (GW) polarization states of unbound spinning compact binaries. Through this rather simple method, we are able to include corrections due to the dominant order spin-orbit interactions, in the quadrupolar approximation and in a semi-analytic way. We invoke the 1.5 post-Newtonian (PN) accurate quasi-Keplerian parametrization for the radial part of the dynamics and impose its temporal evolution in the PN accurate polarization states equations. Further, we compute 1PN accurate amplitude corrections for the polarization states of…
Compact binaries in hyperbolic orbits are plausible gravitational wave (GW) sources for the upcoming and planned GW observatories. We develop an efficient prescription to compute post-Newtonian (PN) accurate ready-to-use GW polarization states for spinning compact binaries, influenced by the dominant order spin-orbit interactions, in hyperbolic orbits. This is achieved by invoking the 1.5PN accurate quasi-Keplerian parameterization for the radial sector of the orbital dynamics. We probe the influences of spins and gravitational radiation reaction on $h_+$ and $h_{\times}$ during the hyperbolic…
The evolution under radiation backreaction of a binary system consisting of a black hole and a companion is studied in the limiting case when the spin of the companion is negligible compared with the spin S of the black hole. To first order in the spin, the motion of the reduced-mass particle excluding radiation effects, is characterized by three constants: the energy E, the magnitude L of the angular momentum and the projection L_S of the angular momentum along the spin S. This motion is quasiperiodic with a period determined by r_{min} and r_{max}. We introduce a new parametrization, making …
We investigate the motion of massive charged and spinning test particles around a charged dyonic black hole spacetime surrounded by perfect fluid scalar dark matter field. We obtain the equations of motion and find the expressions for the four-velocity for the case of a charged particle, and four-momentum components for the case of a spinning particle. The trajectories for various values of electric $Q_{e}$ and magnetic $Q_{m}$ charges are investigated under the influence of dark matter field $λ$. We find the equations of motion of a spinning particle that follows a non-geodesic trajectory via…
We analyzed the thermodynamics of hypothetical exoplanets at very low Keplerian circular orbits in close vicinity of rapidly spinning supermassive black holes. Such black hole exoplanets are heated by strongly blueshifted and focused flux of the incoming cosmic microwave background (CMB) and cooled by the cold part of the local sky containing the black hole shadow. This gives rise to a temperature difference, which can drive processes far from thermodynamic equilibrium in a hypothetical life form inhabiting black hole exoplanets, similar to the case of a planet heated by the radiation of the p…
We compute the third post-Newtonian (3PN) accurate instantaneous contributions to the radiated gravitational wave (GW) energy and angular momentum arising from the hyperbolic passages of non-spinning compact objects. The present computations employ 3PN-accurate instantaneous contributions to the far-zone energy and angular momentum fluxes and the 3PN-accurate Keplerian type parametric solution for compact binaries in hyperbolic orbits.
We formally show that the conservative second post-Newtonian (PN) accurate dynamics of spinning compact binaries moving in eccentric orbits, when spin effects are restricted to the leading order spin-orbit interaction cannot be chaotic for the following two distinct cases: (i) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin and (ii) the binary consists of equal mass compact objects, having two arbitrary spins. We rest our arguments on the recent determination of PN accurate Keplerian-type parametric solutions to the above case…
We study r-mode instability of rotating compact objects composed of asymmetric and self-interacting Fermionic dark matter (dark stars). It is argued that the instability limit the angular frequency of the stars less than half of the Keplerian frequency. This may constrain the stars as alternatives to fast spinning pulsars or rapidly rotating Kerr black holes.
The second post-Newtonian (2PN) contribution to the `plus' and `cross' gravitational wave polarizations associated with gravitational radiation from non-spinning, compact binaries moving in elliptic orbits is computed. The computation starts from our earlier results on 2PN generation, crucially employs the 2PN accurate generalized quasi-Keplerian parametrization of elliptic orbits by Damour, Schäfer and Wex and provides 2PN accurate expressions modulo the tail terms for gravitational wave polarizations incorporating effects of eccentricity and periastron precession.
Several scenarios have been proposed in which the orbits of binary black holes enter the band of a gravitational wave detector with significant eccentricity. To avoid missing these signals or biasing parameter estimation it is important that we consider waveform models that account for eccentricity. The ingredients needed to compute post-Newtonian (PN) waveforms produced by spinning black holes inspiralling on quasi-eccentric orbits have been available for almost two decades at 2 PN order, and this work has recently been extended to 2.5 PN order. However, the computational cost of directly imp…
We derive from first principles third post-Newtonian (3PN) accurate Keplerian-type parametric solution to describe PN-accurate dynamics of non-spinning compact binaries in hyperbolic orbits. Orbital elements and functions of the parametric solution are obtained in terms of the conserved orbital energy and angular momentum in both Arnowitt-Deser-Misner type and modified harmonic coordinates. Elegant checks are provided that include a modified analytic continuation prescription to obtain our independent hyperbolic parametric solution from its eccentric version. A prescription to model gravitatio…
In a previous work we showed that spin can be envisioned as living in a phase space that is dual to the standard phase space of position and momentum. In this work we demonstrate that the second class constraints inherent in this "Dual Phase Space" picture can be solved by introducing a spinorial parameterization of the spinning degrees of freedom. This allows for a purely first class formulation that generalizes the usual relativistic description of spinless particles and provides several insights into the nature of spin and its relationship with spacetime and locality. In particular, we find…
We provide an elegant way of solving analytically the third post-Newtonian (3PN) accurate Kepler equation, associated with the 3PN-accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits. An additional analytic solution is presented to check the correctness of our compact solution and we perform comparisons between our PN-accurate analytic solution and a very accurate numerical solution of the PN-accurate Kepler equation. We adapt our approach to compute crucial 3PN-accurate inputs that will be required to compute analytically both the time and frequency d…
The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also a next-to-leading order effect in the phase of gravitational waves emitted by extreme-mass-ratio inspirals (EMRIs), which are expected to become observable by the LISA space mission. Additionally, exploring the Hamiltonian formalism for spinning bodies is important for the construction of the so-called Effective-One-Body waveform models that should eventuall…
We present numerical simulations of binary neutron star mergers, comparing irrotational binaries to binaries of NSs rotating aligned to the orbital angular momentum. For the first time, we study spinning BNSs employing nuclear physics equations of state, namely the ones of Lattimer and Swesty as well as Shen, Horowitz, and Teige. We study mainly equal mass systems leading to a hypermassive neutron star (HMNS), and analyze in detail its structure and dynamics. In order to exclude gauge artifacts, we introduce a novel coordinate system used for post-processing. The results for our equal mass mod…
Compact binaries consisting of neutron stars / black holes on eccentric orbit undergo a perturbed Keplerian motion. The perturbations are either of relativistic origin or are related to the spin, mass quadrupole and magnetic dipole moments of the binary components. The post-Newtonian motion of such systems decouples into radial and angular parts. We present here for the first time the radial motion of such a binary encoded in a generalized Kepler equation, with the inclusion of all above-mentioned contributions, up to linear order in the perturbations. Together with suitably introduced paramet…
The dynamics of a binary system with two spinning components on an eccentric orbit is studied, with the inclusion of the spin-spin interaction terms appearing at the second post-Newtonian order. A generalized true anomaly parametrization properly describes the radial component of the motion. The average over one radial period of the magnitude of the orbital angular momentum $\bar{L}$ is found to have no nonradiative secular change. All spin-spin terms in the secular radiative loss of the energy and magnitude of orbital angular momentum are given in terms of $\bar{L}$ and other constants of the…
Black-hole spectroscopy is arguably the most promising tool to test gravity in extreme regimes and to probe the ultimate nature of black holes with unparalleled precision. These tests are currently limited by the lack of a ringdown parametrization that is both robust and accurate. We develop an observable-based parametrization of the ringdown of spinning black holes beyond general relativity, which we dub ParSpec (Parametrized Ringdown Spin Expansion Coefficients). This approach is perturbative in the spin, but it can be made arbitrarily precise (at least in principle) through a high-order exp…
We compute here the spin-orbit and spin-spin couplings needed for an accurate computation of the phasing of gravitational waves emitted by comparable-mass binaries on eccentric orbits at the second post-Newtonian (PN) order. We use a quasi-Keplerian parametrization of the orbit free of divergencies in the zero eccentricity limit. We find that spin-spin couplings induce a residual eccentricity for coalescing binaries at 2PN, of the order of $10^{-4}$-$10^{-3}$ for supermassive black hole binaries in the LISA band. Spin-orbit precession also induces a non-trivial pattern in the evolution of the …
A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin orbit and 1PN spin-spin contributions, where the spins are counted …
Individual supermassive black hole binaries in non-circular orbits are possible nanohertz gravitational wave sources for the rapidly maturing Pulsar Timing Array experiments. We develop an accurate and efficient approach to compute Pulsar Timing Array signals due to gravitational waves from inspiraling supermassive black hole binaries in relativistic eccentric orbits. Our approach employs a Keplerian-type parametric solution to model third post-Newtonian accurate precessing eccentric orbits while a novel semi-analytic prescription is provided to model the effects of quadrupolar order gravitati…
The radiation reaction in compact spinning binaries on eccentric orbits due to the quadrupole-monopole interaction is studied. This contribution is of second post-Newtonian order. As result of the precession of spins the magnitude $L$ of the orbital angular momentum is not conserved. Therefore a proper characterization of the perturbed radial motion is provided by the energy $E$ and angular average $\bar{L}$. As powerful computing tools, the generalized true and eccentric anomaly parametrizations are introduced. Then the secular losses in energy and magnitude of orbital angular momentum togeth…
High-Post-Newtonian-Order Dynamics Induced by Tail-of-Tail Interactions: The Non-Geodesic Terms
School of Physics and Astronomy, University of Birmingham（伯明翰大学物理与天文学院）；Institute for Gravitational Wave Astronomy, University of Birmingham（伯明翰大学引力波天文研究所）
We use an effective field theory (EFT) approach to calculate the next to leading order (NLO) gravitational spin-orbit interaction between two spinning compact objects. The NLO spin-orbit interaction provides the most computationally complex sector of the NLO spin effects, previously derived within the EFT approach. In particular, it requires the inclusion of non-stationary cubic self-gravitational interaction, as well as the implementation of a spin supplementary condition (SSC) at higher orders. The EFT calculation is carried out in terms of the non-relativistic gravitational field parametriz…
