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LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

In this paper, we investigate the dynamics of a binary system that orbits a rotating supermassive black hole. Our approach employs Fermi-Walker transport to construct a local inertial reference frame, and to set up a Newtonian binary system. We consider a scenario in which a circular geodesic observer is positioned around a Kerr black hole, and thereby derive the equations of motion governing the binary system. To eliminate the interaction terms between the center of mass (CM) of the binary and its relative coordinates, we introduce a small acceleration for the observer. This adjustment leads to the CM closely following the observer's orbit, deviating from a circular geodesic. Here, we first focus on elucidating the stability conditions in a hierarchical triple system. Subsequently, we discuss the phenomenon of von Zeipel-Lidov-Kozai (vZLK) oscillations, which manifest when the binary system is compact and the initial inclination exceeds a critical angle. In hard binary systems, these oscillations exhibit regular behavior, while in soft binary systems, they exhibit a chaotic character, characterized by irregular periods and amplitudes, albeit remaining stable. Additionally, we observe an orbital flip under circumstances of large initial inclination. As for the motion of the CM, we observe deviations from a purely circular orbit that transform into stable yet chaotic oscillations characterized by minute amplitude variations., Comment: 32 pages, 18 figures. arXiv admin note: substantial text overlap with arXiv:2303.16553

We discuss motion of a binary system around a supermassive black hole. Using Fermi-Walker transport, we construct a local inertial reference frame and set up a Newtonian binary system. Assuming a circular geodesic observer around a Schwarzschild black hole, we write down the equations of motion of a binary. Introducing a small acceleration of the observer, we remove the interaction terms between the center of mass (CM) of a binary and its relative coordinates. The CM follows the observer's orbit, but its motion deviates from an exact circular geodesic. We first solve the relative motion of a binary system, and then find the motion of the CM by the perturbation equations with the small acceleration. We show that there appears the Kozai-Lidov (KL) oscillations when a binary is compact and the initial inclination is larger than a critical angle. In a hard binary system, KL oscillations are regular, whereas in a soft binary system, oscillations are irregular both in period and in amplitude, although stable. We find an orbital flip when the initial inclination is large. As for the motion of the CM, the radial deviations from a circular orbit become stable oscillations with very small amplitude., Comment: 34 pages,12 figures, 2 tables

Extreme-mass-ratio inspirals (EMRIs) are promising target sources for space-based interferometers such as LISA, Taiji, and Tianqin. Depending on the astrophysical environment, such as close perturbers or an accretion disk, EMRI orbital evolution may deviate from the predictions of general relativity in vacuum. In particular, we focus on the resonance jumps, i.e., the changes of the conserved quantities induced by a stationary perturbation to the background Kerr geometry. Using Hamiltonian formulation, we provide a closed relation between the jump in Carter constant and that in the axial component of angular momentum. It is also shown that the obtained relation is consistent with the fitting formulae computed for the tidal resonance in previous works., Comment: 9 pages, 1 figure, submitted to Class. Quantum Grav

Extreme-mass-ratio inspirals are one of the most exciting and promising target sources for space-based interferometers (such as LISA, TianQin). The observation of their emitted gravitational waves will offer stringent tests on general theory of relativity, and provide a wealth of information about the dense environment in galactic centers. To unlock such potential, it is necessary to correctly characterize EMRI signals. However, resonances are a phenomena that occurs in EMRI systems and can impact parameter inference, and therefore the science outcome, if not properly modeled. Here, we explore how to model resonances and develop an efficient implementation. Our previous work has demonstrated that tidal resonances induced by the tidal field of a nearby astrophysical object alters the orbital evolution, leading to a significant dephasing across observable parameter space. Here, we extensively explore a more generic model for the tidal perturber with additional resonance combinations, to study the dependence of resonance strength on the intrinsic orbital and tidal parameters. To analyze the resonant signals, accurate templates that correctly incorporate the effects of the tidal field are required. The evolution through resonances is obtained using a step function, whose amplitude is calculated using an analytic interpolation of the resonance jumps. We benchmark this procedure by comparing our approximate method to a numerical evolution. We find that there is no significant error caused by this simplified prescription, as far as the astronomically reasonable range in the parameter space is concerned. Further, we use Fisher matrices to study both the measurement precision of parameters and the systematic bias due to inaccurate modeling. Modeling of self-force resonances can also be carried out using the implementation presented in this study, which will be crucial for EMRI waveform modeling., Comment: 18 pages, 14 figures

Extreme mass ratio inspirals (EMRIs) will be important sources for future space-based gravitational-wave detectors. In recent work, tidal resonances in binary orbital evolution induced by the tidal field of nearby stars or black holes have been identified as being potentially significant in the context of extreme mass-ratio inspirals. These resonances occur when the three orbital frequencies describing the orbit are commensurate. During the resonance, the orbital parameters of the small body experience a jump leading to a shift in the phase of the gravitational waveform. In this paper, we treat the tidal perturber as stationary and restricted to the equatorial plane, and present a first study of how common and important such resonances are over the entire orbital parameter space. We find that a large proportion of inspirals encounter a low-order resonance in the observationally important regime. While the instantaneous effect of a tidal resonance is small, its effect on the accumulated phase of the gravitational waveform of an EMRI system can be significant due to its many cycles in band; we estimate that the effect is detectable for a significant fraction of sources. We also provide fitting formulae for the induced change in the constants of motion of the orbit due to the tidal resonance for several low-order resonances., Comment: 19 pages, 14 figures

We study the Kozai-Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai-Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulative shift of the periastron time by using obtained osculating orbital elements. If Kozai-Lidov oscillations occur, the cumulative shift curve will bend differently from that of the isolated binary. If such a bending is detected through the radio observation, it will be the first indirect observation of gravitational waves from a triple system., Comment: 22 pages, 24 figures, published by MNRAS

We study gravitational waves from a hierarchical three-body system up to first-order postNewtonian approximation. Under certain conditions, the existence of a nearby third body can cause periodic exchange between eccentricity of an inner binary and relative inclination, known as Kozai-Lidov oscillations. We analyze features of the waveform from the inner binary system undergoing such oscillations. We find that variation caused due to the tertiary companion can be observed in the gravitational waveforms and energy spectra, which should be compared with those from isolated binaries and coplanar three-body system. The detections from future space interferometers will make possible the investigation of the gravitational wave spectrum in mHz range and may fetch signals by sources addressed., Comment: 21 pages, 26 figures

We study a hierarchical triple system with the Kozai-Lidov mechanism, and analyse the cumulative shift of periastron time of a binary pulsar by the emission of gravitational waves. Time evolution of the osculating orbital elements of the triple system is calculated by directly integrating the first-order post-Newtonian equations of motion. The Kozai-Lidov mechanism will bend the evolution curve of the cumulative shift when the eccentricity becomes large. We also investigate the parameter range of mass and semi-major axis of the third companion with which the bending of the cumulative-shift curve could occur within 100 years., Comment: 6 pages, 3 figures, accepted by MNRAS letters

Most III-nitride semiconductors are grown on non-lattice-matched substrates like sapphire or silicon due to the extreme difficulty of obtaining a native GaN substrate. We show that several layered transition-metal dichalcogenides are closely lattice matched to GaN and report the growth of GaN on a range of such layered materials. We report detailed studies of the growth of GaN on mechanically-exfoliated flakes WS$_2$ and MoS$_2$ by metalorganic vapour phase epitaxy. Structural and optical characterization show that strain-free, single-crystal islands of GaN are obtained on the underlying chalcogenide flakes. We obtain strong near-band-edge emission from these layers, and analyse their temperature-dependent photoluminescence properties. We also report a proof-of-concept demonstration of large-area epitaxial growth of GaN on CVD MoS$_2$. Our results show that the transition-metal dichalcogenides can serve as novel near-lattice-matched substrates for nitride growth., Comment: main manuscript: page 1-15, 5 figures; supplementary: page 16-23