The Janis-Newman-Winicour and Papapetrou metrics represent counterparts to the Schwarzschild black hole with scalar and antiscalar background fields, correspondingly (where “anti” is to be understood as in “anti–de Sitter”). There is also a scalar counterpart (the Krori-Bhattacharjee metric) to the Kerr black hole. Here we study analytical connections between these solutions and obtain the exact rotational generalization of the antiscalar Papapetrou spacetime as a viable alternative to the Kerr black hole. The antiscalar metrics appear to be the simplest ones as they do not reveal event horizons and ergospheres, and they do not involve an extra parameter for scalar charge. Static antiscalar field is thermodynamically stable and self-consistent, but this is not the case for the scalar Janis-Newman-Winicour solution; in addition, antiscalar thermodynamics is reducible to black-hole thermodynamics. Lensing, geodetic, and Lense-Thirring effects are found to be practically indistinguishable between antiscalar and vacuum solutions in weak fields. Only strong-field observations might provide a test for the existence of antiscalar background. In particular, the antiscalar solution predicts 5% larger shadows of supermassive compact objects, as compared to the vacuum solution. Another measurable aspect is the 6.92% difference in the frequency of the innermost stable circular orbit characterizing the upper cutoff in the gravitational wave spectrum.

Context. Nuclear star cluster (NSC) mergers, involving the fusion of dense stellar clusters near the centres of galaxies, play a pivotal role in shaping galactic structures. The distribution of stellar orbits has significant effects on the formation and characteristics of extreme mass ratio inspirals (EMRIs). Aims. In this study, we address the orbital distribution of stars in merging NSCs and the subsequent effects on supermassive black hole binary (SMBHB) evolution. Methods. We ran dedicated direct-summation N-body simulations with different initial conditions to do a detailed study of the resulting NSC after their progenitors had merged. Results. Our findings reveal that prograde stars form a flattened structure, while retrograde stars have a more spherical distribution. The axial ratios of the prograde component vary based on the presence and mass ratio of the SMBHs. The fraction of prograde and retrograde stars depends on the merger orbital properties and the SMBH mass ratio. The interactions of retrograde stars with the SMBHB affect the eccentricity and separation evolution of the binary. Our analysis reveals a strong correlation between the angular momentum and eccentricity of the SMBH binary. This relationship could serve as a means to infer information about the stellar dynamics surrounding the binary. We find that prograde orbits are particularly close to the binary of SMBHs, a promising fact regarding EMRI production. Moreover, prograde and retrograde stars have different kinematic structures, with the prograde stars typically rotating faster than the retrograde ones. The line-of-sight velocity and velocity dispersion, as well as the velocity anisotropy of each NSC, depend on the initial merger orbital properties and SMBH mass ratios. The prograde and retrograde stars always show different behaviours. Conclusions. The distribution of stellar orbits and the dynamical properties of each kinematic population can potentially be used as a way to tell the properties of the parent nuclei apart, and has an important impact on expected rates of EMRIs, which will be detected by future gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA).

We present a simple method for estimating fundamental frequencies from orbit’s time series of triaxial dynamical systems based on the zero-crossing technique. The simplicity and high performance of the method make it a viable alternative to more advanced, but rather complex and computationally expensive techniques based on Fourier spectral analysis and iterative torus-mapping with action-angle variables. More importantly, the method provides a simple and quick way to identify irregular orbits and quantify their level of chaoticity, allowing to detect even a subtle onset of chaos. To validate the proposed algorithm, we performed comparison tests with synthetic quasi-periodic signals and with other methods using the triaxial Dehnen potential. We found noticeable differences in frequency maps constructed with our method and methods based on Fourier spectral analysis that we attributed to the way we assign static properties to chaotic orbits. At the same time, our frequency maps turn out to be in very good agreement with the maps obtained using the action-based technique.