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Interaction of a binary supermassive black hole with stars in a galactic nucleus can result in changes to all the elements of the binarys orbit, including the angles that define its orientation. If the nucleus is rotating, the orientation changes can be large, causing large changes in the binarys orbital eccentricity as well. We present a general treatment of this problem based on the Fokker-Planck equation for f, defined as the probability distribution for the binarys orbital elements. First- and second-order diffusion coefficients are derived for the orbital elements of the binary using numerical scattering experiments, and analytic approximations are presented for some of these coefficients. Solutions of the Fokker-Planck equation are then derived under various assumptions about the initial rotational state of the nucleus and the binary hardening rate. We find that the evolution of the orbital elements can become qualitatively different when we introduce nuclear rotation: 1) the orientation of the binarys orbit evolves toward alignment with the plane of rotation of the nucleus; 2) binary orbital eccentricity decreases for aligned binaries and increases for counter-aligned ones. We find that the diffusive (random-walk) component of a binarys evolution is small in nuclei with non-negligible rotation, and we derive the time-evolution equations for the semimajor axis, eccentricity and inclination in that approximation. The aforementioned effects could influence gravitational wave production as well as the relative orientation of host galaxies and radio jets.
The spin angular momentum S of a supermassive black hole (SBH) precesses due to torques from orbiting stars, and the stellar orbits precess due to dragging of inertial frames by the spinning hole. We solve the coupled post-Newtonian equations describ
We compute the isotropic gravitational wave (GW) background produced by binary supermassive black holes (SBHs) in galactic nuclei. In our model, massive binaries evolve at early times via gravitational-slingshot interaction with nearby stars, and at
We generalize the Thomas-Fermi approach to galaxy structure to include self-consistently and non-linearly central supermassive black holes. This approach naturally incorporates the quantum pressure of the warm dark matter (WDM) particles and shows it
When galaxies collide, dynamical friction drives their central supermassive black holes close enought to each other such that gravitational radiation becomes the leading dissipative effect. Gravitational radiation takes away energy, momentum and angu
Within the framework of the complexity equals action and complexity equals volume conjectures, we study the properties of holographic complexity for rotating black holes. We focus on a class of odd-dimensional equal-spinning black holes for which con