The (first-order) gravitational self-force correction to the spin-orbit precession of a spinning compact body along a slightly eccentric orbit around a Schwarzschild black hole is computed through the ninth postNewtonian order and to second order in the eccentricity, improving recent results by Kavanagh et al. [Phys. Rev. D 96, 064012 (2017)]. We show that our higher-accurate theoretical estimates of the spin precession exhibits an improved agreement with corresponding numerical self-force data.

We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the z axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism).

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts.

The energy content of (exact) electromagnetic and gravitational plane waves is studied in terms of super-energy tensors (the Bel, Bel-Robinson and the-less familiar-Chevreton tensors) and natural observers. Starting from the case of single waves, the more interesting situation of colliding waves is then discussed, where the nonlinearities of the Einstein's theory play an important role. The causality properties of the super-momentum four vectors associated with each of these tensors are also investigated when passing from the single-wave regions to the interaction region.

Twisted gravitational waves (TGWs) are nonplanar waves with twisted rays that move along a fixed direction in space. We study further the physical characteristics of a recent class of Ricci-flat solutions of general relativity representing TGWs with wave fronts that have negative Gaussian curvature. In particular, we investigate the influence of TGWs on the polarization of test electromagnetic waves and on the motion of classical spinning test particles in such radiation fields.

We study trapped surfaces from the point of view of local isometric embedding into 3D Riemannian manifolds. When a two-surface is embedded into 3D Euclidean space, the problem of finding all surfaces applicable upon it gives rise to a non-linear partial differential equation of the Monge-Ampere type, first discovered by Darboux, and later reformulated by Weingarten. Even today, this problem remains very difficult, despite some remarkable results. We find an original way of generalizing the Darboux technique, which leads to a coupled set of six non-linear partial differential equations.

We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced by us D. Bini and T. Damour, Phys. Rev. D 96, 104038 2017 PRVDAQ 10.1103/PhysRevD.96.104038, we transcribe our result into a correspondingly improved knowledge of the spin-orbit sector of the effective one-body (EOB) Hamiltonian description of the dynamics of spinning binary systems.

We investigate the hyperbolic scattering of test particles, spinning test particles, and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter.

We compute gravitational self-force (conservative) corrections to tidal invariants for spinning particles moving along circular orbits in a Schwarzschild spacetime. In particular, we consider the square and the cube of the gravitoelectric quadrupolar tidal tensor and the square of the gravitomagnetic quadrupolar tidal tensor. Our results are accurate to first order in spin and through the 9.5 post-Newtonian order. We also compute the associated electric-type and magnetic-type eigenvalues.

We generalize to the Kerr spacetime existing self-force results on tidal invariants for particles moving along circular orbits around a Schwarzschild black hole. We obtain linear-in-mass-ratio (conservative) corrections to the quadratic and cubic electric-type invariants and the quadratic magnetic-type invariant in series of the rotation parameter up to the fourth order and through the ninth and eighth post-Newtonian orders, respectively. We then analytically compute the associated eigenvalues of both electric and magnetic tidal tensors.