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 study tidal effects induced by a particle moving along a slightly eccentric equatorial orbit in a Schwarzschild spacetime within the gravitational self-force framework. We compute the first-order (conservative) corrections in the mass ratio to the eigenvalues of the electric-type and magnetic-type tidal tensors up to the second order in eccentricity and through the 9.5 post-Newtonian order. Previous results on circular orbits are thus generalized and recovered in a proper limit.

Twisted gravitational waves (TGWs) are nonplanar unidirectional Ricci-flat solutions of general relativity. Thus far only TGWs of Petrov type II are implicitly known that depend on a solution of a partial differential equation and have wave fronts with negative Gaussian curvature. A special Petrov type D class of such solutions that depends on an arbitrary function is explicitly studied in this paper and its Killing vectors are worked out.

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.

The dynamics of a quasi two-dimensional isotropic droplet in a cholesteric liquid crystal medium under symmetric shear flow is studied by lattice Boltzmann simulations. We consider a geometry in which the flow direction is along the axis of the cholesteric, as this setup exhibits a significant viscoelastic response to external stress. We find that the dynamics depends on the magnitude of the shear rate, the anchoring strength of the liquid crystal at the droplet interface and the chirality.

We investigate numerically, by a hybrid lattice Boltzmann method, the morphology and the dynamics of an emulsion made of a polar active gel, contractile or extensile, and an isotropic passive fluid. We focus on the case of a highly off-symmetric ratio between the active and passive components. In absence of any activity we observe an hexatic-ordered droplets phase, with some defects in the layout. We study how the morphology of the system is affected by activity both in the contractile and extensile case.