  Entanglement has become central for the characterization of quantum matter
both in and out of equilibrium. In a dynamical context entanglement exhibits
universal linear temporal growth in generic systems, which stems from the
underlying linear light cones as they occur in planar geometries. Inhomogeneous
spacetimes can lead, however, to strongly bent trajectories. While such bent
trajectories crucially impact correlation spreading and therefore the
light-cone structure, it has remained elusive how this influences the
entanglement dynamics. In this work we investigate the real-time evolution of
the entanglement entropy in one-dimensional quantum systems after quenches
which change the underlying spacetime background of the Hamiltonian.
Concretely, we focus on the Rindler space describing the spacetime in close
vicinity to a black hole. As a main result we find that entanglement grows
sublinearly in a generic fashion both for interacting and noninteracting
quantum matter. We further observe that the asymptotic relaxation becomes
exponential, as opposed to algebraic for planar Minkowski spacetimes, and that
in the vicinity of the black hole the relaxation time for large subsystems
becomes independent of the subsystem size. We study entanglement dynamics both
for the case of noninteracting fermions, allowing for exact numerical
solutions, and for random unitary circuits representing a paradigmatic class of
ergodic systems.
