This thesis focuses on the study of accelerating solutions within the context of Einstein-AdS gravity in 2+1 dimensions, exploring both classical and holographic perspectives. These solutions exhibit a diverse range of phases that bear similarities to the C-metric in 3+1 dimensions while displaying certain peculiarities and novelties.

We start by describing the different classes of geometries that can be obtained from analysing the three-dimensional C-metric. After including a domain wall that acts as the external force driving the acceleration, we construct accelerating point particles and accelerating Ba~nados–Teitelboim–Zanelli (BTZ) black holes exhibiting distinct accelerated phases depending on the energy density of the domain wall. Furthermore, we present a novel accelerating black hole that is not continuously connected with the BTZ black hole. A detailed description of the spacetimes and their embedding into AdS$_{3}$ is presented.

From there, we investigate the boundary description of such geometries with particular emphasis on the accelerating BTZ black holes.
We find that the Fefferman–Graham prescription developed for accelerating black holes in four–dimensions leads to a holographic stress tensor that depends on the conformal freedom of the boundary metric. While this behaviour is natural, computing holographic quantities requires choosing a particular conformal representative. As an alternative, we propose that using an Arnowitt–Deser–Misner (ADM) “radial” decomposition offers a more suitable identification of the boundary data. Our findings reveal that the dual conformal field theory lies in a curved background being characterised by the stress tensor of a perfect fluid.

The Euclidean action is also obtained ensuring a well-posed variational principle. This requires including contributions from the internal boundaries generated when including a domain wall to the spacetime. We show that these boundary terms can be expressed in terms of the Nambu–Goto action of the domain wall which is added on top of the standard renormalised Einstein–Hilbert action for AdS$_{3}$.

Finally, we compute the entanglement entropy by using the fact that the solution can be mapped to Rindler-AdS where the Ryu–Takayanagi surface is easily identifiable. As the acceleration increases the accessible region of the conformal boundary decreases and therefore the entanglement entropy also decreases. This is interpreted as a process in which the dual theory loses information due to the acceleration.