Performing numerical simulations of Einstein's equations in higher
dimensions has tremendous potential to provide answers to some of the
most fundamental questions in physics. Besides the study of black
objects in higher dimensions and their stability properties, this
field is also relevant for the problem of black hole formation and
evaporation in particle accelerators and cosmic rays.
In this talk we will introduce a dimensional reduction procedure to
evolve higher-dimensional axially symmetric systems and present some
results of numerical evolutions of head-on collisions of black holes
in five dimensions.
We also discuss the first dynamical evolutions of black holes in four
dimensional asymptotically de Sitter spacetimes. We focus on the
head-on collision of equal mass binaries and compare analytical and
perturbative methods with full blown nonlinear simulations.