General relativity and cosmic structure formation
  Numerical simulations are a versatile tool providing insight into the
complicated process of structure formation in cosmology. This process is mainly
governed by gravity, which is the dominant force on large scales. To date, a
century after the formulation of general relativity, numerical codes for
structure formation still employ Newton's law of gravitation. This
approximation relies on the two assumptions that gravitational fields are weak
and that they are only sourced by non-relativistic matter. While the former
appears well justified on cosmological scales, the latter imposes restrictions
on the nature of the "dark" components of the Universe (dark matter and dark
energy) which are, however, poorly understood. Here we present the first
simulations of cosmic structure formation using equations consistently derived
from general relativity. We study in detail the small relativistic effects for
a standard {\Lambda}CDM cosmology which cannot be obtained within a purely
Newtonian framework. Our particle-mesh N-body code computes all six degrees of
freedom of the metric and consistently solves the geodesic equation for
particles, taking into account the relativistic potentials and the
frame-dragging force. This conceptually clean approach is very general and can
be applied to various settings where the Newtonian approximation fails or
becomes inaccurate, ranging from simulations of models with dynamical dark
energy or warm/hot dark matter to core collapse supernova explosions.
