Speaker
Alex Vano-Vinuales
Description
In the coalescence of compact objects, not only the
properties of the objects and the distorted
spacetime close to them are important, but the far-field
behaviour is also relevant: it is at infinity
that the study of global properties of spacetimes and
unambiguous gravitational wave extraction
are possible. A convenient way of including infinity in
numerical relativity simulations is by
evolving along hyperboloidal slices, which are smooth
spacelike slices that reach future null
infinity - the "location" in spacetime where light rays
arrive and where signals can thus be
unambiguously measured. The hyperboloidal initial value
problem for the Einstein equations can
be addressed through conformal compactification methods,
which we express in terms of
unconstrained evolution schemes based on the BSSN and
conformal Z4 formulations, widely used
in current codes that simulate binary systems. The main
difficulty of the implementation is that
the resulting system of PDEs includes formally diverging
terms at null infinity that require a
special treatment and a careful choice of gauge conditions.
In this first step restricted to spherical
symmetry, we present stable numerical evolutions of a
massless scalar field coupled to the
Einstein equations, including the collapse of a scalar field
perturbation into a black hole and a
scalar field perturbing a Schwarzschild black hole trumpet
geometry. In the second scenario the
simulations were followed long enough to measure the scalar
field's power-law decay tails at
future null infinity at the expected convergence order.
These successful results make this
approach of the hyperboloidal initial value problem a good
candidate for more general numerical
setups. The final goal of this work is to provide a
far-field numerical framework that will
effectively include null infinity in simulations of compact
object mergers.
