International audienceNumerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation dependent. We expose the problem and discuss possible solutions using the Hawking-Hayward quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry, the apparent horizons enjoy a restricted gauge independence in any spherically symmetric foliation, but physical quantities associated with them, such as surface gravity and temperature, are fully gauge dependent. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail as examples

We exploit the parallel between dynamical black holes and cosmological spacetimes to describe the evolution of Friedmann-Lemaître-RobertsonWalker universes from the point of view of an observer in terms of the dynamics of the apparent horizon. Using the Hayward-Kodama formalism of dynamical black holes, we clarify the role of the Clausius relation to derive the Friedmann equations for a universe, in the spirit of Jacobson's work on the thermodynamics of spacetime. We also show how dynamics at the horizon naturally leads to the quantum-mechanical process of Hawking radiation. We comment on the connection of this work with recent ideas to consider our observable Universe as a Bose-Einstein condensate and on the corresponding role of vacuum energy.

Abstract. In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those which then move outwards with respect to the matter have been proposed for use in defining black holes, replacing the global concept of an "event horizon" which has some serious drawbacks for practical applications. We here present results from a study of the properties of both outgoing and ingoing trapping horizons, assuming strict spherical symmetry throughout. We have investigated their causal nature (i.e. whether they are spacelike, timelike or null), making contact with the Misner-SharpHernandez formalism, which has often been used for numerical calculations of spherical collapse. We follow two different approaches, one using a geometrical quantity related to expansions of null geodesic congruences, and the other using the horizon velocity measured with respect to the collapsing matter. After an introduction to these concepts, we then implement them within numerical simulations of stellar collapse, revisiting pioneering calculations from the 1960s where some features of the emergence and subsequent behaviour of trapping horizons could already be seen. Our presentation here is aimed firmly at "real world" applications of interest to astrophysicists and includes the effects of pressure, which may be important for the asymptotic behaviour of the ingoing horizon.