Causal nature and dynamics of trapping horizons in black hole collapse

Abstract

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.

Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations

“…see for example[40] for a review about the condition R = 2M determining a trapped surface in spherical symmetry.2 This function was defined by S&S as C = (M − M b )/R.…”

From primordial black holes abundance to primordial curvature power spectrum (and back)

“…If we use the curvature perturbation on comoving hypersurfaces R −ζ instead of the curvature perturbation on uniform energy density hypersurfaces ζ, then peaks in the K-curvature correspond to peaks in the R-curvature and both generate peaks in the density 5. We refer the interested reader to appendix B of Ref [140]. for more details about the equation of state of a perfect fluid.…”

Observers in Kerr spacetimes: the ergoregion on the equatorial plane

“…However, under quite general conditions on the progenitor, these analysis do not exclude the possibility that considering instability processes a naked singularity can be produced as the result of a gravitational collapse. These studies, based upon a numerical integration of the corresponding field equations, often consider the stability of the progenitor models and investigate the gravitational collapse of differentially rotating neutron stars in full general relativity [69]. Black hole formation is then associated with the formation of trapped surfaces.…”