A proper analytic understanding of the nature of black holes is important from both a fundamental and a phenomenological point of view. The concept of an event horizon has been instrumental in gaining mathematical insight into black hole properties, but it also has its drawbacks. Event horizons are a "teleological" notion, in the sense that one needs to know the entire future development of spacetime to be able to localize them. They also have some counterintuitive properties, such as the tendency to expand in anticipation of matter falling in, without that matter having reached the horizon yet.
An alternative way of characterizing a black hole is the concept of a dynamical horizon, a three-dimensional surface that represents the time evolution of so-called marginally trapped two-spheres, which have the property that the wavefronts of outgoing light neither expand nor contract. Dynamical horizons have a number of attractive properties. Unlike event horizons, one does not need to know the future evolution of spacetime to locate them. They naturally come with an expression relating their growth to an ingoing matter flux as well as a gravitational wave energy flux; under ordinary circumstances the latter is notoriously difficult to define in the strong-field regime. Moreover, dynamical horizons only grow when matter or radiation is actually falling in. Cardiff researchers have been actively involved in the further development of this framework. In particular, in
Booth and Fairhurst, Class. Quantum Grav. 22 (2005) 4515-4550 a Hamiltonian derivation of the dynamical horizon mass was given.
In the context of dynamical horizons, it is interesting to consider whether the Kerr bound on angular momentum holds. In Extremality conditions for isolated and dynamical horizons, Booth and Fairhurst have argued that the standard characterizations of black hole extremality are not meaningful for dynamical horizons. Instead, they provide an alternative local definition of extremality for both isolated and dynamical horizons, based on the integrated horizon angular momentum density squared.
In the absence of infalling matter/energy, a dynamical horizon becomes an "isolated horizon" (Phys Rev Lett 85, 3564 (2000) - Generic Isolated Horizons and Their Applications). Isolated horizons allow for a formulation of the first law of black hole mechanics, which relates infinitesimal changes in mass to changes in area and angular momentum. Interestingly, this can be done with no reference whatsoever to the bulk spacetime away from the horizon (in particular, no assumptions on the asymptotic behavior of spacetime are needed). Isolated horizons can also be formulated in more than four spacetime dimensions, where they have been studied in asymptotically anti-de Sitter spacetimes (A. Ashtekar, T. Pawlowski, and C. Van Den Broeck, Class. Quantum Grav. 24 (2007) 625-644 -
Mechanics of higher-dimensional black holes in asymptotically anti-de Sitter space-times). This has clarified some issues related to the definition of conserved quantities in such spacetimes, which have a bearing on the AdS/CFT conjecture.
Isolated horizons are characterized by a set of mass and angular momentum multipole moments, which again are defined at the horizon itself, with no reference to the rest of spacetime. In loop quantum gravity these have been used to calculate the entropy of axisymmetric, but otherwise arbitrarily deformed black holes (A. Ashtekar, J. Engle, and C. Van Den Broeck, Class. Quantum Grav. 22 (2005) L27-L34 -
Quantum horizons and black hole entropy: Inclusion of distortion and rotation). Their definition easily carries over to dynamical horizons, where they may be of interest in both numerical as well as analytic studies of black hole evolution.
Isolated horizons are null surfaces while dynamical horizons are spacelike. Timelike analogs have also been defined, called timelike membranes, but until recently they were not thought to be associated with the formation and growth of black holes. However, the classic example of the collapse of a homogeneous ball of pressureless dust does involve a timelike membrane but no dynamical horizon. The situation was clarified when it was shown that in more realistic collapse scenarios, any timelike membranes that may be present will be enveloped by dynamical horizons and not be in causal contact with outside observers (I. Booth, L. Brits, J.A. Gonzalez, and C. Van Den Broeck, Class. Quantum Grav. 23 (2006) 413-440 -
Marginally trapped tubes and dynamical horizons).
Slowly Evolving Horizons
When a dynamical horizon is close to equilibrium, it can be characterized as a slowly evolving horizon (I. Booth and S. Fairhurst, Phys. Rev. Lett. 92, 011102 (2004) -
The First Law for Slowly Evolving Horizons). In this case, it is possible to introduce a small parameter which characterizes the rate of evolution of the horizon. Furthermore, many of the properties of isolated horizons can be shown to hold to leading order in the evolution parameter for a slowly evolving horizon.