6 research outputs found
Self-gravitating elastic bodies
Extended objects in GR are often modelled using distributional solutions of
the Einstein equations with point-like sources, or as the limit of
infinitesimally small "test" objects. In this note, I will consider models of
finite self-gravitating extended objects, which make it possible to give a
rigorous treatment of the initial value problem for (finite) extended objects.Comment: 16 pages. Based on a talk given at the 2013 WE-Heraeus seminar on
"Equations of motion in relativistic gravity
Stationary Black Holes: Uniqueness and Beyond
The spectrum of known black-hole solutions to the stationary Einstein
equations has been steadily increasing, sometimes in unexpected ways. In
particular, it has turned out that not all black-hole-equilibrium
configurations are characterized by their mass, angular momentum and global
charges. Moreover, the high degree of symmetry displayed by vacuum and
electro-vacuum black-hole spacetimes ceases to exist in self-gravitating
non-linear field theories. This text aims to review some developments in the
subject and to discuss them in light of the uniqueness theorem for the
Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998.
Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's
authorship. Significantly restructured and updated all sections; changes are
too numerous to be usefully described here. The number of references
increased from 186 to 32
Isolated and dynamical horizons and their applications
Over the past three decades, black holes have played an important role in
quantum gravity, mathematical physics, numerical relativity and gravitational
wave phenomenology. However, conceptual settings and mathematical models used
to discuss them have varied considerably from one area to another. Over the
last five years a new, quasi-local framework was introduced to analyze diverse
facets of black holes in a unified manner. In this framework, evolving black
holes are modeled by dynamical horizons and black holes in equilibrium by
isolated horizons. We review basic properties of these horizons and summarize
applications to mathematical physics, numerical relativity and quantum gravity.
This paradigm has led to significant generalizations of several results in
black hole physics. Specifically, it has introduced a more physical setting for
black hole thermodynamics and for black hole entropy calculations in quantum
gravity; suggested a phenomenological model for hairy black holes; provided
novel techniques to extract physics from numerical simulations; and led to new
laws governing the dynamics of black holes in exact general relativity.Comment: 77 pages, 12 figures. Typos and references correcte