General Covariance and Background Independence in Quantum Gravity

The history of general relativity suggests that in absence of experimental data, constructing a theory on philosophical first principles can lead to a very useful theory as well as to ground-breaking insights about physical reality. The two related concepts of general covariance and background independence are some of these principles and play a central role in general relativity. A definition for them will be proposed and discussed. Constructing a theory of quantum gravity -- the sought-after unification of general relativity and quantum mechanics -- could profit from the same approach. Two popular research areas of quantum gravity, string theory and loop quantum gravity together with spin foams, are being examined whether they comply with these principles.Comment: Submitted as essay in philosophy of physics for the Cambridge Mathematical Tripo

Classification of near-horizon geometries of extremal black holes

Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein-Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.Comment: 70 pages; invited review article for Living Reviews in Relativity; v2 some improvements and references adde

Some recent progress in classical general relativity

In this short survey paper, we shall discuss certain recent results in classical gravity. Our main attention will be restricted to two topics in which we have been involved; the positive mass conjecture and its extensions to the case with horizons, including the Penrose conjecture (Part I), and the interaction of gravity with other force fields and quantum-mechanical particles (Part II). © 2000 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70615/2/JMAPAQ-41-6-3943-1.pd