Mass and Angular Momentum in General Relativity

We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without symmetries, we focus on the discussion of energy-momentum for the gravitational field. We illustrate the difficulties rooted in the Equivalence Principle for defining a local energy-momentum density for the gravitational field. This leads to the understanding of gravitational energy-momentum and angular momentum as non-local observables that make sense, at best, for extended domains of spacetime. After introducing Komar quantities associated with spacetime symmetries, it is shown how total energy-momentum can be unambiguously defined for isolated systems, providing fundamental tests for the internal consistency of General Relativity as well as setting the conceptual basis for the understanding of energy loss by gravitational radiation. Finally, several attempts to formulate quasi-local notions of mass and angular momentum associated with extended but finite spacetime domains are presented, together with some illustrations of the relations between total and quasi-local quantities in the particular context of black hole spacetimes. This article is not intended to be a rigorous and exhaustive review of the subject, but rather an invitation to the topic for non-experts. In this sense we follow essentially the expositions in Szabados 2004, Gourgoulhon 2007, Poisson 2004 and Wald 84, and refer the reader interested in further developments to the existing literature, in particular to the excellent and comprehensive review by Szabados (2004).Comment: 41 pages. Notes based on the lecture given at the C.N.R.S. "School on Mass" (June 2008) in Orleans, France. To appear as proceedings in the book "Mass and Motion in General Relativity", eds. L. Blanchet, A. Spallicci and B. Whiting. Some comments and references added

Structure-Based Analysis of Five Novel Disease-Causing Mutations in 21-Hydroxylase-Deficient Patients

Congenital adrenal hyperplasia (CAH) due to 21-hydroxylase deficiency is the most frequent inborn error of metabolism, and accounts for 90–95% of CAH cases. The affected enzyme, P450C21, is encoded by the CYP21A2 gene, located together with a 98% nucleotide sequence identity CYP21A1P pseudogene, on chromosome 6p21.3. Even though most patients carry CYP21A1P-derived mutations, an increasing number of novel and rare mutations in disease causing alleles were found in the last years. In the present work, we describe five CYP21A2 novel mutations, p.R132C, p.149C, p.M283V, p.E431K and a frameshift g.2511_2512delGG, in four non-classical and one salt wasting patients from Argentina. All novel point mutations are located in CYP21 protein residues that are conserved throughout mammalian species, and none of them were found in control individuals. The putative pathogenic mechanisms of the novel variants were analyzed in silico. A three-dimensional CYP21 structure was generated by homology modeling and the protein design algorithm FoldX was used to calculate changes in stability of CYP21A2 protein. Our analysis revealed changes in protein stability or in the surface charge of the mutant enzymes, which could be related to the clinical manifestation found in patients

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