Geometrical inequalities bounding angular momentum and charges in General Relativity

SERGIO ALEJANDRO DAIN; GABACH CLEMENT, MARIA EUGENIA

LIVING REVIEWS IN RELATIVITY

MAX PLANCK INSTITUT GRAVITATIONAL PHYSICS-ALBERT EINSTEIN INSTITUTE

Lugar: Berlin; Año: 2018 vol. 21

1433-8351

Geometrical inequalities show how certain parameters of a physicalsystem set restrictions on other parameters. For instance, a black hole of givenmass can not rotate too fast, or an ordinary object of given size can not havetoo much electric charge. In this article we are interested in bounds on theangular momentum and electromagnetic charges, in terms of total mass andsize. We are mainly concerned with inequalities for black holes and ordinaryobjects. The former are the most studied systems in this context in GeneralRelativity, and where most results have been found. Ordinary objects, on theother hand, present numerous challenges and many basic questions concerninggeometrical estimates for them are still unanswered.We present the many results in these areas. We make emphasis in identi-fying the mathematical conditions that lead to such estimates, both for blackholes and ordinary objects.