Dain Sergio, Gabach-Clement María Eugenia
Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Instituto de Física Enrique Gaviola, Consejo Nacional de Investigaciones Científicas y Técnicas, Córdoba, Argentina.
Living Rev Relativ. 2018;21(1):5. doi: 10.1007/s41114-018-0014-7. Epub 2018 Jul 5.
Geometrical inequalities show how certain parameters of a physical system set restrictions on other parameters. For instance, a black hole of given mass can not rotate too fast, or an ordinary object of given size can not have too much electric charge. In this article, we are interested in bounds on the angular momentum and electromagnetic charges, in terms of total mass and size. We are mainly concerned with inequalities for black holes and ordinary objects. The former are the most studied systems in this context in General Relativity, and where most results have been found. Ordinary objects, on the other hand, present numerous challenges and many basic questions concerning geometrical estimates for them are still unanswered. We present the many results in these areas. We make emphasis in identifying the mathematical conditions that lead to such estimates, both for black holes and ordinary objects.
几何不等式表明物理系统的某些参数如何对其他参数设置限制。例如，给定质量的黑洞不能旋转得太快，或者给定大小的普通物体不能带有太多电荷。在本文中，我们关注角动量和电磁荷关于总质量和大小的界限。我们主要关注黑洞和普通物体的不等式。前者是广义相对论中在此背景下研究最多的系统，并且已发现了大多数结果。另一方面，普通物体带来了许多挑战，关于它们的几何估计的许多基本问题仍然没有答案。我们展示了这些领域的诸多结果。我们着重确定导致此类估计的数学条件，既适用于黑洞，也适用于普通物体。
