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The following is a timeline of gravitational physics and general relativity.
Timeline of black hole physics
The Penrose–Hawking singularity theorems are a set of results in general relativity that attempt to answer the question of when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation predicts a gravitational singularity in black hole formation. The Hawking singularity theorem is based on the Penrose theorem and it is interpreted as a gravitational singularity in the Big Bang situation. Penrose was awarded the Nobel Prize in Physics in 2020 "for the discovery that black hole formation is a robust prediction of the general theory of relativity", which he shared with Reinhard Genzel and Andrea Ghez.
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.
In the mathematical field of differential geometry, Ricci-flatness is a condition on the curvature of a Riemannian manifold. Ricci-flat manifolds are a special kind of Einstein manifold. In theoretical physics, Ricci-flat Lorentzian manifolds are of fundamental interest, as they are the solutions of Einstein's field equations in a vacuum with vanishing cosmological constant.
A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry.
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450. It is awarded every three years for a notable research work in analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
Fuzzballs are hypothetical objects in superstring theory, intended to provide a fully quantum description of the black holes predicted by general relativity.
An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime.
In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical non-gravitational fields such as the electromagnetic field.
Demetrios Christodoulou is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the Minkowski spacetime of special relativity in the framework of general relativity. Christodoulou is a 1993 MacArthur Fellow.
The hoop conjecture, proposed by Kip Thorne in 1972, states that an imploding object forms a black hole when, and only when, a circular hoop with a specific critical circumference could be placed around the object and rotated about its diameter. In simpler terms, the entirety of the object's mass must be compressed to the point that it resides in a perfect sphere whose radius is equal to that object's Schwarzschild radius, if this requirement is not met, then a black hole will not be formed. The critical circumference required for the imaginary hoop is given by the following equation listed below.
The following outline is provided as an overview of and topical guide to black holes:
The BTZ black hole, named after Máximo Bañados, Claudio Teitelboim, and Jorge Zanelli, is a black hole solution for (2+1)-dimensional topological gravity with a negative cosmological constant.
Yvonne Choquet-Bruhat is a French mathematician and physicist. She has made seminal contributions to the study of Einstein's general theory of relativity, by showing that the Einstein equations can be put into the form of an initial value problem which is well-posed. In 2015, her breakthrough paper was listed by the journal Classical and Quantum Gravity as one of thirteen 'milestone' results in the study of general relativity, across the hundred years in which it had been studied.
Sergiu Klainerman is a mathematician known for his contributions to the study of hyperbolic differential equations and general relativity. He is currently the Eugene Higgins Professor of Mathematics at Princeton University, where he has been teaching since 1987.
András Vasy is an American, Hungarian mathematician working in the areas of partial differential equations, microlocal analysis, scattering theory, and inverse problems. He is currently a professor of mathematics at Stanford University.
In the mathematical field of differential geometry, a maximal surface is a certain kind of submanifold of a Lorentzian manifold. Precisely, given a Lorentzian manifold (M, g), a maximal surface is a spacelike submanifold of M whose mean curvature is zero. As such, maximal surfaces in Lorentzian geometry are directly analogous to minimal surfaces in Riemannian geometry. The difference in terminology between the two settings has to do with the fact that small regions in maximal surfaces are local maximizers of the area functional, while small regions in minimal surfaces are local minimizers of the area functional.
References
- ↑ Fourès-Bruhat, Y. (1952). "Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires". Acta Mathematica. 88 (0): 141–225. doi: 10.1007/BF02392131 . ISSN 0001-5962.
- 1 2 3 Harnett, Kevin (8 March 2018). "To Test Einstein's Equations, Poke a Black Hole". Quanta Magazine .
- ↑ Christodoulou, Demetrios; Klainerman, Sergiu (1993). The global nonlinear stability of the Minkowski space. Princeton mathematical series. Princeton: Princeton university press. ISBN 978-0-691-08777-1.
- ↑ Hintz, Peter; Vasy, András (2018). "The global non-linear stability of the Kerr-de Sitter family of black holes". Acta Mathematica. 220 (1): 1–206. arXiv: 1606.04014 . doi:10.4310/acta.2018.v220.n1.a1. S2CID 119281798.
- ↑ Klainerman, Sergiu; Szeftel, Jeremie (2018-12-20). "Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations". arXiv: 1711.07597 [gr-qc].
- ↑ Nadis, Steve (2022-08-04). "Black Holes Finally Proven Mathematically Stable". Quanta Magazine. Retrieved 2022-08-05.
- ↑ Klainerman, Sergiu; Szeftel, Jeremie (2021-04-23). "Kerr stability for small angular momentum". arXiv: 2104.11857 [math.AP].
- ↑ Giorgi, Elena; Klainerman, Sergiu; Szeftel, Jeremie (2022-05-30). "Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes". arXiv: 2205.14808 [math.AP].
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