# Black hole uniqueness theorems You may have heard that black holes have no hair. That is to say, there is no way to distinguish two black holes as long as they have the same mass, charge, and spin. This is the simplest example of establishing the uniqueness of the solution in General Relativity. More generally, a uniqueness theorem refers to a scenario in a gravitational theory where fixing boundary conditions uniquely determines the solution. Whether there is a uniqueness theorem depends both on the theory and spacetime dimension. With matter fields or in higher dimensions, black hole uniqueness theorems are in general false. With SUSY, it is more likely to have uniqueness theorems. ## Refs - original no-hair theorems - [[1967#Israel]] - [[1968#Israel]] - [[1971#Carter]] - [[1972#Bekenstein]] - reviews - [[HollandsIshibashi2012Review]][](https://arxiv.org/pdf/1206.1164.pdf) - scalar hair [[HerdeiroRadu2015]][](https://arxiv.org/pdf/1504.08209.pdf) - static neutral spherical BH - [[Bekenstein1972]][](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.28.452): static and spherical neutral black hole in flat spacetime cannot be endowed with real scalar field, Proca field or spin-2 meson field - [[MayoBekenstein1996]][](https://arxiv.org/pdf/gr-qc/9602057.pdf): static and spherical BH cannot be endowed with a coupling charged scalar field together with a non-negative self-interacting potential - extreme Kerr - [[2009#Amsel, Horowitz, Marolf, Roberts (Jun, a)]] - [[FiguerasLucietti2009]] - extremal charged Kerr - [[ChruscielNguyen2010]] - detecting of [[0340 Aretakis instability|Aretakis hair]] from gravitational signals: - [[2020#Burko, Khanna, Sabharwal]] - [[2023#Aretakis, Khanna, Sabharwal]] - [[0465 de Sitter black holes|de Sitter black hole]] - [[2023#Katona, Lucietti]] - no short-hair theorem - [[1996#Nunez, Quevedo, Sudarsky]] - [[0169 Kaluza-Klein|KK]] theory with small circle size - [[2024#Albertini, Platt, Wiseman]]