Black holes are considered amongst the most mysterious objects in the universe. Part of their intrigue arises from the fact that they are actually amongst the simplest solutions to Einstein\u2019s field equations of general relativity theory. In fact, black holes can be fully characterized by only three physical quantities: their mass, spin and charge. Since they have no additional \u201chairy\u201d attributes to distinguish them, black holes are said to have \u201cno hair\u201d: Black holes of the same mass, spin, and charge are exactly identical to each other. <\/p>\n\n\n\n
Professor Gaurav Khanna of the University of Rhode Island and UMass Dartmouth alongside his former student Dr. Subir Sabharwal and collaborator\u00a0Dr. Lior Burko of Theiss Research discovered that a special kind of black hole violates black hole uniqueness, the\u00a0so-called \u201cno hair\u201d theorem. Specifically, the team studied extremal black holes \u2014 holes that are \u201csaturated\u201d with the\u00a0maximum charge or spin they can possibly carry. They found that there is a quantity that can be constructed from\u00a0the spacetime curvature at the black hole horizon that is conserved, and measurable by a distant observer. Since\u00a0this quantity depends on how the black hole was formed, and not just on the three classical attributes, it violates\u00a0black hole uniqueness.\u00a0\u00a0This \u00a0quantity constitutes “gravitational hair\u201d and potentially measurable by recent and upcoming gravitational wave\u00a0observatories like LIGO and LISA. The structure of this new hair follows the development of a similar quantity that\u00a0was found by Angelopoulos, Aretakis, and Gajic in the context of a simpler \u201ctoy\u201d model using a scalar field and\u00a0spherical black holes, and extends it to gravitational perturbations of rotating ones.\u00a0\u00a0<\/p>\n\n\n\n
\u201cThis new result is surprising,\u201d said Burko, \u201cbecause the black hole uniqueness theorems are well established, and\u00a0in particular their extension to extreme black holes. There has to be an assumption of the theorems that is not\u00a0satisfied, to explain how the theorems do not apply in this case.\u201d Indeed, the team followed on previous work by\u00a0Aretakis, that found that even though external perturbations of extreme black holes decay as they do also for regular\u00a0black holes, along the event horizon certain perturbation fields evolve in time indefinitely. \u201cThe uniqueness theorems\u00a0assume time independence. But the Aretakis phenomenon explicitly violates time independence along the event\u00a0horizon. This is the loophole through which the hair can pop out and be combed at a great distance by a\u00a0gravitational wave observatory,\u201d said Burko.\u00a0Unlike other work that found hair in black hole scalarization, Burko noted that “in this work we were working with the vacuum Einstein theory, without additional dynamical fields that modify the theory and which may violate the Strong Equivalence Principle.”<\/p>\n\n\n\n
The team used very intensive numerical simulations to generate their results. The simulations involved using dozens of the highest-end Nvidia graphics-processing-units (GPUs) with over 5,000 cores each, in parallel. \u201cEach of these GPUs can perform as many as 7 trillion calculations per second; however, even with such computational capacity the simulations look many weeks to complete,\u201d said Khanna.<\/p>\n\n\n\n