Extreme Black Holes

Gravitational-wave detectors can be used to measure gravitational-field hair of extreme black holes, according to a paper published in the journal Physical Review D.

Extreme Kerr black holes have gravitational hair that can be measured at finite distances and violates the uniqueness theorems. Image credit: Sci-News.com / Zdeněk Bardon / ESO.

“We discovered that extreme black holes — those that are saturated with the maximum charge or spin they can possibly carry — violate black hole uniqueness, the so-called no hair theorem,” said lead author Dr. Lior Burko of Theiss Research and colleagues.

“We found that there is a quantity that can be constructed from the spacetime curvature at the black hole horizon that is conserved, and measurable by a distant observer.”

“Since this quantity depends on how the black hole was formed, and not just on the three classical attributes, it violates black hole uniqueness.”

“This quantity constitutes gravitational hair and potentially measurable by recent and upcoming gravitational-wave observatories like LIGO and LISA.”

The structure of this hair follows the development of a similar quantity that was found by Angelopoulos et al. in the context of a simpler ‘toy’ model using a scalar field and spherical black holes, and extends it to gravitational perturbations of rotating ones.

“This new result is surprising, because the black hole uniqueness theorems are well established, and in particular their extension to extreme black holes,” Dr. Burko said.

“There has to be an assumption of the theorems that is not satisfied, to explain how the theorems do not apply in this case.”

Indeed, the physicists followed on a previous work by Aretakis, that found that even though external perturbations of extreme black holes decay as they do also for regular black holes, along the event horizon certain perturbation fields evolve in time indefinitely.

“The uniqueness theorems assume time independence,” Dr. Burko said.

“But the Aretakis phenomenon explicitly violates time independence along the event horizon.”

“This is the loophole through which the hair can pop out and be combed at a great distance by a gravitational-wave observatory.”

“Unlike other work that found hair in black hole scalarization, 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.”

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Lior M. Burko et al. 2021. Scalar and gravitational hair for extreme Kerr black holes. Phys. Rev. D 103 (2): L021502; doi: 10.1103/PhysRevD.103.L021502