Som & Gaurav’s work on black hole “hair” gets some media attention!

A more detailed version of the story is published here:

Title: Fast spinning black holes develop short-lived “hair” in their gravity that are potentially observable.


This is amongst the best times to be a black hole physicist. Not only did our community just celebrate the 60th anniversary of the mathematical discovery of a rotating black hole by Roy Kerr, it is also eagerly anticipating new observations from the upgraded LIGO and other detectors that measure minute “ripples” in spacetime, so-called gravitational waves, emerging from the collisions of compact astrophysical objects like black holes and neutron stars. Furthermore, we are enthralled by the formal adoption of the space-based LISA mission by the European Space Agency (ESA) that will detect the same types of waves from systems that involve supermassive black holes that are a million or even a billion times more massive than our Sun. LISA will offer us an exquisite map of the spacetime around rotating black holes enabling us to test our understanding of their gravity to unprecedented levels. 

Formal adoption means that the project has the go-ahead to move to the construction phase with a planned 2035 launch.  LISA consists of three spacecrafts configured in a perfect equilateral triangle that will trail behind the Earth around the Sun. Each pair of the spacecrafts will be 1.6 million miles apart and will exchange laser beams to measure the separation down to less than a billionth of an inch level accuracy!

Despite all this progress, black holes are still considered to perhaps be the most mysterious objects that exist in Nature. The ironic thing is that they are actually the simplest and the most elegant astrophysical objects out there! More specifically, Bekenstein’s so-called “no hair” result from the ‘70s suggests that black holes are completely characterized by only three physical attributes – their mass, charge and spin. All other details of the massive dying star, for example, are lost during the formation process of the black hole. That is how simple they are! Not that different from elementary particles in a sense. 

Researchers in our community have exploited “loopholes” within Bekenstein’s assumptions to come up with “hairy” black holes models for decades. Over the past few years, with my students and collaborators, we have discovered a new loophole but one that makes no extraordinary assumptions setting it apart from other models. In fact, we work within the framework of Einstein’s theory of gravity – general relativity, and simply study Kerrr black holes that are spinning very rapidly, while closely maintaining astrophysical relevance. 

About a decade ago, Stefanos Aretakis (currently at UToronto) had shown mathematically that if one saturates a black hole with the maximum charge it can hold  – so-called extremally charged black hole – then it develops new “hair” i.e. a physical attribute that one can measure externally, beyond its mass, charge and spin and one that the hole is unable to “shed” even if one waits forever. This new attribute is referred to as “Aretakis horizon hair” in the literature because it is based on a gradient of a physical field at the black hole’s horizon. Aretakis’ analysis used a simplified physical scenario – a “toy model” using a massless scalar field and a maximally charged, non-spinning black hole; not something we expect to observe astrophysically.   

In a series of recent papers with students, Kevin Quesada-Gonzalez [now at Case Western], Som Dev Bishoji [current PhD student at UMass] and Subir Sabharwal [now working in Finance] and collaborator Lior Burko, we were able to extend Aretakis’ key hair results to the astrophysically relevant case of spinning black holes and to cases in which the spin didn’t quite need to be turned up to the maximum, i.e. for near-extremal Kerr black holes, since it is unlikely that extremal holes form via common astrophysical processes. In addition, we studied the Aretakis hair in the context of the physical gravitational field, bringing the entire concept into the realm of actual potential measurement. Our studies suggest that one can construct similar attributes out of gravitational wave measurements even for near-extremal spinning black holes offering a definite “signature” of sorts for such black holes!  

But what about the no hair theorem? Doesn’t that explicitly forbid such an externally measureable hair? The key loophole we exploited is that our newly discovered gravitational hair is not permanent; it is a “transient” and fairly short-lived for non-extremal holes, but lasts longer and longer as the black hole spins faster and faster approaching extremality. In addition, we used an approximation that ignores important nonlinear effects in the theory which would also result in the hair not lasting forever even in the extremal case. A plausible scenario for measurement would involve a rotating black hole spinning sufficiently fast allowing for the effects of the transient hair to have a measurable impact on a gravitational wave detector like LISA. In other words, our results suggest that once upon a time Interstellar’s Gargantua  actually had hair and Cooper (Matthew McConaughey’s character) would have been able to measure it. 

Exciting times!

This research is supported by the US National Science Foundation. All computations were performed at the Massachusetts Green High Performance Computing Center (MGHPCC) leveraging the resources of the URI Center for Computational Research. Relevant published papers and preprints can be found here: 

[1906.03116] (Transient) Scalar Hair for (Nearly) Extreme Black Holes

[2005.07294] Scalar and gravitational hair for extreme Kerr black holes

[2109.02607] Scalar and Gravitational Transient “Hair” for Near-Extremal Black Holes

[2304.06210] Aretakis Hair for Extreme Kerr Black Holes with Axisymmetric Scalar Perturbations

[2307.03963] An observational signature for extremal black holes