Do black holes really have no hair?

Tim Johannsen

Tim Johannsen is a postdoctoral fellow at Perimeter Institute for Theoretical Physics and the University of Waterloo specializing in black-hole astrophysics and tests of general relativity.

Black holes have no hair – so they say. Formally, this statement refers to several famous theorems in general relativity that were established mostly from the late 1960s to the early 1970s and are collectively known as the no-hair theorem. According to this theorem, a black hole only depends on its mass, angular momentum (or spin), and electric charge and is uniquely described by the Kerr-Newman metric. So, just about everyone would expect that astrophysical black holes are indeed the Kerr black holes of general relativity understanding that any net electric charge would quickly neutralize.

General relativity itself has passed all experimental tests thus far including observations of solar eclipses, double neutron stars, and, very recently, gravitational waves, as well as a variety of solar-system and laboratory tests. Most of these tests, however, were carried out in settings with weak gravitational fields, and general relativity still remains largely untested in the strong-field regime even to this day.

Black holes are prime candidates for such tests, because they are typically surrounded by matter under extreme conditions in a regime of strong spacetime curvature. The study of these compact objects can, therefore, lead to a deeper understanding of their nature and their environment. At the same time, the wealth and precision of observations across (primarily) the electromagnetic spectrum from both ground-based and space observatories is opening up ever increasing possibilities to test fundamental properties of black holes. The masses and spins of numerous stellar-mass and supermassive black holes have already been measured and we are now in a position where we can put general relativity to its ultimate test: the search for black-hole hair.

Will we be up for a big surprise? Well, one certainly came to me some time ago in the form of a request from a cosmetology journal to write an article on hair restoration and the prevention of hair loss. There is a huge effort underway, however, to test the no-hair theorem with a variety of different electromagnetic experiments which operate at frequencies ranging from radio to x-rays. In particular, these include (a) near-infrared and (b) timing observations of stars and pulsars orbiting around Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, respectively, (c) very-long baseline interferometric observations of Sgr A* and the supermassive black hole at the center of the galaxy M87, as well as x-ray observations of (d) fluorescent iron lines, (e) thermal continuum spectra, (f) variability, and (g) polarization.

The methods and status of these experiments are described in my recent review article for Classical and Quantum Gravity, as well as in my topical review “Sgr A* and general relativity” (arXiv:1512.03818) which focuses on the tests involving Sgr A* in greater detail and also discusses the theoretical framework which is required for strong-field tests.

While the monitoring of stars and pulsars on orbits around Sgr A* can rely on a parametrized post-Newtonian framework just as the vast majority of previous weak-field tests of general relativity, observations of black holes and their accretion disks necessarily have to incorporate the strong-field effects experienced by the emitted photons such as light bending, relativistic boosting and beaming, and the gravitational redshift. This requires the modelling of the underlying spacetime in terms of a suitable metric, typically a so-called Kerr-like metric, which depends on one or more free parameters in addition to the mass and spin of the black hole. These parameters are, then, encoded in the observed electromagnetic radiation.


The observed electromagnetic radiation is illustrated here in the simple example of a geometrically thin accretion disk emitting a thermal continuum of radiation with a radially-symmetric flux profile. The figure shows the observed number flux density at 1 keV (per keV, second, and centimeter squared) as a function of the image coordinates (in units of the black-hole mass). The disk image is greatly distorted by all the relativistic effects allowing for a measurement of parameters of the black hole.


One of the most exciting instruments is the Event Horizon Telescope, a global array of millimeter and submillimeter telescopes, which is expected to take the first direct image of a black hole within the next few years. Such an image should feature the so-called shadow of the black hole which is caused by the capture of photons in the immediate vicinity of the black hole. The size and shape of the shadow alone may already be used to place tight constraints on potential deviations from the Kerr metric in a largely model-independent manner, while additional constraints could be inferred from the properties of the accretion disk. Another key instrument is the proposed x-ray observatory Athena+, which will be able to measure time-resolved iron-line spectra with exquisite precision and may test the no-hair theorem via the detection of subtle nuances in such spectra introduced by the properties of Kerr-like spacetimes.

Read the full article in Classical and Quantum Gravity:
Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum
Tim Johannsen
2016 Class. Quantum Grav. 33 124001

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2 thoughts on “Do black holes really have no hair?

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