Black holes and “no-hair”?

Paper title: Verifying the no-hair property of massive compact objects with intermediate-mass-ratio inspirals in advanced gravitational-wave detectors
Authors: Carl L. Rodriguez, Ilya Mandel, Jonathan R. Gair
First Author’s Affiliation: Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) & Dept. of Physics and Astronomy, Northwestern University

(Illustration by Don Davis, from

These authors propose that advanced gravitational wave detectors will be able to directly detect the coalescence of compact objects, such as neutron stars (NS) and black holes (BH). The gravitational waves resulting when a neutron star or stellar-mass black hole inspirals into an intermediate-mass black hole give interesting information about gravitational physics (go here to watch cool videos of BHs colliding). The goal is to directly test general relativity (a review paper is found here).

A significant advance in this field comes from the next generation of detectors and experiments. Two such observatories are Advanced LIGO (Laser Interferometer Gravitational-wave Observatory, a project with two interferometers in Washington and one in Louisiana) and Virgo (near Pisa, Italy). Advanced LIGO should achieve sufficient sensitivity by 2015 to detect compact binaries as they interact and coalesce. This paper specifically develops the technique to detect high-mass systems with a total mass in the range of 25 to 100 solar masses, where one component is greater than one solar mass and the other less than 99 solar masses. The systems in this study are called Intermediate-mass-ratio inspirals (IMRIs) because the mass ratios between the two objects (the more massive object at the center and the object spiraling inward) are between 10:1 and 100:1.

Do objects like this really exist? Observational and theoretical models suggest the presence of intermediate-mass black holes (IMBHs) with masses ranging from about one hundred to ten thousand solar masses, but questions about their formation and prevalence still exist (see Miller and Colbert 2004 for a review). One formation mechanism is the “runaway merger scenario”, in which massive stars collide very rapidly and grow a massive star, which then collapses to an IMBH. Alternatively, IMBHs may form when many compact objects merge at the dense center of a globular cluster. Other scenarios exist, and the discussion of mechanisms could merit an entire paper of its own. In any case, based on the assumptions in this paper, the proposed Advanced LIGO should detect IMRIs at rates of one to 30 events per year, with a detector frequency of about 100-500 Hz.


Because some of the appeal, and also the challenge, of reading and understanding this paper is to acquire knowledge of the terminology used in the field of gravitational waves (with awesome names like “no-hair” theorem), I will describe some of what I consider the most important terms used throughout the paper. This should make the methods and results somewhat easier to follow.

  • The “no-hair” theorem of general relativity (GR) predicts that a central object should have a space-time with higher-order multipole moments that can be expressed as a function of its mass and spin. What? In other words, a BH can be uniquely characterized by its mass and spin. Hence, by measuring the mass, spin, and mass-quadrupole moment, the authors propose that they can test the hypothesis of whether the compact objects are Kerr black holes and what role GR plays in the inspiral when two objects interact.
  • A Kerr black hole is a BH that has mass and angular momentum, rotates around its central axis, but has no electrical charge.
  • Multipole moments are the coefficients of a series expansion that defines a field, such as the space-time geometry. Two multipole moments are mass and angular momentum.
  • The mass-quadrupole moment signifies a deviation from the Kerr BH case.
  • The Fisher matrix formalism is used to determine the precision of a parameter that is being estimated, in this case the quadruple moment. For more detail on the setup, the paper references Poisson and Will (1995). Numerical solutions are difficult, and some analytical parameter combinations and some numerical implementation techniques are suggested in the paper.


The results section addresses two cases, one in which the central body in the IMRI is a Kerr black hole, and another in which the central body has a non-Kerr mass-quadrupole moment. The authors test cases with a range of masses and spins.

1. Assuming a Kerr BH, the ability of Advanced LIGO to measure an anomalous quadruple moment depends on the parameters (such as the mass) of the system. The authors find that a “more extreme mass ratio” (a system with a more massive central object compared to the companion) yields the most sensitivity from the detector. However, the mass-quadrupole moment is difficult to constrain and limits the precision of the tests of the no-hair theorem. For the Kerr BH case, the detection of an IMBH could rule out exotic objects like boson stars.

2. The second case tests how confident the authors could be with a non-Kerr BH detection — in other words, how do they know that they have found an exotic super-massive object? They investigate how the mass parameter correlates with the quadrupole moment, and claim that they could detect non-Kerr quadrupole moments in IMRI signals detected by Advanced LIGO, especially for the case of a highly spinning central body and relatively small central mass.

About Adele Plunkett

I am a Fellow at European Southern Observatory (ESO), stationed in Chile with duties at the ALMA observatory. My research focus involves observing star forming regions using radio, mm-, and sub-mm telescopes. I completed my PhD at Yale University, where I worked with Prof. Hector Arce. Born and raised in Texas, I studied physics as an undergrad at Middlebury College in Vermont. I love all things related to travel, mountains, and traveling to mountains.

1 Comment

  1. I wish I were a physicist to be able to work on Advanced LIGO and be a participant in those discoveries. For now I have to leave my guitar aside and finish school. Thanks for your motivating blog.



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