doi:10.1038/nindia.2013.113 Published online 26 August 2013

If a black hole spins, it is heavier

K. S. Jayaraman

Theoretical physicists at the Indian Institute of Science (IISc) in Bangalore have for the first time established a correlation between two fundamental and important facets of black holes (BHs) — their mass and their spin . The finding is expected to significantly aid understanding of these mysterious cosmic bodies — the powerful jets that emanate from them and some fundamental processes directly involved with their spin.

A black hole is a region of spacetime from which gravity prevents anything from escaping, even light. Depending on its initial mass, a star may become a white dwarf or a neutron star or collapse into a BH when it exhausts its nuclear fuel. Generally a star with initial mass more than 10 times the mass of the Sun is converted into a BH at the end of its life. A BH is characterized by three fundamental parameters: mass, spin and charge. (The charge is not so important astrophysically. Even if a black hole is born with non-zero charge by attracting opposite charges from its surrounding, it will become charge neutral.)

Since it evolves from a rapidly rotating massive star, astrophysicists believe that the BH inherits this character and has an intrinsic rotation. The rotating stellar mantle forms an 'accretion disk' around the BH during its formation. As the BH accretes, its mass and spin both evolve. When it completes stellar collapse, the final mass and spin become the fundamental parameters of the newly formed BH.

Banibrata Mukhopadhyay with co-researcher Indrani Banerjee (left)

Until the last decade, while the masses of several BHs had been determined independently through observation, there was no estimate of their spin. The IISc researchers posed the question: is it possible to correlate the mass and spin of BHs? And if the mass of a BH is known, can one predict its spin? "It was generally thought that the mass and spin of black holes are independent but our discovery shows that they are correlated", Banibrata Mukhopadhyay, one of the authors, told Nature India.

A BH is described by the famous equation established by Albert Einstein in 1916 that relates the mass and gravitational force of a body. Soon after that, Karl Schwarzschild found the exact solution of the equation for non-rotating BHs. However, it took almost another half a century before Roy Kerr established a solution for rotating BHs in 1963. "Until the last decade, there was no concrete observational evidence for rotating black holes," Mukhopadhyay said.

The accretion disks, due to their high density and temperature, are effective emitters of neutrinos. The IISc team found a correlation among the accretion rate of such disks, the mass and the spin of the BHs, through the observed neutrino flux at their formation stage. "We have found that for a fixed accretion rate, the mass of BHs increases with the increasing spin," Mukhopadhyay said. "Hence, the spins are correlated with the masses."

The researchers say their work shows that spinning BHs are more massive than non-spinning BHs for a given rate of accretion during the formation stage. However, they found that slowly spinning BHs can turn out to be more massive if the accretion rate at their formation stage was higher compared to their faster spinning cousins.

Since the mass of BHs in nature is known to vary widely, the finding demands the existence of spinning BHs, Mukhopadhyay says. While the mass of the BHs is relatively easier to determine from observation, measurement of spin is far more complicated, he said. "So far, measurements of spins for the same BHs by different groups yield different results. With the help of our work this ambiguity can be removed," the researchers say.

According to the IISc team their theory predicts that the maximum mass of BHs can be as high as 85 solar masses, which tallies with that inferred from observed data. Moreover, if the mass and spin of BHs are known from observations, theory can predict the scenario under which they were formed, since the formation accretion rate can then be predicted.

"Our findings also provide a range of possible mass for BHs and their respective spins, which could be useful in constraining the models predicting spins of BHs with known masses," they claim.


  1. Banerjee, I. & Mukhopadhyay, B. Establishing a relation between the mass and the spin of stellar-mass black holes. Phys. Rev. Lett. 111, 061101-061105 (2013) | Article | PubMed |
  2. Schwarzschild, K. Uber das gravitationsfeld eines massenpunktes nach der Einsteinschen theorie. Sitzber. K. Preuss. Aka. 7, 189 (1916)
  3. Kerr, R. P. Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11, 237-238 (1963) | Article | ISI | ADS |