Professor C.V. Vishveshwara, or Vishu as he is known to many of his friends, colleagues and students, was the first to explore the stability of black holes. Vishu’s work is fundamental to our understanding of black holes and began a new chapter in how to study them. Unfortunately, his work is not credited as much as it should be and this blog is about his seminal work, its relevance to the first discovery of gravitational waves and its implication for future studies of black holes.
In his 1970 paper (Nature, Vol. 227, page 936) , Vishu explored how black holes respond to external perturbations. He showed that regardless of what the perturbation is black holes get rid of any deformation imparted to them by radiating gravitational waves and the radiated waves have a frequency and decay time that depended only on their mass. This result was later extended to spinning black holes which showed that imprint in the spectrum of gravitational waves from deformed black holes are their mass and spin frequency. This was a truly remarkable result as it meant that we could study the properties of black holes by perturbing them or deforming them. But how would one go about deforming a black hole!
A pair of black holes in a binary evolve by emitting gravitational waves of ever greater amplitude and frequency. The emitted waves drain the rotational energy of the binary making the two black holes spiral in and eventually plunge towards each other. When two black holes come together and merge a new black hole forms that is initially highly deformed. At this moment the radiation that was all the time increasing in amplitude and pitch suddenly ends with a constant frequency and decays exponentially. These characteristic waves are technically termed quasi-normal modes, which is why Vishu, a great scientist with an equally great sense of humour and wit, calls himself “Quasimodo of black holes“. They are not unlike the dying tones of a bell struck with a hammer and are often called the ringdown radiation.
This is what we found at the end of a 200 millisecond-long gravitational wave signal, named GW150914, observed with the two LIGO detectors in Hanford and Livingston, on September 14, 2015. As far as we can tell the way the signal ends is completely in agreement with the prediction Vishveshwara made almost five decades ago.
In 1975 I was struggling to decide what I should study at the University: engineering, music or physics. It was Vishu’s public lecture during a science festival at our college in Bangalore, that helped me resolve my dilemma and motivated me to pursue physics. That’s why in a book dedicated to honour Vishu on his sixtieth birthday in 1997 that I wrote “I will consider myself to be most fortunate if some day I can come and tell you that we have seen the quasi-normal modes to conclude your quest on the trail of a black hole and to begin a new era in gravitational astronomy”. I am so glad I was able to do that earlier this month.
GW150914 is the first of what we expect to be a myriad of other binary black holes we hope to observe as LIGO detectors improve in sensitivity and other detectors like Virgo, KAGRA and LIGO-India, join the force over the next decade. Some of those signals will be strong enough to not just get a glimpse of quasi-normal modes but to actually confirm that they consist of a spectrum of modes that is consistent with the mass and spin of the black holes that emitted the signal. Still further in the future, with Einstein Telescope or Laser Interferometer Space Antenna we will observe even stronger quasi-normal modes, which should reveal the properties of the parent black holes, hence proving that black holes have memory. Confirming this would be a further testament to Einstein’s theory of gravity.