The University of Cambridge recently lost a crown jewel in Professor Stephen Hawking, with the renowned physicist passing away at the age of 76, on 14 March 2018. Interestingly, having been born on the 300th anniversary of Galileo Galilei’s death, Professor Hawking passed away on the 139th anniversary of Albert Einstein’s birth.

*My message of condolence on the demise of Professor Stephen Hawking at Gonville and Caius College, where he was a Fellow*

Professor Hawking was a pioneer in the field of theoretical cosmology and physics. He was the *Lucasian Professor of Mathematics* (a position once held by Isaac Newton himself) in the Department of Applied Mathematics and Theoretical Physics, University of Cambridge for 30 years (1979-2009)! His book *A Brief History of Time* was so popular that it appeared on the best-seller list of the *Sunday Times *for a record-breaking 237 weeks.

His many scientific contributions included his work on gravitational singularity theorems and the prediction that black holes emit radiation, known as Hawking Radiation after him. The simplest type of black hole, in which the core does not rotate and just has a singularity and event horizon, is known as a Schwarzschild Black Hole after the German physicist Karl Schwarzschild who pioneered much of the very early theory behind black holes in the early twentieth century. In 1963, physicist Roy Kerr discovered a solution to Einstein’s field equations of General Relativity that described a spinning object, and suggested that anything which collapsed would eventually settle down into a spinning black hole. It spins since the star from which the black hole is formed was itself spinning. A general cycle of the formation of a black hole is given in the illustration below:

A rotating black hole would bulge outward near its equator due to its rotation (the faster the spin, the more the bulge). In the mid-1960s, Roger Penrose devoted himself to the study of black holes and proved an important theorem which showed that a gravitational collapse of a large dying star must result in a singularity, where space-time cannot be continued and classical general relativity breaks down. He, along with American theoretical physicist John Archibald Wheeler, went on to prove that any non-rotating star would end up after such a collapse as a perfectly spherical black hole, whose size would depend solely on its mass. In the late 1960s, Penrose started collaborating with Stephen Hawking, in more investigations into the subject. They applied a new, complex mathematical model derived from the theory of general relativity, which led to Hawking proving the first of several *singularity theorems*. Such theorems provided a set of sufficient conditions for the existence of a gravitational singularity in space-time, and showed that, far from being mathematical curiosities which appear only in special cases, singularities are actually a fairly generic feature of general relativity.

As complex as it may seem, a black hole can essentially be described by just three quantities: how much mass went into it, how fast it is spinning (by its angular momentum) and its electrical charge, in what has come to be known as the “No Hair Theorem”, after Wheeler’s comment that “black holes have no hair”, by which he meant that any other information about the matter which formed a black hole (for which `hair’ is a metaphor) remains permanently inaccessible to external observers within its event horizon and is all but irrelevant.

*Sir Roger Penrose*

Brandon Carter and Stephen Hawking proved the *No-Hair Theorem* mathematically in the early 1970s, showing that the size and shape of a rotating black hole would depend only on its mass and rate of rotation, and not on the black hole mechanics, analogous to the laws of thermodynamics, by relating mass to energy, area to entropy, and surface gravity to temperature.

*Evidence of spinning nature of some black holes is given by this Chandra and XMM-Newton observations of iron atoms in the hot gas orbiting 3 stellar black holes (Cygnus X-1, XTE J1650-500, GX 339-4). The gravity of a black hole shifts X-rays from iron atoms to lower energies, producing a strongly skewed X-ray signal. The orbit of a particle near a black hole depends on the curvature of space around the black hole, which also depends on how fast the black hole is spinning. A spinning black hole drags space around with it and allows atoms to orbit nearer to the black hole than is possible for a non-spinning black hole. The tighter orbit means stronger gravitational effects, which means that more of the X-rays from iron atoms are shifted to lower energies.*

In 1974, Hawking shocked the physics world by showing that black holes should in fact thermally create and emit sub-atomic particles, known today as *Hawking Radiation*, until they exhaust their energy and evaporate completely. According to this theory, black holes are not completely black, and neither do they last forever.

Hawking showed how the strong gravitational field around a black hole can affect the production of matching pairs of particles and anti-particles, as is happening all the time in apparently empty space according to quantum theory. If the particles are created just outside the event horizon of a black hole, then it is possible that a member of the pair may escape, and in this way the black hole would gradually lose mass. In proving this, Hawking was the first to set out a theory of cosmology that could be described by a union of the general theory of relativity and quantum mechanics (speaking of which, the one other major point that he believed in was the interpretation of quantum mechanics that states that all possible alternate histories and futures are real, each representing an actual `universe’, often called the ‘many worlds’ interpretation).

In his passing away, we have lost a gem, a scientist who will always be written about, in the pages of history, in a glorious way. I have heard that he wanted the Hawking Radiation equation carved on his tombstone, and that goes a long way to show that Professor Hawking was a man who lived, breathed and died with the strong belief and virtue of his work and legacy; a legacy a seeker of truth (in nature and reality) created that is arguably above any created in this generation.