Wednesday, May 25, 2011

Kerr Black Holes

Cracking the Einstein Code - over an hour long free lecture by John P. Kerr at itunes

Kerr black holes were postulated by the theorist, Roy Kerr, picture at left, in the 1960s. He postulated that a rotating star could collapse into a black hole with a rotating ring of neutrons at its center rather than the usual singularity. Kerr believed that since there wasn't a singularity at the center, one might be able to travel through the black hole without being crushed by the singularity. Another theoretically possible scenario is that a person could enter the Kerr black hole and exit through a white hole on the other side (a white hole would actually push everything away from it using some form of exotic matter with negative energy), and, in this way, one could travel through spacetime.

In 1963 the New Zealand mathematician Roy Kerr, picture at left, achieved something that had eluded scientists for 47 years - he found the solution of Einstein's equations which describes the space outside a rotating star or black hole. Kerr's solution has been described as "the most important exact solution to any equation in physics".
Shortly after Einstein wrote down his gravitational field equations in 1915, Karl Schwarzschild found a solution which describes a non-rotating spherical star or black hole. However, it is known that all stars rotate, and that Schwarzschild's solution is at best an approximation. Kerr's achievement of finding an exact solution for the rotating case - something many had doubted could be done - was therefore a revolution in astrophysics. It ushered in a decade which might be called the Golden Age of Black Hole Physics, when General Relativity saw a Renaissance.

In the words of the legendary astrophysicist S. Chandrasekhar (Nobel laureate, 1983, picture at left): "In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. This shuddering before the beautiful, this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound."

Over the 41 years since its discovery the Kerr solution has been pivotal in deepening our understanding of astrophysics and gravitation theory. Many new effects arise in the Kerr solution - a rotating object drags space with it, in a way which would not be possible in Newton's theory.

In recent years a wealth of new astronomical observations has provided strong evidence for the existence of rotating Kerr black holes. Most impressively, it has recently been shown from observations of matter falling into the supermassive black hole in the centre of our own galaxy that it must be rotating at close to half of the maximum rate allowed by the Kerr solution.

Roy Kerr's contributions have been recognised by the award of the Hughes Medal (1984) of the Royal Society, and the Hector Medal (1982) and the Rutherford Medal (1993) of the Royal Society of New Zealand.

Visiting a Kerr Black Hole:

Comparing spinning and non spinning black holes:

Cracking the Einstein Code
Relativity and the Birth of Black Hole Physics
Fulvio Melia

Chapter 1
The scene could have been straight out of Universal Studios, Hollywood. Two men are breathing rhythmically in a smoke-filled modest little room facing south toward the capital of Texas. They sit quietly no more than an arm’s length apart, lost in thought. Roy Kerr, the younger of the two, is hunched over a secondhand desk with his back to the door, studying the equations he has just scribbled in a notebook. His older friend and mentor, Alfred Schild (1921–1977), picture at left, puffs away at a pipe while occupying a worn-out armchair to his right. It is late morning, and rays of sunlight filter through the bushes outside the window, creating a mosaic of light and shadow across the paneled walls.

At stake in this drama is the breakthrough solution to Einstein’s equations of general relativity that have defied the greatest scientific minds of the twentieth century. So impenetrable is this description of nature, that Einstein himself succeeded only partially in divining its impact on the meaning of space and time. But it is now 1963, and the freshly minted mathematician out of Cambridge University, settling in at Schild’s newly established Center for Relativity at the University of Texas at Austin, is about to crack the great physicist’s famous code.

Much has been written about Albert Einstein (1879–1955) and his profound influence on our view of the universe, but very little is known about the golden age of relativity, spanning the period 1960–75 following his death. This book is the story of the brilliant young scientists of that era who accepted the challenge of unraveling the mysteries hidden within the seemingly unfathomable language of general relativity, culminating with Kerr’s uncloaking of one of the most important and famous equations in all of science.

It is not always possible to discern the reasons why a scientific investigation meanders raggedly or slowly toward its ultimate goal, but in the development of relativity, the complexity of its mathematical formalism is certainly one of them. The difficulty of designing suitable experiments to test Einstein’s theory is another. But neither of these reasons emerged for want of interest. Einstein became an instant celebrity soon after founding general relativity in 1915–16, with the quick, auspicious confirmation of one of his predictions—that gravity should bend the path of light as well as that of any particle with mass. This result resounded across the front pages of newspapers around the world, and scientists took note of the new ideas almost right away.

Indeed, only a few months after Einstein’s publications began circulating around Europe, Karl Schwarzschild (1873–1916), picture at left, a soldier on the Russian front, amazingly already succeeded in finding a description of space and time consistent with Einstein’s theory, but only for a highly idealized situation, that is, for the gravitational field surrounding a static, spherically symmetric mass. Einstein greeted Schwarzschild’s news with enthusiasm, and his solution is used to this day to describe phenomena in regions of strong gravity. How odd, then, that arguably the most elegant scientific theory ever devised should slowly wither into the decades that followed this remarkable beginning. Those who knew him best have written that already by the 1930s Einstein’s interest in general relativity had almost completely lapsed. Having by then moved to Princeton, he could count the number of colleagues working in this field on just one hand. Relativity theory had become irrelevant to science—a situation that sadly persisted up until Einstein’s death. He would never know about the breathtaking discovery that would be announced just a few years later—a splendid confirmation of another prediction made several decades earlier.

This experimental achievement—a compelling demonstration in 1960 by the Harvard physicists Robert Pound and Glen Rebka that time slows down in the presence of gravity—sparked the revolution that followed during relativity’s golden age, leading to that special moment in Roy Kerr’s sepia-tinted office shortly afterward.

In the intervening years, failure to uncover practical applications of Einstein’s theory was compounded by the lack of progress in the experimental verification of general relativity as the correct description of nature. Ironically, part of the problem was the Schwarzschild solution itself, which in time would be used to predict that truly bizarre objects, variously called dark or frozen stars, must exist somewhere in the cosmos. Today we call them black holes, but back then no one—particularly Einstein—believed they could be real. Yet the Schwarzschild solution clearly demonstrated that the end result of a gravitational collapse must be the formation of a singularity—a point of infinite density—that creates a closed pocket of space and time forever disconnected from the outside world.

Many thought that nature could not possibly create something so unreasonable, believing that no object in the universe is truly static and that, at the very least, its rotation would inhibit any collapse toward a singularity. And so began the search for the “holy grail” of relativity—a description of space and time surrounding a spinning object. Everything we see in the universe rotates, the argument went, so in order to demonstrate that Einstein’s theory is a true description of gravity, we must be able to show that his equations do in fact describe space and time surrounding a spinning mass.

But what a challenge this turned out to be! Some of the world’s most renowned physicists spent their entire careers working on this problem, making some progress, but losing interest or hope in their waning years. Of course, by the middle of the twentieth century, quantum mechanics had forged well ahead of relativity in relevance and measurability, cementing its place as the overarching theory in the physics pantheon. It didn’t help that relativity and quantum mechanics seemed to be incompatible with each other, since the former uses perfectly measurable locations and times, whereas the latter is essentially a theory of spatial imprecision.

The Pound-Rebka experiment changed all that, principally because even the quantum mechanicists could not easily discount its remarkable implications. In fact, among the staunchest supporters of relativity and its relevance to modern physics was Vitaly Ginzburg, co-recipient of the 2003 Nobel Prize in physics for his work in the 1950s on superconductivity, a phenomenon in which some materials carry currents freely, without any resistance, by virtue of a quantum effect that becomes important at very low temperatures.

Though his interests were mainly in quantum mechanics, Ginzburg would nonetheless become an inspirational figure to many young physicists drawn to Einstein’s theory in the early 1960s. Listening to him, the twenty-eight-year-old Roy Kerr understood that “cracking Einstein’s code” was indeed the challenge he should ply with his mathematical talents—a task that would soon bring him to that fateful day sitting next to Alfred Schild in his smoke-filled office.

But the story begins well before Kerr’s arrival in Texas, even before Einstein himself, in fact. Musings concerning the nature of space and the meaning of time began to appear thousands of years earlier, in places such as the Greek colony of Elea in southern Italy. Before we explore the evolution in Einstein’s thinking that led to his theory of general relativity, and the inspired work that followed during its golden age, we will therefore begin by tracing some of the incipient thinking that led to the problem in the first place. Our journey commences in the fifth century BC with the Greek philosopher Zeno, a man clearly far ahead of his time. Zeno realized even back then that the notion of an absolute space independent of time was paradoxical—anticipating by several thousand years the eventual unification of the two into the structure we now refer to as simply spacetime.

This post is in memory of pioneering black hole researcher Doctor Robert Hamilton Boyer (December 11, 1932 to August 1, 1966), picture below, who was killed by Charles Whitman on August 1, 1966. He was only 33 when he was murdered. Mr. Boyer was a former mathematics instructor at the University of Texas at Austin and a Rhodes Scholar. He had just completed a month of teaching in Mexico. He was visiting friends in Austin, and was on his way to Liverpool University, where he would have taught applied mathematics and be nearer to his pregnant wife Lyndsey and their children. Upset by a national airline strike, Boyer left his friends' house to buy a train ticket. On his way, he was to stop at the Main Building to take care of some last-minute business. He was shot in the back and died immediately:

1 comment:

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