General Relativity: The most beautiful of theories

Applications and trends after 100 years

Carlo Rovelli

• Publisher: De Gruyter
• Year: 2015
• eBook ISBN: 9783110383645
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Generalising Newton's law of gravitation, general relativity is one of the pillars of modern physics. While applications in the beginning were restricted to isolated effects such as a proper understanding of Mercury's orbit, the second half of the twentieth century saw a massive development of applications. These include cosmology, gravitational waves, and even very practical results for satellite based positioning systems as well as different approaches to unite general relativity with another very successful branch of physics – quantum theory.

On the occassion of general relativity's centennial, leading scientists in the different branches of gravitational research review the history and recent advances in the main fields of applications of the theory, which was referred to by Lev Landau as "the most beautiful of the existing physical theories".

Contributions from:

• Andy C. Fabian, Anthony L. Lasenby, Astrophysical black Holes
• Neil Ashby, GNSS and other applications of General Relativity
• Gene Byrd, Arthur Chernin, Pekka Teerikorpi, Mauri Vaaltonen, Observations of general Relativity at strong and weaks limits
• Ignazio Ciufolini, General Relativity and dragging of inertial frames
• Carlo Rovelli, The strange world of quantum spacetime

Andrew C. Fabian and Anthony N. Lasenby

Astrophysical black holes

Abstract: Black holes are exotic relativistic objects which are common in the Universe. It has now been realised that they play a major role in the evolution of galaxies. Accretion of matter into them provides the power source for millions of high-energy sources spanning the entire electromagnetic spectrum. Observations of stars orbiting close to the centre of our Galaxy provide detailed clear evidence for the presence of a 4 million Solar mass black hole. Gas accreting onto distant supermassive black holes produces the most luminous persistent sources of radiation observed, outshining galaxies as quasars. The energy generated by such displays may even profoundly affect the fate of a galaxy. We briefly review the history of black holes and relativistic astrophysics before exploring the observational evidence for black holes and reviewing current observations including black hole mass and spin. In parallel (and in italic) we outline the general relativistic derivation of the physical properties of black holes relevant to observation. Finally we speculate on future observations and touch on black hole thermodynamics and the extraction of energy from rotating black holes.

1 Introduction

Black holes are exotic relativistic objects which are common in the Universe. It has now been realised that they play a major role in the evolution of galaxies, and accretion around them, and jets launched from them, provide the power source for millions of high-energy sources spanning the entire electromagnetic spectrum. In this chapter we consider black holes from an astrophysical point of view, and highlight their astrophysical roles as well as providing details of the General Relativistic phenomena which are vital for their understanding.

To aid the reader in appreciating both aspects, we have provided two tracks through the material of this Chapter. Track 1 provides an overview of their astrophysical role and of their history within 20th and 21st century astrophysics. Track 2 (in italic text) provides the mathematical and physical details of what black holes are, and provides derivations of their properties within General Relativity. These two tracks are tied together in a way which we hope readers with a variety of astrophysical interests and persuasions will find useful.

Andrew C. Fabian: Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, UK

Anthony N. Lasenby: Kavli Institute for Cosmology, Madingley Road, Cambridge, CB3 0HA and Cavendish Laboratory, J.J. Thomson Avenue, Cambridge, CB3 0HE, UK

2 A brief history of astrophysical black holes

2.1 Early history

Although the term “black hole” was coined by J. A. Wheeler in 1967, the concept of a black hole is over two hundred years old. In 1783, John Michell [41] was considering how to measure the mass of a star by the effect of its gravity on the speed of the light it emitted. Newton had earlier theorized that light consists of small particles. Michell realized that if a star had the same density as the Sun yet was 500 times larger in size, then light could not escape from it. The star would thus be invisible. He noted, however, that if it was orbited by a luminous star, the measurable motion of that star would betray the presence of the invisible one.

This prescient, but largely forgotten paper, embodies two important concepts. The first is that Newtonian light and gravity predicts a minimum radius R = 2GM/c² for a body of mass M from within which the body would not be visible. The second is that it can still be detected by its gravitational influence on neighbouring stars. The radius is now known as the Schwarzschild radius of General Relativity and is the radius of the event horizon of a non-spinning black hole. Black holes are now known to be common due to their gravitational effect on nearby stars and gas. Pursuing Newtonian black holes further leads to logical inconsistencies and also the problem that relativity requires the speed of light to be constant.

The concept re-emerged after the publication of Eintein’s General Theory of Relativity in 1915 when Karl Schwarzschild found a solution for a point mass. Einstein himself “had not expected that the exact solution to the problem could be formulated”. It was not realised at the time that the solution represented an object which would turn out to be common in the Universe. Chandrasekhar in 1931 [9] discovered an upper limit to the mass of a degenerate star and which implied the formation of black holes (although this was not spelled out). Eddington, who wrote the first book of General Relativity to appear in English, considered the inevitability of complete gravitational collapse to be a reductio ad absurdum of Chandrasekhar’s formula. The concept was again ignored for a further two decades, apart from work by Oppenheimer and Snyder [50] who considered the collapse of a homogenous sphere of pressureless gas in GR, and found that the sphere becomes cut off from communication with the rest of the Universe. In fact, what they had discovered was the inevitability of the formation of a black hole when there is no pressure support.

With this ...

Table of contents

• De Gruyter Studies in Mathematical Physics
• Title Page
• Copyright Page
• Table of Contents
• The most beautiful physical theory
• Astrophysical black holes
• Observations of General Relativity at strong and weak limits
• General Relativity and dragging of inertial frames
• GNSS and other applications of General Relativity
• The strange world of quantum spacetime
• Index
• List of contributors
• De Gruyter Studies in Mathematical Physics