Hawking on the Big Bang and Black Holes by Stephen Hawking

Author:Stephen Hawking [Hawking, Stephen]
Language: eng
Format: epub
ISBN: 9789810210786
Google: aKcJO8CZ1kIC
Amazon: 9810210795
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Goodreads: 83699
Published: 2010-07-24T13:13:04+00:00

1 5 . The path-integral approach to quantum gravity

S. W. HAWKI N G

15.1 Introduction

Classical general relativity is a very complete theory. It prescribes not only the equations which govern the gravitational field but also the motion of bodies under the inftuence of this field. However it fails in two respects to give a fully satisfactory description of the observed universe.

Firstly, it treats the gravitational field in a purely classical manner whereas all other observed fields seem to be quantized. Second, a number of theorems (see Hawking and Ellis, 1973) have shown that it leads inevitably to singularities of spacetime. The singularities are predicted to occur at the beginning of the present expansion of the universe (the big bang) and in the collapse of stars to form black holes. At these singularities, classical general relativity would break down completely, or rather it would be incomplete because it would not prescribe what came out of a singularity (in other words, it would not provide boundary conditions for the field equations at the singular points). For both the above reasons one would like to develop a quantum theory of gravity. There is no well defined prescription for deriving such a theory from classical general relativity. One has to use intuition and general considerations to try to construct a theory which is complete, consistent and which agrees with classical general relativity for macroscopic bodies and low curvatures of spacetime. It has to be admitted that we do not yet have a theory which satisfies the above three criteria, especially the first and second. However, some partial results have been obtained which are so compelling that it is difficult to believe that they will not be part of the final complete picture.

These results relate to the conection between black holes and thermodynamics which has already been described in chapters 6 and 1 3 by Carter and Gibbons. In the present article it will be shown how this relationship between gravitation and thermodynamics appears also when one quantizes the gravitational field itself.

There are three main approaches to quantizing gravity:

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