Feynman Lectures on Gravitation

Abstract

In the early 1960s Feynman lectured to physics undergraduates and, with the assistance of his colleagues Leighton and Sands, produced the three-volume classic Feynman Lectures in Physics.These lectures were delivered in the mornings. In the afternoons Feynman was giving postgraduate lectures on gravitation. This book is based on notes compiled by two students on that course: Morinigo and Wagner. Their notes were checked and approved by Feynman and were available at Caltech. They have now been edited by Brian Hatfield and made more widely available.The book has a substantial preface by John Preskill and Kip Thorne, and an introduction entitled 'Quantum Gravity' by Brian Hatfield. You should read these before going on to the lectures themselves.Preskill and Thorne identify three categories of potential readers of this book.1. Those with a postgraduate training in theoretical physics.2. 'Readers with a solid undergraduate training in physics'.3. 'Admirers of Feynman who do not have a strong physics background'.The title of the book is perhaps misleading: readers in category 2 who think that this book is an extension of the Feynman Lectures in Physics may be disappointed. It is not: it is a book aimed mainly at those in category 1. If you want to get to grips with gravitation (and general relativity) then you need to read an introductory text first e.g. General Relativity by I R Kenyon (Oxford: Oxford University Press) or A Unified Grand Tour of Theoretical Physics by Ian D Lawrie (Bristol: IoP). But there is no Royal Road.As pointed out in the preface and in the introduction, the book represents Feynman's thinking about gravitation some 40 years ago: the lecture course was part of his attempts to understand the subject himself, and for readers in all three categories it is this that makes the book one of interest: the opportunity to observe how a great physicist attempts to tackle some of the hardest challenges of physics. However, the book was written 40 years ago, and since then there have been many discoveries: black holes and the cosmic microwave background have been observed. There have also been theoretical developments.Unless you are a category 1 reader, you will find there are substantial passages you will need to skip over. There are also substantial sections throughout the book accessible to all, such as the following excerpt from lecture 13 (there are 16 lectures) in a section entitled 'Disappearing galaxies and energy conservation'.'Let me also say something that people who worry about mathematical proofs and inconsistencies seem not to know. There is no way of showing mathematically that a physical conclusion is wrong or inconsistent. All that can be shown is that the mathematical assumptions are wrong. If we find that certain mathematical assumptions lead to a logically inconsistent description of Nature, we change the assumptions, not nature.'If you admire Feynman, then you are likely to enjoy this book. If you want an introduction to gravitation and relativity, there are other more recent and ...

Microscopic formulation of black holes in string theory

“…There are many singular classical solutions of general relativity (for standard textbooks on classical general relativity, see, e.g., [6,7,8,9,10]), including the Schwarzschild black hole and the Big Bang model of cosmology. Black holes and their higher dimensional analogues (black branes) also appear as solutions of low energy string theory.…”

“…Let us briefly review some general properties of black holes [6,7,8,9,10]. Black holes are objects which result as end points of gravitational collapse of matter.…”

“…The geometry of the solution corresponds to a spacetime symmetry consisting of rotations SO(2) 1,2 × SO(2) 3,4 × SO(6) 5,6,7,8,9,10 plus Killing vectors (∂ t , ∂ 1 , . .…”

“…(W denotes a gravitational wave and not a winding mode.) The final configuration corresponds to D5 branes along x 5,6,7,8,9 and D1 branes along x 5 , with a non-zero amount of (left-moving) momentum. If the number of the three sets of M2 branes are Q 1 , Q 5 and N respectively, then these will correspond to the numbers of D1-, D5-branes and the quantized left-moving momentum respectively.…”

“…Here G d N denotes the d-dimensional Newton's constant. V T 4 is the volume of the four-torus in the directions x 6,7,8,9 , while R 5 is the radius of the circle along x 5 .…”