General Relativity

Proceedings of the Forty Sixth Scottish Universities Summer School in Physics, Aberdeen, July 1995

G.S Hall

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351446020
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

General Relativity provides an unusually broad survey of the current state of this field. Chapters on mathematical relativity cover many topics, including initial value problems, a new approach to the partial differential equations of physics, and work on exact solutions. The chapters on relativistic cosmology and black holes explore cosmology. Other chapters deal with gravitational waves, experimental relativity, quantum gravity, and aspects of computing in relativity. The book will be useful both to postgraduates and to established workers in the field.

Partial Differential Equations of Physics

Robert Geroch

Enrico Fermi Institute Chicago

1 Introduction

The physical world is traditionally organized into various systems: electromagnetism, perfect fluids, Klein-Gordon fields, elastic media, gravitation, etc. Our descriptions of these individual systems have certain features in common: use of fields on a fixed space-time manifold M, a geometrical interpretation of the fields in terms of M, partial differential equations on these fields, an initial-value formulation for these equations. Yet beyond these common features there are numerous differences of detail: some systems of equations are linear, and some are not; some have constraints, and some do not; some arise from Lagrangians, and some do not; some are first-order, and some higher-order. Systems also differ in other respects, e.g. as to what fields they need as background, what interactions they permit (or require). It almost seems as though, in the end, every physical system has its own special character.

It might be useful to have a systematic treatment of the fields and equations that arise in the description of physical systems. Thus, there would be a general definition of a ‘field’, and a general form for a system of partial differential equations on such fields. The treatment would consist of a framework sufficiently broad to encompass the systems found in nature, but no broader. One would, for example, treat the initial-value formulation once and for all within this broad framework, with the formulations for individual physical systems emerging as special cases. In a similar way, one would treat—within a quite general context—constraints, the geometrical character of physical fields, how some systems require other fields as a background, how interactions operate, etc. The goal of such a treatment would be to get a better grip on the structural features of the partial differential equations of physics. Here are two examples of issues on which such a treatment might shed light. What, if any, is the physical basis on which the various fields on the manifold M are grouped into separate physical systems? Thus, for instance, the fields (n, F_ab, p, u^a) are grouped into (n, ρ, u^a) (a perfect fluid), and (F_ab) (electromag...

Table of contents

• Cover Page
• Title Page
• Copy Right Page
• Content Page
• Mathematics of General Relativity
• Partial Differential Equations of Physics
• Gravitostatics and Rotating Bodies
• A Guide to Basic Exact Solutions
• Relativistic Cosmology
• Black Holes in Cosmology and Astrophysics
• Source of Gravitational Waves
• Detection of Gravitational Waves
• The Confrontation between General Relativity and Experiment. A 1995 Update
• Algebraic Computing in General Relativity
• Numerical Computing in General Relativity
• Quantum Gravity
• Poster Abstracts
• Participants’ Addresses
• Index