Frontiers in general relativity / Peter A. Hogan and Dirk Puetzfeld.

Format:

Book

Author/Creator:

Hogan, P. A. (Peter A.), author.

Puetzfeld, Dirk, author.

Series:

Lecture Notes in Physics

Lecture Notes in Physics ; v.984

Language:

English

Subjects (All):

General relativity (Physics).

Physical Description:

1 online resource (250 pages) : illustrations

Edition:

1st ed.

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

This book discusses some of the open questions addressed by researchers in general relativity.Photons and particles play important roles in the theoretical framework, since they are involved in analyzing and measuring gravitational fields and in constructing mathematical models of gravitational fields of various types.

Contents:

Intro

Preface

Contents

About the Authors

1 Congruences of World Lines

1.1 Time-Like Conguences

1.2 Null Geodesic Congruences

1.3 The World Function and Deviation Equations

References

2 Bivector Formalism in General Relativity

2.1 Bivectors and Electromagnetic Fields

2.2 Electromagnetic Radiation

2.3 Bivectors and Gravitational Fields

2.4 The Kerr Space-Time

2.5 Passage to Charged Kerr Space-Time

2.6 Using the Bianchi Identities

3 Hypothetical Objects in Electromagnetism and Gravity

3.1 Part I: A Light-Like Charge

3.2 Geometry Based on a Non-geodesic Null World Line

3.3 Maxwell Field of a Charge with Non-geodesic World Line

3.4 Part II: A Kerr Black Hole and Light-Like Matter

3.5 Axial Symmetry

3.6 Energy-Momentum-Stress Tensor

3.7 Two Conservation Laws

4 Bateman Waves

4.1 Electromagnetic Radiation

4.2 Bateman Electromagnetic Waves

4.3 Some `Spherical' Electromagnetic Waves

4.4 Gravitational Radiation

4.5 Bateman Gravitational Waves

4.6 Some `Spherical' Gravitational Waves

5 Gravitational (Clock) Compass

5.1 Determination of the Gravitational Field by Means of Test Bodies

5.2 Gravitational Compass

General Solution

Vacuum Solution

Summary

5.3 Determination of the Gravitational Field by Means of Clocks

Frequency Ratio in Flat Space-Time

Frequency Ratio in Curved Space-Time

5.4 Gravitational Clock Compass

Special Spacetimes

Plane Gravitational Waves

Waves Radial Relative to r=0

6 de Sitter Cosmology

6.1 Null Hyperplanes in Space-Times of Constant Curvature

6.2 Intersecting Null Hyperplanes

6.3 Generalized Kerr-Schild Space-Times and Gravitational Waves

6.4 de Sitter Space-Time Revisited.

6.5 Collision of Gravitational Waves and ≠0

6.6 Post Collision Physical Properties

7 Small Magnetic Black Hole

7.1 Magnetic Poles

7.2 Background Space-Time/External Fields

7.3 Magnetic Black Hole Perturbation of Background

7.4 Equations of Motion in First Approximation

7.5 Equations of Motion in Second Approximation

7.6 Review of Approximations

8 Run-Away Reissner-Nordström Particle

8.1 Robinson-Trautman Solutions of the Einstein-Maxwell Equations

8.2 Accelerating Reissner-Nordström Particle

8.3 Perturbations of a Reissner-Nordström Particle

8.4 Equations of Motion of a Reissner-Nordström Particle

8.5 Energy Radiation Rate and Run-Away Motion

8.6 Run-Away Magnetic Reissner-Nordström Particle

A Congruences of World Lines

A.1 Properties of ηabcd

B Bateman Waves in the Linear Approximation

B.1 Covariant Treatment on General Space-Time

B.2 Ricci Identities and Bianchi Identities

C Gravitational (Clock) Compass

C.1 Coordinates for Minkowskian Space-Time

C.2 Plane Gravitational Waves I

C.3 Plane Gravitational Waves II

C.4 Waves Moving Radially Relative to r=0

D de Sitter Cosmology

D.1 Properties of Generalised Kerr-Schild Metrics

Reference

E Small Magnetic Black Hole

E.1 The Electromagnetic Field

Index.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

3-030-69370-8

OCLC:

1245664333