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Colliding Plane Waves in General Relativity [Minkštas viršelis]

  • Formatas: Paperback / softback, 256 pages, aukštis x plotis x storis: 234x157x12 mm, weight: 387 g
  • Serija: Dover Books on Physics
  • Išleidimo metai: 29-Apr-2016
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486801217
  • ISBN-13: 9780486801216
Kitos knygos pagal šią temą:
Colliding Plane Waves in General RelativityDidesnis paveikslėlis
  • Formatas: Paperback / softback, 256 pages, aukštis x plotis x storis: 234x157x12 mm, weight: 387 g
  • Serija: Dover Books on Physics
  • Išleidimo metai: 29-Apr-2016
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486801217
  • ISBN-13: 9780486801216
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780486801216.html
Raktažodžiai:
This monograph is a survey of recent research on the collision and interaction of gravitational and electromagnetic waves, a topic of particular importance to general relativity. 1991 edition, with updated postscript.


This monograph is a survey of recent research on the collision and interaction of gravitational and electromagnetic waves. "This is a particularly important topic in general relativity," the author notes, "since the theory predicts that there will be a nonlinear interaction between such waves." A new postscript updates developments since the book's initial 1991 publication.
1 Introduction
1(3)
1.1 Why consider wave interactions?
1(1)
1.2 Simplifying assumptions
2(2)
2 Elements Of General Relativity
4(7)
2.1 Basic notation
4(1)
2.2 Components of the curvature tensor
5(2)
2.3 Spin coefficients
7(3)
2.4 Einstein-Maxwell fields
10(1)
3 Colliding Impulsive Gravitational Waves
11(6)
3.1 The approaching waves
11(2)
3.2 The solution describing the interaction
13(2)
3.3 The structure of the solution
15(2)
4 Plane Waves
17(9)
4.1 The class of pp-waves
17(1)
4.2 The class of plane waves
18(3)
4.3 Particular cases
21(1)
4.4 Global properties
22(4)
5 Geometrical Considerations
26(8)
5.1 The focusing of congruences
26(3)
5.2 General theorems
29(2)
5.3 Colliding waves
31(3)
6 The Field Equations
34(8)
6.1 The coordinate system
34(2)
6.2 The derivation of the field equations
36(3)
6.3 The Einstein and Einstein-Maxwell equations
39(1)
6.4 Integrating the field equations
40(2)
7 Boundary Conditions
42(6)
7.1 General discussion
42(1)
7.2 Junction conditions for colliding plane waves
43(5)
8 Singularity Structure
48(15)
8.1 Singularities
48(2)
8.2 The singularity in region IV
50(3)
8.3 The Khan--Penrose solution
53(5)
8.4 The structure of other solutions
58(5)
9 The Szekeres Class Of Vacuum Solutions
63(6)
9.1 The solution in region IV
63(3)
9.2 The approaching waves
66(1)
9.3 The singularity structure
67(2)
10 Other Vacuum Solutions With Aligned Polarization
69(26)
10.1 A general method
69(5)
10.2 The non-singular `solution' of Stoyanov
74(2)
10.3 The solution of Ferrari and Ibanez and Griffiths
76(3)
10.4 The soliton solution of Ferrari and Ibanez
79(2)
10.5 The degenerate Ferrari--Ibanez solutions
81(4)
10.6 An odd order solution
85(1)
10.7 The second Yurtsever and the Feinstein-Ibanez solutions
86(4)
10.8 The first Yurtsever solutions
90(2)
10.9 Further explicit solutions
92(3)
11 Ernst's Equation For Colliding Gravitational Waves
95(8)
11.1 A derivation of the Ernst equation
95(3)
11.2 Boundary conditions
98(2)
11.3 Colinear solutions
100(3)
12 Solution-Generating Techniques
103(15)
12.1 The colinear case
103(2)
12.2 Rotations and Ehlers transformations
105(3)
12.3 Geroch transformations
108(2)
12.4 The Neugebauer--Kramer involution
110(3)
12.5 A combined transformation
113(1)
12.6 Other methods
114(4)
13 Vacuum Solutions With Non-Aligned Polarization
118(13)
13.1 The Nutku--Halil solution
118(2)
13.2 The Panov solution
120(1)
13.3 The Chandrasekhar--Xanthopoulos solution
121(6)
13.4 Other solutions
127(4)
14 The Initial Value Problem
131(6)
14.1 The initial data
131(1)
14.2 The colinear case
132(3)
14.3 The non-colinear case
135(2)
15 Colliding Electromagnetic Waves: The Bell--Szekeres Solution
137(9)
15.1 The Bell--Szekeres solution
137(2)
15.2 The structure of the solution
139(3)
15.3 Extensions of the solution
142(1)
15.4 A non-colinear collision
143(3)
16 Ernst's Equation For Colliding Electromagnetic Waves
146(10)
16.1 The field equations
146(5)
16.2 A simple class of solutions
151(2)
16.3 The Bell-Szekeres solution
153(3)
17 Colliding Electromagnetic Waves: Exact Solutions
156(12)
17.1 A technique of Chandrasekhar and Xanthopoulos
156(2)
17.2 Two particular examples
158(2)
17.3 Another type D solution
160(3)
17.4 A technique of Halilsoy
163(2)
17.5 Other solutions
165(3)
18 Colliding Electromagnetic Waves: Diagonal Solutions
168(9)
18.1 The generation technique of Panov
168(1)
18.2 An alternative approach
169(4)
18.3 Electromagnetic Gowdy cosmologies
173(3)
18.4 Other methods
176(1)
19 Electromagnetic Waves Colliding With Gravitational Waves
177(7)
19.1 A simple example
177(1)
19.2 General initial data
178(2)
19.3 A general class of solutions
180(4)
20 Other Sources
184(17)
20.1 Scalar fields
184(2)
20.2 Perfect fluid solutions
186(3)
20.3 Null fluids and the uniqueness problem
189(3)
20.4 Plane shells of matter
192(2)
20.5 Neutrino fields
194(5)
20.6 Other null fields
199(2)
21 Related Results
201(7)
21.1 Other wave interactions
201(1)
21.2 Collisions in non-flat backgrounds
202(1)
21.3 Solitons
203(2)
21.4 Alternative gravitational theories
205(1)
21.5 Numerical techniques
206(2)
22 Conclusions And Prospects
208(6)
22.1 General conclusions
208(2)
22.2 Prospects for further work
210(4)
Appendix: Coordinate Systems 214(2)
References 216(12)
Index 228(5)
Postscript 233