Edited by Ray d'Inverno
Publisher: Cambridge University Press
Print Publication Year: 1992
Online Publication Date:December 2009
Online ISBN:9780511524639
Hardback ISBN:9780521439763
Paperback ISBN:9780521017350
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511524639.006
Subjects: Cosmology, Relativity and Gravitation, Astrophysics
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Abstract. Penrose has described a method for computing a solution for the characteristic initial value problem for the spin-2 equation for the Weyl spinor. This method uses the spinorial properties in an essential way. From the symmetrized derivatives of the Weyl spinor which are known from the null datum on a cone one can compute all the derivatives by using the field equation and thus one is able to write down a power series expansion for a solution of the equation. A recursive algorithm for computing the higher terms in the power series is presented and the possibility of its implementation on a computer is discussed.
INTRODUCTION
Due to the nonlinear nature of general relativity it is very difficult to obtain exact solutions of the field equations that are in addition of at least some physical significance. Prominent examples are the Schwarzschild, Kerr and Friedmann solutions. Given a concrete physical problem it is more often than not rather hopeless to try to solve the equations using analytical techniques only. Therefore, in recent years, attention has turned towards the methods of numerical relativity where one can hope to obtain answers to concrete questions in a reasonable amount of time given enough powerful machines. However, it is still a formidable task to obtain a reliable code. There is first of all the inherent complexity of the field equations themselves when written out in full without the imposition of symmetries or other simplifying assumptions.
pp. i-vi
pp. vii-ix
pp. x-xii
pp. xiii-xiv
pp. xv-xx
PART A - THEORETICAL APPROACHES: Read PDF
pp. 1-2
Numerical relativity on a transputer array: Read PDF
pp. 3-19
Some aspects of the characteristic initial value problem in numerical relativity: Read PDF
pp. 20-33
The characteristic initial value problem in general relativity: Read PDF
pp. 34-40
Algebraic approach to the characteristic initial value problem in general relativity: Read PDF
pp. 41-49
On hyperboloidal hypersurfaces: Read PDF
pp. 50-58
The initial value problem on null cones: Read PDF
pp. 59-68
Introduction to dual-null dynamics: Read PDF
pp. 69-78
On colliding plane wave space-times: Read PDF
pp. 79-82
Boundary conditions for the momentum constraint: Read PDF
pp. 83-93
On the choice of matter model in general relativity: Read PDF
pp. 94-102
A mathematical approach to numerical relativity: Read PDF
pp. 103-113
Making sense of the effects of rotation in general relativity: Read PDF
pp. 114-129
Stability of charged boson stars and catastrophe theory: Read PDF
pp. 130-140
PART B - PRACTICAL APPROACHES: Read PDF
pp. 141-142
Numerical asymptotics: Read PDF
pp. 143-162
Instabilities in rapidly rotating polytropes: Read PDF
pp. 163-181
Gravitational radiation from coalescing binary neutron stars: Read PDF
pp. 182-201
“Critical” behaviour in massless scalar field collapse: Read PDF
pp. 202-222
Godunov-type methods applied to general relativistic stellar collapse: Read PDF
pp. 223-229
Astrophysical sources of gravitational waves and neutrinos: Read PDF
pp. 230-246
Gravitational radiation from 3D gravitational stellar core collapse: Read PDF
pp. 247-257
A vacuum fully relativistic 3D numerical code: Read PDF
pp. 258-264
Solution of elliptic equations in numerical relativity using multiquadrics: Read PDF
pp. 265-280
Self-gravitating thin discs around rotating black holes: Read PDF
pp. 281-291
An ADI scheme for a black hole problem: Read PDF
pp. 292-296
Time-symmetric ADI and causal reconnection: Read PDF
pp. 297-307
The numerical study of topological defects: Read PDF
pp. 308-334
Computations of bubble growth during the cosmological quark-hadron transition: Read PDF
pp. 335-344
Initial data of axisymmetric gravitational waves with a cosmological constant: Read PDF
pp. 345-352
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