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Initial value formulation (general relativity)
open-in-new
<h2 id="see-also">See also</h2> <ul><li><a href="/facts/ADM_formalism/48tVaQfr">ADM formalism</a></li></ul> <h2 id="notes">Notes</h2> <ul><li>Arnowitt, Richard; Deser, Stanley; Misner, Charles W. (1962). "The dynamics of general relativity". In Witten, L. (ed.). <i>Gravitation: An Introduction to Current Research</i>. Wiley. pp. 227–265.</li> <li>Bruhat, Yvonne (1962). "The Cauchy Problem". In Witten, L. (ed.). <i>Gravitation: An Introduction to Current Research</i>. Wiley. p. 130.</li> <li>Fourès-Bruhat, Yvonne (1952). <a href="https://doi.org/10.1007%2FBF02392131">"Théoréme d'existence pour certains systémes d'équations aux derivées partielles non linéaires"</a>. <i>Acta Mathematica</i>. 88 (1): 141–225. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1952AcMa...88..141F">1952AcMa...88..141F</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF02392131">10.1007/BF02392131</a>.</li> <li>Gourgoulhon, Eric (2007). <i>3+1 Formalism and Bases of Numerical Relativity</i>. <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/gr-qc/0703035">gr-qc/0703035</a>. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2007gr.qc.....3035G">2007gr.qc.....3035G</a>.</li> <li>Hawking, Stephen W.; Ellis, George F. R. (1973). <i>The large scale structure of space-time</i>. Cambridge University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-521-09906-4.</li> <li>Kalvakota, Vaibhav R. (July 1, 2021). "<a href="https://web.ma.utexas.edu/mp_arc/c/21/21-33.pdf">A brief account of the Cauchy problem in General Relativity</a>".</li> <li>Lehner, Luis (2001). "Numerical Relativity: A review". <i>Class. Quantum Grav</i>. 18 (17): R25 – R86. <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/gr-qc/0106072">gr-qc/0106072</a>. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2001CQGra..18R..25L">2001CQGra..18R..25L</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1088%2F0264-9381%2F18%2F17%2F202">10.1088/0264-9381/18/17/202</a>. <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:9715975">9715975</a>.</li> <li>Misner, Charles W.; Thorne, Kip. S.; Wheeler, John A. (1973). <i>Gravitation</i>. W. H. Freeman. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-7167-0344-0.</li> <li>Reula, Oscar A. (1998). <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5253804">"Hyperbolic Methods for Einstein's Equations"</a>. <i>Living Rev. Relativ</i>. 1 (1): 3. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1998LRR.....1....3R">1998LRR.....1....3R</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.12942%2Flrr-1998-3">10.12942/lrr-1998-3</a>. <a href="/facts/PMC_(identifier)/dX1zMt71">PMC</a> <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5253804">5253804</a>. <a href="/facts/PMID_(identifier)/JlHAvMHt">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/28191833">28191833</a>.</li> <li><a href="/facts/Robert_M._Wald/RSBJhccg">Wald, Robert M.</a> (1984). <i><a href="/facts/General_Relativity_(book)/lYIGX0gc">General Relativity</a></i>. Chicago: University of Chicago Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-226-87033-2.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Cf. Hawking & Ellis 1973, sec. 7.1. - Hawking, Stephen W.; Ellis, George F. R. (1973). The large scale structure of space-time. Cambridge University Press. ISBN 0-521-09906-4. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Arnowitt, Deser & Misner 1962; for a pedagogical introduction, see Misner, Thorne & Wheeler 1973, §21.4–§21.7. - Arnowitt, Richard; Deser, Stanley; Misner, Charles W. (1962). "The dynamics of general relativity". In Witten, L. (ed.). Gravitation: An Introduction to Current Research. Wiley. pp. 227–265. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Fourès-Bruhat 1952 and Bruhat 1962; for a pedagogical introduction, see Wald 1984, ch. 10; an online review can be found in Reula 1998. - Fourès-Bruhat, Yvonne (1952). "Théoréme d'existence pour certains systémes d'équations aux derivées partielles non linéaires". Acta Mathematica. 88 (1): 141–225. Bibcode:1952AcMa...88..141F. doi:10.1007/BF02392131. <a href="https://doi.org/10.1007%2FBF02392131" target="_blank">https://doi.org/10.1007%2FBF02392131</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>See Gourgoulhon 2007. - Gourgoulhon, Eric (2007). 3+1 Formalism and Bases of Numerical Relativity. arXiv:gr-qc/0703035. Bibcode:2007gr.qc.....3035G. <a href="https://arxiv.org/abs/gr-qc/0703035" target="_blank">https://arxiv.org/abs/gr-qc/0703035</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>For a review of the basics of numerical relativity, including the problems alluded to here and further difficulties, see Lehner 2001. - Lehner, Luis (2001). "Numerical Relativity: A review". Class. Quantum Grav. 18 (17): R25 – R86. arXiv:gr-qc/0106072. Bibcode:2001CQGra..18R..25L. doi:10.1088/0264-9381/18/17/202. S2CID 9715975. <a href="https://arxiv.org/abs/gr-qc/0106072" target="_blank">https://arxiv.org/abs/gr-qc/0106072</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> </ol>