Book contents
- Frontmatter
- Contents
- 1 Introduction to Modern Methods for Classical and Quantum Fields in General Relativity
- 2 Geometry of Black Hole Spacetimes
- 3 An Introduction to Conformal Geometry and Tractor Calculus, with a view to Applications in General Relativity
- 4 An Introduction to Quantum Field Theory on Curved Spacetimes
- 5 A Minicourse on Microlocal Analysis for Wave Propagation
- References
3 - An Introduction to Conformal Geometry and Tractor Calculus, with a view to Applications in General Relativity
Published online by Cambridge University Press: 21 December 2017
Book contents
- Frontmatter
- Contents
- 1 Introduction to Modern Methods for Classical and Quantum Fields in General Relativity
- 2 Geometry of Black Hole Spacetimes
- 3 An Introduction to Conformal Geometry and Tractor Calculus, with a view to Applications in General Relativity
- 4 An Introduction to Quantum Field Theory on Curved Spacetimes
- 5 A Minicourse on Microlocal Analysis for Wave Propagation
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Asymptotic Analysis in General Relativity , pp. 86 - 170Publisher: Cambridge University PressPrint publication year: 2018
References
[1] , , and , On the heat equation and the index theorem, Inventiones Mathematicae, 19 (1973), 279–330.Google Scholar
[2] , , and , Thomas's structure bundle for conformal, projective and related structures, Rocky Mountain J.Math.,
Mountain J.Math., 24 (1994), 1191–1217.Google Scholar
[3] , , and , Invariant theory for conformal and CR geometry, Annals of Mathematics,
of Mathematics, 139 (1994), 491–552.Google Scholar
[4] , Conformal structure and spin geometry, in Dirac Operators: Yesterday and Today, (, , , and , Eds.), International Press, (2005), 163–191.Google Scholar
[5] and , Conformally invariant non-local operators, Pacific Journal of Mathematics,
Journal of Mathematics, 201 (2001), 19–60.Google Scholar
[6] , Infinitesimal automorphisms and deformations of parabolic geometries, . Math. Soc., 10 (2008), 415–437.
[7] and , Stand ard tractors and the conformal ambient metric construction, Annals Global Anal.Geom.,
Global Anal.Geom., 24 (2003), 231–259.Google Scholar
[8] and , Tractor bundles for irreducible parabolic geometries, in S.M.F. Colloques, Seminaires & Congres,
S.M.F. Colloques, Seminaires & Congres, 4 (2000), 129–154.Google Scholar
[9] and , Tractor calculi for parabolic geometries, Trans. Amer. Math. Soc.,
. Amer. Math. Soc., 354 (2002), 1511–1548.Google Scholar
[10] , , and , Projective BGG equations, algebraic sets, and compactifications of Einstein geometries, Math. Soc., 86 (2012), 433–454.
[11] , , and , Holonomy reductions of Cartan geometries and curved orbit decompositions, Duke Math. J.,
Math. J., 163 (2014), 5, 1035–1070.Google Scholar
[12] , , Parabolic Geometries I: Background and General Theory, Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2009.
[13] , Problèmes de Neumann non linéaires sur les variètès riemanniennes, . Anal., 57 (1984), 154–206.
[14] , Conformal Tractor Calculus for Stationary and Static Spacetimes, MSc thesis, University of Auckland, 2012.
[15] and , On the extendability of parallel sections of linear connections, Ann. Mat. Pura Appl. (4), 195 (2016), 1237–1253.
[16] , The electron wave equation in de-Sitter space, Ann. Math., 36 (1935), 657–669.
[17] and , The Ambient Metric, Annals of Mathematics Studies, 178.
Princeton University Press, 2012. Available online: http://arxiv.org/ pdf/0710.0919v2.pdfGoogle Scholar
[18] , Conformal geometry of a subspace, Trans. Amer. Math. Soc., 56 (1944), 309–433.
[19] , Conformal infinity, Living Rev. Relativity,
Rev. Relativity, 7 (2004), 1. [Online Aricle]: cited 21/04/2014, http://www.livingreviews.org/lrr-2004-1Google Scholar
[20] and , Local twistors and the conformal field equations, . Phys., 41 (2000), 437–443.
[21] , Conformal Einstein evolution, in Proceedings of the Tubingen Workshop on the Conformal Structure of Space-times, ( and , Eds.), Springer Lecture Notes in Physics, 604 (2002), 1–50.
[22] , Local characterization of singularities in general relativity, . Phys., 9 (1968), 450–465.
[23] , Asymptotic structure of space-time, in Asymptotic Structure of Space- Time, ( and , Eds.), Springer, (1977), 1–105.Google Scholar
[24] , Almost Einstein and Poincare–Einstein manifolds in Riemannian signature, J.Geometry and Physics, 60 (2010), 182–204.
[25] , Aspects of parabolic invariant theory, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II,
ai Rendiconti del Circolo Matematico di Palermo, Serie II, 59 (1999), 25–47.Google Scholar
[26] , Conformal de Rham Hodge theory and operators generalising the Q-curvature, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II,
ai Rendiconti del Circolo Matematico di Palermo, Serie II, 75 (2005), 109–137.Google Scholar
[27] , Invariant theory and calculus for conformal geometries, Advances in Mathematics,
in Mathematics, 163 (2001), 206–257.Google Scholar
[28] , , and , Poincare–Einstein holography for forms via conformal geometry in the bulk, Mem. Amer. Math. Soc., 235 (2014), 1–101.
[29] and , Obstructions to conformally Einstein metrics in n dimensions, . Phys., 56 (2006), 450–484.
[30] and , Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus, Communications in Mathematical Physics,
in Mathematical Physics, 235 (2003), 339–378.Google Scholar
[31] and , The ambient obstruction tensor and the conformal deformation complex, Pacific Journal of Mathematics,
Journal of Mathematics, 226 (2006), 309–351.Google Scholar
[32] and , forthcoming.
[33] and , Boundary calculus for conformally compact manifolds, Indiana Univ. Math. J., 63 (2014), 119–163.
[34] and , Generalising the Willmore equation: submanifold conformal invariants from a boundary Yamabe problem, preprint, arXiv:1407.6742v1 [hep-th], (2014).
[35] and , Conformal hypersurface geometry via a boundary Loewner-Nirenberg-Yamabe problem, arXiv:1506.02723 [math.DG] (2015).
[36] , , , and , Conformally invariant powers of the Laplacian. , Math. Soc., 46 (1992), 557–565.
[37] and , Subtleties concerning conformal tractor bundles, Cent. Eur. ., 10 (2012), 1721–1732.
[38] , A Conformally Invariant Third Order Neumann-Type Operator for Hypersurfaces, MSc thesis, University of Auckland, 2003.
[39] , , , Conformal Einstein spaces, Gen. Relativity Gravitation,
. Relativity Gravitation, 17 (1985), 343–352.Google Scholar
[40] , Ambitwistors and Einstein's equations, Class. Quant. Grav., 2 (1985), 555–563.
[41] , Conformal Killing forms with normalisation condition, Rend. Circ. Mat. Palermo Suppl. No. 75 (2005), 279–292.
[42] , A conformal extension theorem based on null conformal geodesics, . Phys., 50, 112502, (2009).
[43] , The conformal field equations and the tractor formalism in general relativity, conference presentation, BritGrav 10, Dublin, 7th April 2010. Slides available online: http://www.dcu.ie/nolanb/Luebbe.pdf
[44] and , An extension theorem for conformal gauge singularities, . Phys., 50, 112501, (2009).
[45] , Seminar on the Atiyah-Singer index theorem. With contributions by , , , , and . Annals of Mathematics Studies, No. 57, Princeton University Press, 1965.Google Scholar
[46] , A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary), SIGMA,
, 4 (2008), Paper 036, 3 pp.Google Scholar
[47] , Asymptotic properties of fields and space-times, Phys. Rev. Lett., 10 (1963), 66–68.
[48] , The light cone at infinity, in Relativistic Theories of Gravitation, (, Ed.), Pergamon Press, Oxford, UK, (1964), 369–373.Google Scholar
[49] , Structure of space-time, in Battelle Rencontres, (, and , Eds.),W.A. Benjamin, Inc., New York, NY, USA, (1968), 121–235.Google Scholar
[50] , Zero rest-mass fields including gravitation: asymptotic behaviour, Proc. R. Soc. Lond., A284 (1965), 159–203.Google Scholar
[51] , , Twistor theory: an approach to the quantisation of fields and space-time, Physics Reports (Section C of Physics Letters), 6 (1972), 241–316.
[52] , Tractor calculus and invariants for conformal submanifolds, MSc thesis, University of Auckland, 2006.
[53] , Natural differential operators on Riemannian manifolds and representations of the orthogonal and special orthogonal groups, Geom., 10 (1975), 647–660.
[54] , A conformal wave equation, Proc. Nat. Acad. Sci. USA, 21 (1935), 484–487.
[55] , Manufacturing Conformal Invariants of Hypersurfaces, PhD thesis, University of Auckland, 2013.
- 14
- Cited by