Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-27T23:22:16.430Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  06 November 2020

Kirill Krasnov
Affiliation:
University of Nottingham
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Formulations of General Relativity
Gravity, Spinors and Differential Forms
, pp. 365 - 368
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agricola, Ilka. 2008. Old and new on the exceptional group G2. Notices Amer. Math. Soc., 55(8), 922929.Google Scholar
Aldrovandi, Ruben, and Pereira, José Geraldo. 2013. Teleparallel Gravity. Vol. 173. Dordrecht: Springer.CrossRefGoogle Scholar
Alexander, S., Marciano, A., and Smolin, L. 2014. Gravitational origin of the weak interaction’s chirality. Phys. Rev. D, 89(6), 065017.CrossRefGoogle Scholar
Alexandrov, S., and Krasnov, K. 2009. Hamiltonian analysis of non-chiral Plebanski theory and its generalizations. Class. Quant. Grav, 26, 055005.Google Scholar
Arnowitt, R. L., Deser, S., and Misner, C. W. 1960. Canonical variables for general relativity. Phys. Rev, 117, 1595.Google Scholar
Ashtekar, A. 1987. New Hamiltonian formulation of general relativity. Phys. Rev. D, 36, 1587.Google Scholar
Atiyah, M. F., Hitchin, Nigel J., and Singer, I. M. 1978. Self-duality in four-dimensional Riemannian geometry. Proc. Roy. Soc. Lond., A362, 425461.Google Scholar
Atiyah, Michael, Dunajski, Maciej, and Mason, Lionel. 2017. Twistor theory at fifty: From contour integrals to twistor strings. Proc. Roy. Soc. Lond., A473(2206), 20170530.Google Scholar
Basile, T., Bekaert, X., and Boulanger, N. 2016. Note about a pure spin-connection formulation of general relativity and spin-2 duality in (A)dS. Phys. Rev. D, 93(12), 124047.Google Scholar
Beke, D. 2011. Scalar-Tensor theory as a singular subsector of Λ(ϕ) Plebanski gravity. e-Print: arXiv:1111.1139 [gr-qc]CrossRefGoogle Scholar
Beke, D., Palmisano, G., and Speziale, S. 2012. Pauli-Fierz mass term in modified Plebanski gravity. JHEP, 1203, 069.Google Scholar
Besse, A. L. 2008. Einstein Manifolds. Berlin: Springer (original edition 1987).Google Scholar
Birmingham, Danny, Blau, Matthias, Rakowski, Mark, and Thompson, George. 1991. Topological field theory. Phys. Rept., 209, 129340.CrossRefGoogle Scholar
Blau, Matthias, and Thompson, George. 2016. Chern-Simons Theory with Complex Gauge Group on Seifert Fibred 3-Manifolds. e-Print: arXiv:1812.10966 [hep-th]Google Scholar
Bott, R. and Tu, L. W. 1982. Differential Forms in Algebraic Topology. Berlin: Springer.Google Scholar
Brans, C. H. 1974. Complex structures and representations of the einstein equations. J. Math. Phys., 15, 15591566.Google Scholar
Cahen, M., Debever, R., and Defrise, L. 1967. A complex vectorial formalism in general relativity. J. Math. Mech., 16, 761785.Google Scholar
Capovilla, R., Jacobson, T., Dell, J., and Mason, L. J. 1991. Self-dual two forms and gravity. Class. Quant. Grav, 8, 41.Google Scholar
Capovilla, R., Montesinos, M., Prieto, V. A., and Rojas, E. 2001. BF gravity and the Immirzi parameter. Class. Quant. Grav, 18, L49.Google Scholar
Carroll, S. 2019. An Introduction to General Relativity: Spacetime and Geometry. New York: Cambridge University Press.Google Scholar
Cheung, Clifford, and Remmen, Grant N. 2017. Hidden simplicity of the gravity action. JHEP, 09, 002.Google Scholar
de Haro, S., Solodukhin, S. N., and Skenderis, K. 2001. Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence. Commun. Math. Phys, 217, 595.Google Scholar
Deser, S. 1970. Selfinteraction and gauge invariance. Gen. Rel. Grav, 1, 9.CrossRefGoogle Scholar
Dray, T., Kulkarni, R., and Samuel, J.. 1989. Duality and conformal structure. J. of Math. Phys., 30, 13061309.CrossRefGoogle Scholar
Dubrovin, B. A., Novikov, A. T., and Fomenko, S. P. 1985. Modern Geometry Methods and Applications: Part II: The Geometry and Topology of Manifolds. Berlin: Springer.CrossRefGoogle Scholar
Fine, Joel, Krasnov, Kirill, and Panov, Dmitri. 2014. A gauge theoretic approach to Einstein 4-manifolds. New York J. Math., 20, 293323.Google Scholar
Frankel, T. 2012. The Geometry of Physics: An Introduction, 3rd ed. Boston, MA: Cambridge.Google Scholar
Freidel, L., and Starodubtsev, A. 2005. Quantum Gravity in Terms of Topological Observables. e-Print: hep-th/0501191Google Scholar
Freidel, L., Krasnov, K., and Puzio, R. 1999. BF description of higher dimensional gravity theories. Adv. Theor. Math. Phys, 3, 1289.Google Scholar
Freidel, Laurent. 2008. Modified gravity without new degrees of freedom. e-Print: arXiv:0812.3200 [gr-qc]Google Scholar
Friedrich, Th., Kath, I., Moroianu, A., and Semmelmann, U. 1997. On nearly parallel G2-structures. J. Geom. Phys., 23(3–4), 259286.CrossRefGoogle Scholar
Goenner, Hubert F. M. 2014. On the history of unified field theories. Part II. (ca. 1930–ca. 1965). Living Rev. Rel., 17, 5.Google Scholar
Goroff, Marc H., and Sagnotti, Augusto. 1986. The ultraviolet behavior of Einstein gravity. Nucl. Phys., B266, 709736.CrossRefGoogle Scholar
Gray, Alfred. 1969. Vector cross products on manifolds. Trans. Amer. Math. Soc., 141, 465504.Google Scholar
Haggett, S. A. and Tod, K. P. 1994. An Introduction to Twistor Theory, 2nd ed. New York: Cambridge.CrossRefGoogle Scholar
Hehl, F. W. 2012. Gauge theory of gravity and spacetime. Einstein Stud. 13, 145169.Google Scholar
Heisenberg, Lavinia. 2018. A systematic approach to generalisations of general relativity and their cosmological implications. Phys. Rept. 796, 1113.Google Scholar
Hejna, M. 2006. Symmetric Affine Theories and Nonlinear Einstein-Proca System. e-Print: gr-qc/0611118Google Scholar
Herfray, Yannick, and Krasnov, Kirill. 2015. New First Order Lagrangian for General Relativity. e-Print: arXiv:1503.08640 [gr-qc]Google Scholar
Herfray, Yannick, Krasnov, Kirill, Scarinci, Carlos, and Shtanov, Yuri. 2016a. A 4D gravity theory and G2-holonomy manifolds. Adv. Theor. Math. Phys. 22, 20012034.Google Scholar
Herfray, Yannick, Krasnov, Kirill, and Shtanov, Yuri. 2016b. Anisotropic singularities in chiral modified gravity. Class. Quant. Grav., 33, 235001.Google Scholar
Herfray, Yannick, Krasnov, Kirill, and Scarinci, Carlos. 2017. 6D interpretation of 3D gravity. Class. Quant. Grav., 34(4), 045007.Google Scholar
Hitchin, Nigel J. 2000. The geometry of three-forms in six dimensions. J. Diff. Geom., 55(3), 547576.Google Scholar
Hitchin, N. 2014. Differentiable manifolds. Lectures notes available from: https://people.maths.ox.ac.uk/hitchin/Google Scholar
Holst, S. 1996. Barbero’s Hamiltonian derived from a generalized Hilbert-Palatini action. Phys. Rev. D, 53, 5966.Google Scholar
Israel, W. 1970. Differential forms in general relativity. Comm. Dublin Inst. Adv. Studies, Ser. A., 19.Google Scholar
Jacobson, Ted, and Lee, Smolin. 1988. Covariant action for Ashtekar’s form of canonical gravity. Class. Quant. Grav., 5, 583.Google Scholar
Jordan, P., Ehlers, J., and Kundt, W. 2009. Strenge Lösungen der Feldgleichungen der Allgemeinen Relativitätstheorie. Gen. Rel. Grav., 41, 21912280.Google Scholar
Krasnov, K. 2011. Pure connection action principle for general relativity. Phys. Rev. Lett, 106, 251103.Google Scholar
Krasnov, Kirill. 2017a. Dynamics of 3-forms in seven dimensions. Class. Quant. Grav., 34(22), 225007.Google Scholar
Krasnov, Kirill. 2017b. Self-dual gravity. Class. Quant. Grav., 34(9), 095001.Google Scholar
Krasnov, Kirill. 2018. Field redefinitions and Plebanski formalism for GR. Class. Quant. Grav., 35(14), 147001.Google Scholar
Landau, L. D. and Lifshitz, E. M. 1987. The Classical Theory of Fields, 4th ed. New York: Elsevier.Google Scholar
Lisi, A. G., Smolin, L., and Speziale, S. 2010. Unification of gravity, gauge fields, and Higgs bosons. J. Phys. A, 43, 445401.CrossRefGoogle Scholar
MacDowell, S. W., and Mansouri, F. 1977. Unified geometric theory of gravity and supergravity. Phys. Rev. Lett, 38, 739.Google Scholar
Mitsou, Ermis. 2019. Spin connection formulations of real Lorentzian general relativity. Class. Quant. Grav., 36, 045008.Google Scholar
Nakahara, M. 2003. Geometry, Topology and Physics, 2nd ed. New York: Taylor and Francis.Google Scholar
Newman, Ezra, and Penrose, Roger. 1962. An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys., 3, 566578.Google Scholar
Peldan, P. 1992. Connection formulation of (2+1)-dimensional Einstein gravity and topologically massive gravity. Class. Quant. Grav, 9, 2079.CrossRefGoogle Scholar
Peldan, Peter. 1994. Actions for gravity, with generalizations: A review. Class. Quant. Grav., 11, 10871132.Google Scholar
Penrose, R. 1960. A spinor approach to general relativity. Annals Phys., 10, 171201.Google Scholar
Penrose, R. and Rindler, W. 1999. Spinors and Space-Time I: Two-Spinor Calculus and Relativistic Fields. New York: Cambridge (original edition 1984).Google Scholar
Perez, A. 2013. The spin foam approach to quantum gravity. Living Rev. Rel, 16, 3.Google Scholar
Petrov, A. Z. 2000. The classification of spaces defining gravitational fields. Gen. Rel. Grav., 32, 16611663.Google Scholar
Pietri, R. De, and Freidel, L. 1999. so(4) Plebanski action and relativistic spin foam model. Class. Quant. Grav, 16, 2187.Google Scholar
Plebanski, J. F. 1977. On the separation of Einsteinian substructures. J. Math. Phys., 18, 2511.Google Scholar
Pope, C. 2010. Kaluza-Klein theory. Lecture notes available from: http://people.physics.tamu.edu/pope/ihplec.pdfGoogle Scholar
Reese Harvey, F. 1990. Spinors and Calibrations. New York: Academic Press.Google Scholar
Reshetikhin, N., and Turaev, V. G. 1991. Invariants of three manifolds via link polynomials and quantum groups. Invent. Math., 103, 547597.CrossRefGoogle Scholar
Roberts, Justin. 1997. Refined state-sum invariants of 3- and 4-manifolds. Pages 217–234 of: Geometric topology (Athens, GA, 1993). AMS/IP Stud. Adv. Math., vol. 2. Amer. Math. Soc., Providence, RI.CrossRefGoogle Scholar
Smolin, L. 2009. The Plebanski action extended to a unification of gravity and Yang-Mills theory. Phys. Rev. D, 80, 124017.CrossRefGoogle Scholar
Sparks, James. 2011. Sasaki-Einstein Manifolds. Surveys Diff. Geom., 16, 265324.Google Scholar
Speziale, S. 2010. Bi-metric theory of gravity from the non-chiral Plebanski action. Phys. Rev. D, 82, 064003.Google Scholar
Stelle, K. S., and West, P. C. 1980. Spontaneously Broken De Sitter symmetry and the gravitational holonomy group. Phys. Rev. D, 21, 1466.Google Scholar
Taubes, A.H. 1966. The Riemann-Christoffel tensor and tetrad and self-dual formalisms. Pages 360–368 of: Perspectives in Geometry (Essays in honor of V. Hlavaty), ed. Hoffmann, Indianapolis, IN: Indiana University Press.Google Scholar
Taubes, C. H. 2011. Differential Geometry: Bundles, Connections, Metrics and Curvature. New York: Oxford.Google Scholar
Urbantke, H. 1984. On integrability properties of SU(2) Yang-Mills fields. I. Infinitesimal part. J. Math. Phys., 25(7), 23212324.Google Scholar
Ward, R. S. 1980. Self-dual space-times with cosmological constant. Commun. Math. Phys., 78, 117.Google Scholar
Weinberg, S. 1972. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Hoboken, NJ: Wiley.Google Scholar
West, P. C. 1978. A geometric gravity Lagrangian. Phys. Lett. B, 76, 569.Google Scholar
Wise, Derek K. 2010. MacDowell-Mansouri gravity and Cartan geometry. Class. Quant. Grav., 27, 155010.CrossRefGoogle Scholar
Witten, E. 1988. (2+1)-Dimensional gravity as an exactly soluble system. Nucl. Phys. B, 311, 46.Google Scholar
Zee, A. 2013. Einstein Gravity in a Nutshell. Princeton, NJ: Princeton University Press.Google Scholar
Zinoviev, Y. M. 2005. On Dual Formulation of Gravity. e-Print: hep-th/0504210Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Kirill Krasnov, University of Nottingham
  • Book: Formulations of General Relativity
  • Online publication: 06 November 2020
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Kirill Krasnov, University of Nottingham
  • Book: Formulations of General Relativity
  • Online publication: 06 November 2020
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Kirill Krasnov, University of Nottingham
  • Book: Formulations of General Relativity
  • Online publication: 06 November 2020
Available formats
×