Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-5b777bbd6c-ks5gx Total loading time: 0 Render date: 2025-06-25T13:15:13.986Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  24 April 2025

Horatiu Nastase
Horatiu Nastase
Affiliation:
Universidade Estadual Paulista, São Paulo
Get access
Type
Chapter
Information
General Relativity
A Graduate Course
 , pp. 375 - 380
Publisher: Cambridge University Press
Print publication year: 2025

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.)

Book purchase

Temporarily unavailable

References

Wald, R. M., “General relativity,” University of Chicago Press, 1984.CrossRefGoogle Scholar
Misner, C. W., Thorne, K. S. and Wheeler, J. A., “Gravitation,” W. H. Freeman and Co., 1970.Google Scholar
Hawking, S. W. and Ellis, G. F. R., “The large scale structure of space-time,” Cambridge University Press, 1973.CrossRefGoogle Scholar
Peebles, P. J. E., “Principles of physical cosmology,” Princeton University Press, 1993.Google Scholar
Landau, L. D. and Lifshitz, E. M., “The classical theory of fields,” Butterworth-Heinemann, 4th edition, 1980.Google Scholar
Abbott, B. P. et al. [LIGO Scientific and Virgo], “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett. 116, no.6, 061102 (2016) [arXiv:1602.03837 [gr-qc]].Google Scholar
Abbott, R. et al. [LIGO Scientific, KAGRA and VIRGO], “Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences,” Astrophys. J. Lett. 915, no.1, L5 (2021) [arXiv:2106.15163 [astro-ph.HE]].CrossRefGoogle Scholar
Abbott, B. P. et al. [LIGO Scientific and Virgo], Phys. Rev. Lett. 119, no.16, 161101 (2017) doi:10.1103/PhysRevLett.119.161101 [arXiv:1710.05832 [gr-qc]].Google Scholar
Einstein, A. and Rosen, N., “On Gravitational Waves,” J. Franklin Inst. 223, 43–54 (1937)CrossRefGoogle Scholar
Akiyama, K. et al. [Event Horizon Telescope], “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,” Astrophys. J. Lett. 875, L1 (2019) [arXiv:1906.11238 [astro-ph.GA]].Google Scholar
Akiyama, K. et al. [Event Horizon Telescope], “First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way,” Astrophys. J. Lett. 930, no.2, L12 (2022) [arXiv:2311.08680 [astro-ph.HE]].Google Scholar
Dodelson, Scott, “Gravitational lensing,” Cambridge University Press, 2017.CrossRefGoogle Scholar
Van Nieuwenhuizen, P., “Supergravity,” Phys. Rept. 68, 189–398 (1981).CrossRefGoogle Scholar
Witten, E., “(2+1)-Dimensional Gravity as an Exactly Soluble System,” Nucl. Phys. B 311, 46 (1988).CrossRefGoogle Scholar
Achucarro, A. and Townsend, P. K., “A Chern-Simons Action for Three-Dimensional Anti-de Sitter Supergravity Theories,” Phys. Lett. B 180, 89 (1986).CrossRefGoogle Scholar
van Nieuwenhuizen, P., Phys. Rev. D 32, 872 (1985) doi:10.1103/PhysRevD.32.872.CrossRefGoogle Scholar
Nastase, H., “D=4 Einstein Gravity from Higher D CS and BI Gravity and an Alternative to Dimensional Reduction,” [arXiv:hep-th/0703034 [hep-th]].Google Scholar
Lanczos, C., Ann. Math. 39 (1938) 842 doi: /10.2307/1968467.CrossRefGoogle Scholar
Lovelock, D., Math, J.. Phys. 12 (1971) 498 doi:10.1063/1.1665613.Google Scholar
Nastase, H., “Towards a Chern-Simons M Theory of OSp(1|32) x OSp(1|32),” [arXiv:hep-th/0306269 [hep-th]].Google Scholar
Alvarez-Gaume, L. and Witten, E., “Gravitational Anomalies,” Nucl. Phys. B 234, 269 (1984).CrossRefGoogle Scholar
Witten, E., “Global Gravitational Anomalies,” Commun. Math. Phys. 100, 197 (1985).CrossRefGoogle Scholar
Deser, S. and Schwimmer, A., “Geometric Classification of Conformal Anomalies in Arbitrary Dimensions,” Phys. Lett. B 309, 279–284 (1993) [arXiv:hep-th/9302047 [hep-th]].CrossRefGoogle Scholar
Henningson, M. and Skenderis, K., “The Holographic Weyl anomaly,” JHEP 07, 023 (1998) [arXiv:hep-th/9806087 [hep-th]].Google Scholar
Henningson, M. and Skenderis, K., “Holography and the Weyl anomaly,” Fortsch. Phys. 48, 125–128 (2000) [arXiv:hep-th/9812032 [hep-th]].Google Scholar
Komargodski, Z. and Schwimmer, A., “On Renormalization Group Flows in Four Dimensions,” JHEP 12, 099 (2011) [arXiv:1107.3987 [hep-th]].Google Scholar
Balasubramanian, V. and Kraus, P., “A Stress Tensor for Anti-de Sitter Gravity,” Commun. Math. Phys. 208, 413–428 (1999) [arXiv:hep-th/9902121 [hep-th]].CrossRefGoogle Scholar
Ashtekar, A., “New Variables for Classical and Quantum Gravity,” Phys. Rev. Lett. 57, 2244–2247 (1986).CrossRefGoogle ScholarPubMed
Henneaux, M., Schomblond, C. and Nelson, J. E., “Derivation of Ashtekar Variables from Tetrad Gravity,” Phys. Rev. D 39, 434–437 (1989).CrossRefGoogle ScholarPubMed
Alves, D. W. F. and Nastase, H., “Hopfion solutions in gravity and a null fluid/gravity conjecture,” [arXiv:1812.08630 [hep-th]].Google Scholar
Filipe Costa, L. and Herdeiro, C. A. R., “A Gravito-Electromagnetic Analogy Based on Tidal Tensors,” Phys. Rev. D 78, 024021 (2008) [arXiv:gr-qc/0612140 [gr-qc]].Google Scholar
Ruggiero, M. L. and Tartaglia, A., “Gravitomagnetic Effects,” Nuovo Cim. B 117, 743–768 (2002) [arXiv:gr-qc/0207065 [gr-qc]].Google Scholar
Kang, K. and Nastase, H., “Planckian Scattering Effects and Black Hole Production in Low M(Pl) Scenarios,” Phys. Rev. D 71, 124035 (2005) [arXiv:hep-th/0409099 [hep-th]].CrossRefGoogle Scholar
Bardeen, J. M., Carter, B. and Hawking, S. W., “The Four Laws of Black Hole Mechanics,” Commun. Math. Phys. 31, 161–170 (1973).CrossRefGoogle Scholar
Bekenstein, J. D., “Black Holes and Entropy,” Phys. Rev. D 7, 2333–2346 (1973).CrossRefGoogle Scholar
Hawking, S. W., “Particle Creation by Black Holes,” Commun. Math. Phys. 43, 199–220 (1975) [erratum: Commun. Math. Phys. 46, 206 (1976)].CrossRefGoogle Scholar
Nastase, H., “Introduction to the ADS/CFT Correspondence,” Cambridge University Press, 2015, ISBN 978-1-107-08585-5, 978-1-316-35530-5.CrossRefGoogle Scholar
Almheiri, A., Hartman, T., Maldacena, J., Shaghoulian, E. and Tajdini, A., “The Entropy of Hawking Radiation,” Rev. Mod. Phys. 93, no.3, 035002 (2021) [arXiv:2006.06872 [hep-th]].CrossRefGoogle Scholar
Wald, R. M., “Black Hole Entropy Is the Noether Charge,” Phys. Rev. D 48, no.8, R3427-R3431 (1993) [arXiv:gr-qc/9307038 [gr-qc]].CrossRefGoogle Scholar
Jacobson, T., Kang, G. and Myers, R. C., “On Black Hole Entropy,” Phys. Rev. D 49, 6587–6598 (1994) [arXiv:gr-qc/9312023 [gr-qc]].CrossRefGoogle ScholarPubMed
Iyer, V. and Wald, R. M., “Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy,” Phys. Rev. D 50, 846–864 (1994) [arXiv:gr-qc/9403028 [gr-qc]].CrossRefGoogle Scholar
Sen, A., “Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity,” JHEP 09, 038 (2005) [arXiv:hep-th/0506177 [hep-th]].Google Scholar
Ferrara, S., Kallosh, R. and Strominger, A., “N=2 Extremal Black Holes,” Phys. Rev. D 52, R5412–R5416 (1995) [arXiv:hep-th/9508072 [hep-th]].CrossRefGoogle ScholarPubMed
Ferrara, S. and Kallosh, R., “Supersymmetry and Attractors,” Phys. Rev. D 54, 1514–1524 (1996) [arXiv:hep-th/9602136 [hep-th]].Google ScholarPubMed
Ferrara, S. and Kallosh, R., “Universality of Supersymmetric Attractors,” Phys. Rev. D 54, 1525–1534 (1996) [arXiv:hep-th/9603090 [hep-th]].Google ScholarPubMed
Goldstein, K., Iizuka, N., Jena, R. P. and Trivedi, S. P., “Non-supersymmetric Attractors,” Phys. Rev. D 72, 124021 (2005) [arXiv:hep-th/0507096 [hep-th]].CrossRefGoogle Scholar
Astefanesei, D., Nastase, H., Yavartanoo, H. and Yun, S., “Moduli Flow and Non-supersymmetric AdS Attractors,” JHEP 04, 074 (2008) [arXiv:0711.0036 [hep-th]].Google Scholar
Penrose, R., “Gravitational Collapse and Space-Time Singularities,” Phys. Rev. Lett. 14, 57–59 (1965).CrossRefGoogle Scholar
Hawking, S., “The Occurrence of Singularities in Cosmology,” Proc. Roy. Soc. Lond. A 294, 511–521 (1966).Google Scholar
Geroch, R. P., “Singularities in Closed Universes,” Phys. Rev. Lett. 17, 445–447 (1966).CrossRefGoogle Scholar
Hawking, S., “The Occurrence of Singularities in Cosmology. II,” Proc. Roy. Soc. Lond. A 295, 490–493 (1966).Google Scholar
Hawking, S., “The Occurrence of Singularities in Cosmology. III. Causality and Singularities,” Proc. Roy. Soc. Lond. A 300, 187–201 (1967).Google Scholar
Hawking, S. W. and Penrose, R., “The Singularities of Gravitational Collapse and Cosmology,” Proc. Roy. Soc. Lond. A 314, 529–548 (1970).Google Scholar
Borde, A., “Regular Black Holes and Topology Change,” Phys. Rev. D 55, 7615–7617 (1997) [arXiv:gr-qc/9612057 [gr-qc]].CrossRefGoogle Scholar
Morris, M. S. and Thorne, K. S., “Wormholes in Space-Time and Their Use for Interstellar Travel: A Tool for Teaching General Relativity,” Am. J. Phys. 56, 395–412 (1988).CrossRefGoogle Scholar
Morris, M. S., Thorne, K. S. and Yurtsever, U., “Wormholes, Time Machines, and the Weak Energy Condition,” Phys. Rev. Lett. 61, 1446–1449 (1988).CrossRefGoogle ScholarPubMed
Goldberger, W. D. and Rothstein, I. Z., “An Effective Field Theory of Gravity for Extended Objects,” Phys. Rev. D 73, 104029 (2006) [arXiv:hep-th/0409156 [hep-th]].CrossRefGoogle Scholar
Goldberger, W. D. and Rothstein, I. Z., “Dissipative Effects in the Worldline Approach to Black Hole Dynamics,” Phys. Rev. D 73, 104030 (2006) [arXiv:hep-th/0511133 [hep-th]].CrossRefGoogle Scholar
Porto, R. A., “The Effective Field Theorist’s Approach to Gravitational Dynamics,” Phys. Rept. 633, 1–104 (2016) [arXiv:1601.04914 [hep-th]].CrossRefGoogle Scholar
Goldberger, W. D., “Effective Field Theory for Compact Binary Dynamics,” [arXiv:2212.06677 [hep-th]].Google Scholar
Goldberger, W. D., “Les Houches Lectures on Effective Field Theories and Gravitational Radiation,” [arXiv:hep-ph/0701129 [hep-ph]].Google Scholar
Levi, M., “Effective Field Theories of Post-Newtonian Gravity: A Comprehensive Review,” Rept. Prog. Phys. 83, no.7, 075901 (2020) [arXiv:1807.01699 [hep-th]].CrossRefGoogle ScholarPubMed
Sturani, R., “Fundamental Gravity and Gravitational Waves,” Symmetry 13, no.12, 2384 (2021).CrossRefGoogle Scholar
Monteiro, R., O’Connell, D. and White, C. D., “Black Holes and the Double Copy,” JHEP 12, 056 (2014) [arXiv:1410.0239 [hep-th]].Google Scholar
Luna, A., Monteiro, R., O’Connell, D. and White, C. D., “The Classical Double Copy for Taub–NUT Spacetime,” Phys. Lett. B 750, 272–277 (2015) [arXiv:1507.01869 [hep-th]].CrossRefGoogle Scholar
Luna, A., Monteiro, R., Nicholson, I. and O’Connell, D., “Type D Spacetimes and the Weyl Double Copy,” Class. Quant. Grav. 36, 065003 (2019) [arXiv:1810.08183 [hep-th]].CrossRefGoogle Scholar
Bern, Z., Cheung, C., Roiban, R., Shen, C. H., Solon, M. P. and Zeng, M., “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” JHEP 10, 206 (2019) [arXiv:1908.01493].Google Scholar
White, C. D., “Twistorial Foundation for the Classical Double Copy,” Phys. Rev. Lett. 126, no.6, 061602 (2021) [arXiv:2012.02479 [hep-th]].CrossRefGoogle ScholarPubMed
Chacón, E., Nagy, S. and White, C. D., “The Weyl Double Copy from Twistor Space,” JHEP 05, 2239 (2021) [arXiv:2103.16441].Google Scholar
Godazgar, H., Godazgar, M., Monteiro, R., Peinador Veiga, D. and Pope, C. N., “Asymptotic Weyl Double Copy,” JHEP 11, 126 (2021) [arXiv:2109.07866 [hep-th]].Google Scholar
Thorne, Kip S., Price, Richard H., MacDonald, Douglas A., “Black holes: The membrane paradigm,” Yale University Press, 1986.Google Scholar
Rangamani, M., “Gravity and Hydrodynamics: Lectures on the Fluid-Gravity Correspondence,” Class. Quant. Grav. 26, 224003 (2009) [arXiv:0905.4352 [hep-th]].CrossRefGoogle Scholar
Hubeny, V. E., Minwalla, S. and Rangamani, M., [arXiv:1107.5780 [hep-th]].Google Scholar
Eling, C., Fouxon, I. and Oz, Y., “The Incompressible Navier-Stokes Equations from Membrane Dynamics,” Phys. Lett. B 680, 496 (2009) [arXiv:0905.3638 [hep-th]].CrossRefGoogle Scholar
Eling, C. and Oz, Y., “Relativistic CFT Hydrodynamics from the Membrane Paradigm,” JHEP 1002, 069 (2010) [arXiv:0906.4999 [hep-th]].Google Scholar
Eling, C., Fouxon, I. and Oz, Y., “Gravity and a Geometrization of Turbulence: An Intriguing Correspondence,” arXiv:1004.2632.Google Scholar
Eling, C., Neiman, Y. and Oz, Y., “Membrane Paradigm and Holographic Hydrodynamics,” J. Phys. Conf. Ser. 314, 012032 (2011) [arXiv:1012.2572 [hep-th]].CrossRefGoogle Scholar
Bhattacharyya, S., Minwalla, S. and Wadia, S. R., “The Incompressible Non-relativistic Navier-Stokes Equation from Gravity,” JHEP 0908, 059 (2009) [arXiv:0810.1545 [hep-th]].Google Scholar
Bhattacharyya, S., Hubeny, V. E., Minwalla, S. and Rangamani, M., “Nonlinear Fluid Dynamics from Gravity,” JHEP 0802, 045 (2008) [arXiv:0712.2456 [hep-th]].Google Scholar
Bredberg, I., Keeler, C., Lysov, V. and Strominger, A., “Wilsonian Approach to Fluid/Gravity Duality,” JHEP 1103, 141 (2011) [arXiv:1006.1902 [hep-th]].Google Scholar
Bredberg, I., Keeler, C., Lysov, V. and Strominger, A., “From Navier-Stokes to Einstein,” JHEP 1207, 146 (2012) [arXiv:1101.2451].Google Scholar
Nastase, H., “String theory methods for condensed matter physics,” Cambridge University Press, 2017, ISBN 978-1-316-85304-7, 978-1-107-18038-3.CrossRefGoogle Scholar
Berenstein, D. E., Maldacena, J. M. and Nastase, H. S., “Strings in Flat Space and pp waves from N=4 superYang-Mills,” JHEP 0204, 013 (2002) [hep-th/0202021].Google Scholar
Penrose, R., “Any Spacetime Has a Plane Wave as a Limit,” Differential Geometry and Relativity, Reidel, Dordrecht (1974), pp 271–275.Google Scholar
Aichelburg, P. C. and Sexl, R. U., “On the Gravitational Field of a Massless Particle,” Gen. Rel. Grav. 2, 303 (1971).CrossRefGoogle Scholar
Horowitz, G. T. and Steif, A. R., “Space-Time Singularities in String Theory,” Phys. Rev. Lett. 64, 260 (1990).CrossRefGoogle Scholar
Khan, K. A. and Penrose, R., “Scattering of Two Impulsive Gravitational Plane Waves,” Nature 229, 185–186 (1971)CrossRefGoogle ScholarPubMed
Kang, K. and Nastase, H., “Planckian Scattering Effects and Black Hole Production in Low M(Pl) Scenarios,” Phys. Rev. D 71, 124035 (2005) [arXiv:hep-th/0409099 [hep-th]].CrossRefGoogle Scholar
Nastase, H., “On High Energy Scattering Inside Gravitational Backgrounds,” [arXiv:hep-th/0410124 [hep-th]].Google Scholar
Vilenkin, A., “Gravitational Field of Vacuum Domain Walls and Strings,” Phys. Rev. D 23, 852 (1981).CrossRefGoogle Scholar
Vilenkin, A., “Gravitational Field of Vacuum Domain Walls,” Phys. Lett. 133B, 177 (1983).Google Scholar
Gott, J. R., III, “Gravitational Lensing Effects of Vacuum Strings: Exact Solutions,” Astrophys. J. 288, 422 (1985).CrossRefGoogle Scholar
Banados, M., Teitelboim, C. and Zanelli, J., “The Black Hole in Three-dimensional Spacetime,” Phys. Rev. Lett. 69, 1849 (1992) [hep-th/9204099].CrossRefGoogle ScholarPubMed
Carlip, S., “The (2+1)-Dimensional Black Hole,” Class. Quant. Grav. 12, 2853 (1995) [gr-qc/9506079].CrossRefGoogle Scholar
Nǎstase, H., “Cosmology and String Theory,” Fundam. Theor. Phys. 197, pp. (2019) Springer, 2019, ISBN 978-3-030-15076-1, 978-3-030-15077-8CrossRefGoogle Scholar
Taub, A. H., “Empty Space-Times Admitting a Three Parameter Group of Motions,” Annals Math. 53, 472 (1951).CrossRefGoogle Scholar
Newman, E., Tamburino, L. and Unti, T., “Empty Space Generalization of the Schwarzschild Metric,” J. Math. Phys. 4, 915 (1963).CrossRefGoogle Scholar
Misner, C. W., “The Flatter Regions of Newman, Unti and Tamburino’s Generalized Schwarzschild Space,” J. Math. Phys. 4, 924 (1963).CrossRefGoogle Scholar
Hawking, S. W. and Ellis, G. F. R., “The large scale structure of space-time,” Cambrigde University Press, 1973.CrossRefGoogle Scholar
Hawking, S. W., “Gravitational Instantons,” Phys. Lett. A 60, 81 (1977).CrossRefGoogle Scholar
Page, D. N., “Taub–Nut Instanton with an Horizon,” Phys. Lett. 78B, 249 (1978).Google Scholar
Eguchi, T. and Hanson, A. J., “Asymptotically Flat Selfdual Solutions to Euclidean Gravity,” Phys. Lett. 74B, 249 (1978).Google Scholar
Gibbons, G. W. and Hawking, S. W., “Gravitational Multi-Instantons,” Phys. Lett. 78B, 430 (1978).Google Scholar
Eguchi, T. and Hanson, A. J., “Selfdual Solutions to Euclidean Gravity,” Annals Phys. 120, 82 (1979).CrossRefGoogle Scholar
Eguchi, T. and Hanson, A. J., “Gravitational Instantons,” Gen. Rel. Grav. 11, 315 (1979).CrossRefGoogle Scholar
Godel, K., “An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation,” Rev. Mod. Phys. 21, 447–450 (1949).CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org 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
  • Horatiu Nastase, Universidade Estadual Paulista, São Paulo
  • Book: General Relativity
  • Online publication: 24 April 2025
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
  • Horatiu Nastase, Universidade Estadual Paulista, São Paulo
  • Book: General Relativity
  • Online publication: 24 April 2025
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
  • Horatiu Nastase, Universidade Estadual Paulista, São Paulo
  • Book: General Relativity
  • Online publication: 24 April 2025
Available formats
×