Skip to main content
Top

2014 | OriginalPaper | Chapter

Lovelock Theory, Black Holes and Holography

Author : José D. Edelstein

Published in: Progress in Mathematical Relativity, Gravitation and Cosmology

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Lovelock theory is the natural extension of general relativity to higher dimensions. It can be also thought of as a toy model for ghost-free higher curvature gravity. It admits a family of AdS vacua, most (but not all) of them supporting black holes that display interesting features. This provides an appealing arena to explore different holographic aspects in the context of the AdS/CFT correspondence.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Footnotes
1
If λ < 0, there is no a priori lower bound for it and it is clear that Λ + becomes positive.
 
2
Recall that it is the branch crossing g = 0 with slope Υ′[0] = 1.
 
3
Other components of the metric fluctuations must be considered as well, but they are irrelevant for our current discussion.
 
4
Notice that we are splitting time and space indices and, thus, from now on vectors are understood as (d − 2) dimensional objects.
 
5
The same computation can be carried out with vector and scalar gravitons, and the result in these two cases will be obvious from the present analysis.
 
Literature
2.
go back to reference C. Lanczos: A Remarkable property of the Riemann-Christoffel tensor in four dimensions. Annals Math. 39, 842 (1938).MathSciNetCrossRef C. Lanczos: A Remarkable property of the Riemann-Christoffel tensor in four dimensions. Annals Math. 39, 842 (1938).MathSciNetCrossRef
3.
go back to reference G. Giribet: The large D limit of dimensionally continued gravity. arXiv:1303.1982 [gr-qc]. G. Giribet: The large D limit of dimensionally continued gravity. arXiv:1303.1982 [gr-qc].
4.
go back to reference C. P. Bachas, P. Bain and M. B. Green: Curvature terms in D-brane actions and their M theory origin. JHEP 9905, 011 (1999) [hep-th/9903210].MathSciNetCrossRef C. P. Bachas, P. Bain and M. B. Green: Curvature terms in D-brane actions and their M theory origin. JHEP 9905, 011 (1999) [hep-th/9903210].MathSciNetCrossRef
5.
go back to reference Y. Kats and P. Petrov: Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory. JHEP 0901, 044 (2009) [arXiv:0712.0743 [hep-th]]. Y. Kats and P. Petrov: Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory. JHEP 0901, 044 (2009) [arXiv:0712.0743 [hep-th]].
6.
go back to reference A. Buchel, R. C. Myers and A. Sinha: Beyond \(\eta /s = 1/4\pi\). JHEP 0903, 084 (2009) [arXiv:0812.2521 [hep-th]]. A. Buchel, R. C. Myers and A. Sinha: Beyond \(\eta /s = 1/4\pi\). JHEP 0903, 084 (2009) [arXiv:0812.2521 [hep-th]].
7.
go back to reference A. H. Chamseddine: Topological gauge theory of gravity in five-dimensions and all odd dimensions. Phys. Lett. B 233, 291 (1989).MathSciNetCrossRef A. H. Chamseddine: Topological gauge theory of gravity in five-dimensions and all odd dimensions. Phys. Lett. B 233, 291 (1989).MathSciNetCrossRef
8.
go back to reference D. Boulware and S. Deser: String generated gravity models. Phys. Rev. Lett. 55, 2656 (1985).CrossRef D. Boulware and S. Deser: String generated gravity models. Phys. Rev. Lett. 55, 2656 (1985).CrossRef
9.
go back to reference D. M. Hofman: Higher derivative gravity, causality and positivity of energy in a UV complete QFT. Nucl. Phys. B 823, 174 (2009) [arXiv:0907.1625 [hep-th]]. D. M. Hofman: Higher derivative gravity, causality and positivity of energy in a UV complete QFT. Nucl. Phys. B 823, 174 (2009) [arXiv:0907.1625 [hep-th]].
10.
go back to reference X. O. Camanho and J. D. Edelstein, A Lovelock black hole bestiary. Class. Quant. Grav. 30, 035009 (2013) [arXiv:1103.3669 [hep-th]]. X. O. Camanho and J. D. Edelstein, A Lovelock black hole bestiary. Class. Quant. Grav. 30, 035009 (2013) [arXiv:1103.3669 [hep-th]].
11.
go back to reference J. T. Wheeler: Symmetric solutions to the Gauss-Bonnet extended Einstein equations. Nucl. Phys. B 268, 737 (1986).CrossRef J. T. Wheeler: Symmetric solutions to the Gauss-Bonnet extended Einstein equations. Nucl. Phys. B 268, 737 (1986).CrossRef
12.
go back to reference J. T. Wheeler: Symmetric solutions to the maximally Gauss-bonnet extended Einstein equations. Nucl. Phys. B 273, 732 (1986).CrossRefMATH J. T. Wheeler: Symmetric solutions to the maximally Gauss-bonnet extended Einstein equations. Nucl. Phys. B 273, 732 (1986).CrossRefMATH
13.
go back to reference D. Kastor, S. Ray and J. Traschen: Mass and Free Energy of Lovelock Black Holes. Class. Quant. Grav. 28, 195022 (2011) [arXiv:1106.2764 [hep-th]]. D. Kastor, S. Ray and J. Traschen: Mass and Free Energy of Lovelock Black Holes. Class. Quant. Grav. 28, 195022 (2011) [arXiv:1106.2764 [hep-th]].
14.
go back to reference X. O. Camanho, J. D. Edelstein, G. Giribet and A. Gomberoff: New type of phase transition in gravitational theories. Phys. Rev. D 86, 124048 (2012) [arXiv:1204.6737 [hep-th]]. X. O. Camanho, J. D. Edelstein, G. Giribet and A. Gomberoff: New type of phase transition in gravitational theories. Phys. Rev. D 86, 124048 (2012) [arXiv:1204.6737 [hep-th]].
15.
go back to reference X. O. Camanho, J. D. Edelstein, G. Giribet and A. Gomberoff: Generalized phase transitions in Lovelock theory. To appear (2013). X. O. Camanho, J. D. Edelstein, G. Giribet and A. Gomberoff: Generalized phase transitions in Lovelock theory. To appear (2013).
16.
go back to reference X. O. Camanho: Phase transitions in general gravity theories. These Proceedings (2013). X. O. Camanho: Phase transitions in general gravity theories. These Proceedings (2013).
17.
go back to reference J. de Boer, M. Kulaxizi and A. Parnachev: Holographic Lovelock gravities and black holes. JHEP 1006, 008 (2010) [arXiv:0912.1877 [hep-th]]. J. de Boer, M. Kulaxizi and A. Parnachev: Holographic Lovelock gravities and black holes. JHEP 1006, 008 (2010) [arXiv:0912.1877 [hep-th]].
18.
go back to reference X. O. Camanho and J. D. Edelstein: Causality in AdS/CFT and Lovelock theory. JHEP 1006, 099 (2010) [arXiv:0912.1944 [hep-th]]. X. O. Camanho and J. D. Edelstein: Causality in AdS/CFT and Lovelock theory. JHEP 1006, 099 (2010) [arXiv:0912.1944 [hep-th]].
19.
20.
go back to reference S. ’i. Nojiri and S. D. Odintsov: Anti-de Sitter black hole thermodynamics in higher derivative gravity and new confining deconfining phases in dual CFT. Phys. Lett. B 521, 87 (2001) [Erratum-ibid. B 542, 301 (2002)] [hep-th/0109122]. S. ’i. Nojiri and S. D. Odintsov: Anti-de Sitter black hole thermodynamics in higher derivative gravity and new confining deconfining phases in dual CFT. Phys. Lett. B 521, 87 (2001) [Erratum-ibid. B 542, 301 (2002)] [hep-th/0109122].
21.
go back to reference Y. M. Cho and I. P. Neupane: Anti-de Sitter black holes, thermal phase transition and holography in higher curvature gravity. Phys. Rev. D 66, 024044 (2002) [hep-th/0202140].MathSciNetCrossRef Y. M. Cho and I. P. Neupane: Anti-de Sitter black holes, thermal phase transition and holography in higher curvature gravity. Phys. Rev. D 66, 024044 (2002) [hep-th/0202140].MathSciNetCrossRef
22.
23.
go back to reference T. Jacobson and R. C. Myers: Black hole entropy and higher curvature interactions. Phys. Rev. Lett. 70, 3684 (1993) [hep-th/9305016].MathSciNetCrossRefMATH T. Jacobson and R. C. Myers: Black hole entropy and higher curvature interactions. Phys. Rev. Lett. 70, 3684 (1993) [hep-th/9305016].MathSciNetCrossRefMATH
24.
25.
go back to reference J. M. Maldacena: The Large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998) [hep-th/9711200].MathSciNetMATH J. M. Maldacena: The Large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998) [hep-th/9711200].MathSciNetMATH
26.
go back to reference S. S. Gubser, I. R. Klebanov and A. M. Polyakov: Gauge theory correlators from noncritical string theory. Phys. Lett. B 428, 105 (1998) [hep-th/9802109].MathSciNetCrossRef S. S. Gubser, I. R. Klebanov and A. M. Polyakov: Gauge theory correlators from noncritical string theory. Phys. Lett. B 428, 105 (1998) [hep-th/9802109].MathSciNetCrossRef
27.
go back to reference E. Witten: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253 (1998) [hep-th/9802150].MathSciNetMATH E. Witten: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253 (1998) [hep-th/9802150].MathSciNetMATH
28.
go back to reference H. Osborn and A. C. Petkou: Implications of conformal invariance in field theories for general dimensions. Annals Phys. 231, 311 (1994) [hep-th/9307010].MathSciNetCrossRefMATH H. Osborn and A. C. Petkou: Implications of conformal invariance in field theories for general dimensions. Annals Phys. 231, 311 (1994) [hep-th/9307010].MathSciNetCrossRefMATH
29.
go back to reference A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha and M. Smolkin: Holographic GB gravity in arbitrary dimensions. JHEP 1003, 111 (2010) [arXiv:0911.4257 [hep-th]]. A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha and M. Smolkin: Holographic GB gravity in arbitrary dimensions. JHEP 1003, 111 (2010) [arXiv:0911.4257 [hep-th]].
30.
go back to reference X. O. Camanho, J. D. Edelstein and M. F. Paulos: Lovelock theories, holography and the fate of the viscosity bound. JHEP 1105, 127 (2011) [arXiv:1010.1682 [hep-th]]. X. O. Camanho, J. D. Edelstein and M. F. Paulos: Lovelock theories, holography and the fate of the viscosity bound. JHEP 1105, 127 (2011) [arXiv:1010.1682 [hep-th]].
31.
go back to reference J. Erdmenger and H. Osborn: Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions. Nucl. Phys. B 483, 431 (1997) [hep-th/9605009].MathSciNetCrossRefMATH J. Erdmenger and H. Osborn: Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions. Nucl. Phys. B 483, 431 (1997) [hep-th/9605009].MathSciNetCrossRefMATH
32.
go back to reference D. M. Hofman and J. Maldacena: Conformal collider physics: Energy and charge correlations. JHEP 0805, 012 (2008) [arXiv:0803.1467 [hep-th]]. D. M. Hofman and J. Maldacena: Conformal collider physics: Energy and charge correlations. JHEP 0805, 012 (2008) [arXiv:0803.1467 [hep-th]].
33.
go back to reference X. O. Camanho and J. D. Edelstein: Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity. JHEP 1004, 007 (2010) [arXiv:0911.3160 [hep-th]]. X. O. Camanho and J. D. Edelstein: Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity. JHEP 1004, 007 (2010) [arXiv:0911.3160 [hep-th]].
34.
go back to reference M. Kulaxizi and A. Parnachev: Supersymmetry constraints in holographic gravities. Phys. Rev. D 82, 066001 (2010) [arXiv:0912.4244 [hep-th]]. M. Kulaxizi and A. Parnachev: Supersymmetry constraints in holographic gravities. Phys. Rev. D 82, 066001 (2010) [arXiv:0912.4244 [hep-th]].
35.
go back to reference A. Buchel and R. C. Myers: Causality of holographic hydrodynamics. JHEP 0908, 016 (2009) [arXiv:0906.2922 [hep-th]]. A. Buchel and R. C. Myers: Causality of holographic hydrodynamics. JHEP 0908, 016 (2009) [arXiv:0906.2922 [hep-th]].
36.
go back to reference J. de Boer, M. Kulaxizi and A. Parnachev: AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound. JHEP 1003, 087 (2010) [arXiv:0910.5347 [hep-th]]. J. de Boer, M. Kulaxizi and A. Parnachev: AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound. JHEP 1003, 087 (2010) [arXiv:0910.5347 [hep-th]].
37.
go back to reference M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida: The viscosity bound and causality violation. Phys. Rev. Lett. 100, 191601 (2008) [arXiv:0802.3318 [hep-th]]. M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida: The viscosity bound and causality violation. Phys. Rev. Lett. 100, 191601 (2008) [arXiv:0802.3318 [hep-th]].
38.
go back to reference M. F. Paulos: Holographic phase space: c-functions and black holes as renormalization group flows. JHEP 1105, 043 (2011) [arXiv:1101.5993 [hep-th]]. M. F. Paulos: Holographic phase space: c-functions and black holes as renormalization group flows. JHEP 1105, 043 (2011) [arXiv:1101.5993 [hep-th]].
39.
go back to reference R. C. Myers, M. F. Paulos and A. Sinha. Holographic studies of quasi-topological gravity. JHEP 1008, 035 (2010) [arXiv:1004.2055 [hep-th]]. R. C. Myers, M. F. Paulos and A. Sinha. Holographic studies of quasi-topological gravity. JHEP 1008, 035 (2010) [arXiv:1004.2055 [hep-th]].
Metadata
Title
Lovelock Theory, Black Holes and Holography
Author
José D. Edelstein
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-40157-2_2

Premium Partner