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Higher Order Gravity Theories and Their Black Hole Solutions

  • Chapter
Physics of Black Holes

Part of the book series: Lecture Notes in Physics ((LNP,volume 769))

abstract

In this chapter, we will discuss a particular higher order gravity theory, Lovelock theory, that generalises in higher dimensions than 4, general relativity. After briefly motivating modifications of gravity, we will introduce the theory in question and we will argue that it is a unique, mathematically sensible, and physically interesting extension of general relativity. We will see, by using the formalism of differential forms, the relation of Lovelock gravity to differential geometry and topology of even-dimensional manifolds. We will then discuss a generic staticity theorem, quite similar to Birkhoff’s theorem in general relativity, which will give us the charged static black hole solutions. We will examine their asymptotic behaviour, analyse their horizon structure and briefly their thermodynamics. For the thermodynamics we will give a geometric justification of why the usual entropy–area relation is broken. We will then examine the distributional matching conditions for Lovelock theory. We will see how induced four-dimensional Einstein–Hilbert terms result on the brane geometry from the higher order Lovelock terms. With the junction conditions at hand, we will go back to the black hole solutions and give applications for braneworlds: perturbations of codimension 1 braneworlds and the exact solution for braneworld cosmology as well as the determination of maximally symmetric codimension 2 braneworlds. In both cases, the staticity theorem evoked beforehand will give us the general solution for braneworld cosmology in codimension 1 and maximal symmetry warped branes of codimension 2. We will then end with a discussion of the simplest Kaluza–Klein reduction of Lovelock theory to a four-dimensional vector–scalar–tensor theory which has the unique property of retaining second-order field equations. We will comment briefly the non-linear generalisation of Maxwell’s theory and scalar–tensor theory. We will conclude by listing some open problems and common difficulties.

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References

  1. R. M. Wald, General Relativity (University Press, Chicago, USA 1984) 491p

    MATH  Google Scholar 

  2. C. M. Will, The confrontation between general relativity and experiment, gr-qc/0510072

    Google Scholar 

  3. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge 1993).

    MATH  Google Scholar 

  4. A. G. Riess et al. and Supernova Search Team Collaboration, Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116, 1009 (1998) [astro-ph/9805201].

    ADS  Google Scholar 

  5. A. G. Riess et al. and Supernova Search Team Collaboration, Type Ia supernova discoveries at z > 1 from the Hubble space telescope: Evidence for past deceleration and constraints on dark energy evolution, Astrophys. J. 607, 665 (2004) [astro-ph/0402512].

    ADS  Google Scholar 

  6. S. Perlmutter et al. and Supernova Cosmology Project Collaboration, Measurements of omega and lambda from 42 high-redshift supernovae, Astrophys. J. 517, 565 (1999) [astro-ph/9812133].

    ADS  Google Scholar 

  7. S. M. Carroll, Living Rev. Rel. 4, 1 (2001) [arXiv:astro-ph/0004075].

    Google Scholar 

  8. J. Polchinski, arXiv:hep-th/0603249.

    Google Scholar 

  9. R. Bousso, arXiv:0708.4231 [hep-th].

    Google Scholar 

  10. C. Brans and R. H. Dicke, Phys. Rev. 124, 925 (1961).

    MATH  ADS  MathSciNet  Google Scholar 

  11. T. Damour and G. Esposito-Farese, Class. Quant. Grav. 9, 2093 (1992).

    MATH  ADS  MathSciNet  Google Scholar 

  12. C. Eling, T. Jacobson and D. Mattingly, arXiv:gr-qc/0410001.

    Google Scholar 

  13. Woodard, R. P.: Lect. Notes Phys. 720, 403 (2007) [arXiv:astro-ph/0601672].

    ADS  Google Scholar 

  14. S. M. Carroll, A. De Felice, V. Duvvuri, D. A. Easson, M. Trodden and M. S. Turner, Phys. Rev. D 71, 063513 (2005) [arXiv:astro-ph/0410031].

    ADS  Google Scholar 

  15. B. Whitt, Phys. Lett. B 145, 176 (1984).

    ADS  MathSciNet  Google Scholar 

  16. B. Zwiebach, Phys. Lett. B 156, 315 (1985).

    ADS  Google Scholar 

  17. D. J. Gross and J. H. Sloan, The quartic effective action for the heterotic string, Nucl. Phys. B 291, 41 (1987).

    ADS  MathSciNet  Google Scholar 

  18. R. R. Metsaev and A. A. Tseytlin, Order alpha-prime (two loop) [quivalence of the string equations of motion and the sigma model Weyl invariance conditions: Dependence on the dilaton and the antisymmetric tensor, Nucl. Phys. B 293, 385 (1987).

    ADS  MathSciNet  Google Scholar 

  19. D. Lovelock, J. Math. Phys. 12, 498 (1971).

    MATH  Google Scholar 

  20. C. Lanczos, Z. Phys. 73, 147 (1932).

    ADS  Google Scholar 

  21. C. Lanczos, Ann. Math. 39, 842 (1938).

    MathSciNet  Google Scholar 

  22. B. Zumino, Gravity theories in more than four-dimensions, Phys. Rept. 137, 109 (1986).

    ADS  MathSciNet  Google Scholar 

  23. I. Antoniadis, J. Rizos and K. Tamvakis, Nucl. Phys. B 415, 497 (1994) [arXiv:hep-th/9305025].

    ADS  Google Scholar 

  24. B. A. Campbell, M. J. Duncan, N. Kaloper and K. A. Olive, Nucl. Phys. B 351, 778 (1991).

    MathSciNet  Google Scholar 

  25. J. Madore, On the nature of the initial singularity in a Lanczos cosmological model, Phys. Lett. A 111, 238 (1985).

    MathSciNet  Google Scholar 

  26. N. Deruelle and J. Madore, The Friedmann universe as an attractor of a Kaluza-Klein cosmology, Mod. Phys. Lett. A 1, 237 (1986).

    ADS  MathSciNet  Google Scholar 

  27. D. G. Boulware and S. Deser, Phys. Rev. Lett. 55, 2656 (1985).

    ADS  Google Scholar 

  28. J. T. Wheeler, Nucl. Phys. B 273, 732 (1986).

    MATH  ADS  Google Scholar 

  29. J. T. Wheeler, Nucl. Phys. B 268, 737 (1986).

    ADS  Google Scholar 

  30. D. L. Wiltshire, Phys. Lett. B 169, 36 (1986).

    ADS  MathSciNet  Google Scholar 

  31. R. C. Myers and J. Z. Simon, Phys. Rev. D 38, 2434 (1988).

    ADS  MathSciNet  Google Scholar 

  32. M. H. Dehghani and R. B. Mann, Phys. Rev. D 72, 124006 (2005) [arXiv:hep-th/0510083].

    ADS  MathSciNet  Google Scholar 

  33. M. H. Dehghani, Phys. Rev. D 67, 064017 (2003) [arXiv:hep-th/0211191].

    ADS  MathSciNet  Google Scholar 

  34. S. H. Hendi and M. H. Dehghani, arXiv:0802.1813 [hep-th].

    Google Scholar 

  35. D. Kastor and R. B. Mann, JHEP 0604, 048 (2006) [arXiv:hep-th/0603168].

    ADS  MathSciNet  Google Scholar 

  36. S. Deser and B. Tekin, Energy in generic higher curvature gravity theories, Phys. Rev. D 67, 084009 (2003) [hep-th/0212292].

    ADS  MathSciNet  Google Scholar 

  37. G. Kofinas and R. Olea, JHEP 0711, 069 (2007) [arXiv:0708.0782 [hep-th]].

    Google Scholar 

  38. G. Kofinas and R. Olea, Phys. Rev. D 74, 084035 (2006) [arXiv:hep-th/0606253].

    ADS  MathSciNet  Google Scholar 

  39. J. P. Gregory and A. Padilla, Braneworld holography in Gauss-Bonnet gravity, Class. Quant. Grav. 20, 4221 (2003) [hep-th/0304250].

    MATH  ADS  MathSciNet  Google Scholar 

  40. A. Padilla, Class. Quant. Grav. 22, 681 (2005) [arXiv:hep-th/0406157].

    MATH  ADS  MathSciNet  Google Scholar 

  41. R. Gregory, arXiv:0804.2595 [hep-th].

    Google Scholar 

  42. H. Collins and B. Holdom, Phys. Rev. D 62, 124008 (2000) [arXiv:hep-th/0006158].

    ADS  MathSciNet  Google Scholar 

  43. G. R. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485, 208 (2000) [arXiv:hep-th/0005016].

    MATH  ADS  MathSciNet  Google Scholar 

  44. C. Charmousis and J. F. Dufaux, Phys. Rev. D 70, 106002 (2004) [arXiv:hep-th/0311267].

    ADS  MathSciNet  Google Scholar 

  45. M. Minamitsuji and M. Sasaki, Prog. Theor. Phys. 112, 451 (2004) [arXiv:hep-th/0404166].

    MATH  ADS  MathSciNet  Google Scholar 

  46. W. Israel, Nuovo Cim. B 44S10, 1 (1966).

    ADS  Google Scholar 

  47. W. Israel, Nuovo Cim. B 48, 463 (1967) [Erratum).

    Google Scholar 

  48. G. Darmois, Mémorial des sciences mathématiques, XXV (1927).

    Google Scholar 

  49. N. Deruelle and T. Dolezel, Phys. Rev. D 62, 103502 (2000) [arXiv:gr-qc/0004021].

    ADS  MathSciNet  Google Scholar 

  50. N. E. Mavromatos and J. Rizos, String inspired higher-curvature terms and the Randall-Sundrum scenario, Phys. Rev. D 62, 124004 (2000) [hep-th/0008074].

    ADS  MathSciNet  Google Scholar 

  51. N. E. Mavromatos and J. Rizos, Exact solutions and the cosmological constant problem in dilatonic domain wall higher-curvature string gravity, Int. J. Mod. Phys. A 18, 57 (2003) [hep-th/0205299].

    MATH  ADS  MathSciNet  Google Scholar 

  52. K. A. Meissner and M. Olechowski, Brane localization of gravity in higher derivative theory, Phys. Rev. D 65, 064017 (2002) [hep-th/0106203].

    ADS  MathSciNet  Google Scholar 

  53. Y. M. Cho, I. P. Neupane and P. S. Wesson, No ghost state of Gauss-Bonnet interaction in warped background, Nucl. Phys. B 621, 388 (2002) [hep-th/0104227].

    MATH  ADS  MathSciNet  Google Scholar 

  54. N. Deruelle and M. Sasaki, Newton’s law on an Einstein ‘Gauss-Bonnet’ brane, gr-qc/0306032.

    Google Scholar 

  55. A. Jakobek, K. A. Meissner and M. Olechowski, New brane solutions in higher order gravity, Nucl. Phys. B 645, 217 (2002) [hep-th/0206254].

    MATH  ADS  MathSciNet  Google Scholar 

  56. K. A. Meissner and M. Olechowski, Domain walls without cosmological constant in higher order gravity, Phys. Rev. Lett. 86, 3708 (2001) [hep-th/0009122].

    ADS  Google Scholar 

  57. P. Binetruy, C. Charmousis, S. C. Davis and J. F. Dufaux, Avoidance of naked singularities in dilatonic brane world scenarios with a Gauss-Bonnet term, Phys. Lett. B 544, 183 (2002) [hep-th/0206089].

    MATH  ADS  MathSciNet  Google Scholar 

  58. C. Charmousis, S. C. Davis and J. F. Dufaux, JHEP 0312, 029 (2003) [arXiv:hep-th/0309083].

    ADS  MathSciNet  Google Scholar 

  59. C. Charmousis and J. F. Dufaux, Class. Quant. Grav. 19, 4671 (2002) [arXiv:hep-th/0202107].

    MATH  ADS  MathSciNet  Google Scholar 

  60. N. Deruelle and J. Madore, arXiv:gr-qc/0305004.

    Google Scholar 

  61. S. C. Davis, Phys. Rev. D 67, 024030 (2003) [arXiv:hep-th/0208205].

    ADS  MathSciNet  Google Scholar 

  62. E. Gravanis and S. Willison, Phys. Lett. B 562, 118 (2003) [arXiv:hep-th/0209076].

    MATH  ADS  MathSciNet  Google Scholar 

  63. R. C. Myers, Phys. Rev. D 36, 392 (1987).

    ADS  MathSciNet  Google Scholar 

  64. J. F. Dufaux, J. E. Lidsey, R. Maartens and M. Sami, Phys. Rev. D 70, 083525 (2004) [arXiv:hep-th/0404161].

    ADS  Google Scholar 

  65. J. E. Lidsey and N. J. Nunes, Phys. Rev. D 67, 103510 (2003) [arXiv:astro-ph/0303168].

    ADS  MathSciNet  Google Scholar 

  66. G. Kofinas, R. Maartens and E. Papantonopoulos, Brane cosmology with curvature corrections, hep-th/0307138.

    Google Scholar 

  67. P. Bostock, R. Gregory, I. Navarro and J. Santiago, Phys. Rev. Lett. 92, 221601 (2004) [arXiv:hep-th/0311074].

    ADS  MathSciNet  Google Scholar 

  68. C. Charmousis and A. Papazoglou, arXiv:0804.2121 [hep-th].

    Google Scholar 

  69. C. Charmousis and R. Zegers, Phys. Rev. D 72, 064005 (2005) [arXiv:hep-th/0502171].

    ADS  MathSciNet  Google Scholar 

  70. R. Zegers, arXiv:0801.2262 [gr-qc].

    Google Scholar 

  71. F. Mueller-Hoissen, Nucl. Phys. B 337, 709 (1990).

    ADS  Google Scholar 

  72. F. Mueller-Hoissen, Phys. Lett. B 201, 325 (1988).

    ADS  MathSciNet  Google Scholar 

  73. F. Mueller-Hoissen, Class. Quant. Grav. 5, L35 (1988).

    ADS  Google Scholar 

  74. R. C. Myers, Phys. Rev. D 36, 392 (1987).

    Google Scholar 

  75. N. Deruelle and J. Madore, arXiv:gr-qc/0305004.

    Google Scholar 

  76. T. Eguchi, P.B. Gilkey and A.J. Hanson, Phys. Rep. 66(6), 213–293 (1980).

    Google Scholar 

  77. P.B. Gilkey, Invariance Theory, the Heat Equation and the Atiyah-Singer Index Theorem (Publish or Perish Inc., Houston 1984) ISBN 0-914098-20-9.

    Google Scholar 

  78. S.-S. Chern, Ann. Math. 45, 747–752 (1944).

    MathSciNet  Google Scholar 

  79. S.-S. Chern, Ann. Math. 46, 674–684 (1945).

    MathSciNet  Google Scholar 

  80. M. Spivak, A Comprehensive Introduction to Differential Geometry (Publish or Perish, Houston 1999).

    Google Scholar 

  81. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2752 (1977).

    MathSciNet  ADS  Google Scholar 

  82. C. Barcelo, R. Maartens, C. F. Sopuerta and F. Viniegra, Phys. Rev. D 67, 064023 (2003) [arXiv:hep-th/0211013].

    ADS  MathSciNet  Google Scholar 

  83. T. Kobayashi and T. Tanaka, arXiv:gr-qc/0412139.

    Google Scholar 

  84. R. Zegers, J. Math. Phys. 46, 072502 (2005) [arXiv:gr-qc/0505016].

    Google Scholar 

  85. P. Bowcock, C. Charmousis and R. Gregory, Class. Quant. Grav. 17, 4745 (2000) [arXiv:hep-th/0007177].

    MATH  MathSciNet  ADS  Google Scholar 

  86. J. Crisostomo, R. Troncoso and J. Zanelli, Black hole scan, Phys. Rev. D 62, 084013 (2001) [hep-th/0003271].

    ADS  MathSciNet  Google Scholar 

  87. R. G. Cai, Phys. Rev. D 65, 084014 (2002) [arXiv:hep-th/0109133].

    ADS  MathSciNet  Google Scholar 

  88. R. Gregory and A. Padilla, Nested braneworlds and strong brane gravity, Phys. Rev. D 65, 084013 (2002) [hep-th/0104262].

    ADS  MathSciNet  Google Scholar 

  89. S. Deser and B. Tekin, Phys. Rev. D 67, 084009 (2003) [arXiv:hep-th/0212292].

    ADS  MathSciNet  Google Scholar 

  90. C. Charmousis and A. Padilla, arXiv:0807.2864

    Google Scholar 

  91. C. de Rham and A. J. Tolley, JCAP 0607, 004 (2006) [arXiv:hep-th/0605122].

    Google Scholar 

  92. G. W. Gibbons and M. J. Perry, Proc. Roy. Soc. Lond. A 358, 467 (1978).

    ADS  MathSciNet  Google Scholar 

  93. P. H. Ginsparg and M. J. Perry, Nucl. Phys. B 222, 245 (1983).

    ADS  MathSciNet  Google Scholar 

  94. S. W. Hawking, G. T. Horowitz and S. F. Ross, Phys. Rev. D 51, 4302 (1995) [arXiv:gr-qc/9409013].

    ADS  MathSciNet  Google Scholar 

  95. C. Garraffo, G. Giribet, E. Gravanis and S. Willison, arXiv:0711.2992 [gr-qc].

    Google Scholar 

  96. T. Clunan, S. F. Ross and D. J. Smith, Class. Quant. Grav. 21, 3447 (2004) [arXiv:gr-qc/0402044].

    MATH  ADS  MathSciNet  Google Scholar 

  97. V. Iyer and R. M. Wald, Phys. Rev. D 50, 846 (1994) [arXiv:gr-qc/9403028].

    ADS  MathSciNet  Google Scholar 

  98. V. Iyer and R. M. Wald, Phys. Rev. D 52, 4430 (1995) [arXiv:gr-qc/9503052].

    ADS  MathSciNet  Google Scholar 

  99. B. Linet, J. Math. Phys. 27, 1817 (1986).

    MATH  ADS  MathSciNet  Google Scholar 

  100. G. T. Horowitz and R. C. Myers, Phys. Rev. D 59, 026005 (1999) [arXiv:hep-th/9808079].

    ADS  MathSciNet  Google Scholar 

  101. J. A. G. Vickers, Class. Quant. Grav. 4, 1 (1987).

    MATH  ADS  MathSciNet  Google Scholar 

  102. V. P. Frolov, W. Israel and W. G. Unruh, Phys. Rev. D 39, 1084 (1989).

    ADS  MathSciNet  Google Scholar 

  103. W. G. Unruh, G. Hayward, W. Israel and D. Mcmanus, Phys. Rev. Lett. 62, 2897 (1989).

    MATH  ADS  MathSciNet  Google Scholar 

  104. B. Boisseau, C. Charmousis and B. Linet, Phys. Rev. D 55, 616 (1997) [arXiv:gr-qc/9607029].

    ADS  Google Scholar 

  105. C. Barrabes and W. Israel, Phys. Rev. D 43, 1129 (1991).

    ADS  MathSciNet  Google Scholar 

  106. C. Charmousis and R. Zegers, Phys. Rev. D 72, 064005 (2005) [arXiv:hep-th/0502171].

    ADS  MathSciNet  Google Scholar 

  107. C. Charmousis and R. Zegers, JHEP 0508, 075 (2005) [arXiv:hep-th/0502170].

    ADS  MathSciNet  Google Scholar 

  108. M. R. Anderson, F. Bonjour, R. Gregory and J. Stewart, Phys. Rev. D 56, 8014 (1997) [arXiv:hep-ph/9707324].

    ADS  MathSciNet  Google Scholar 

  109. G. Kofinas, arXiv:hep-th/0412299.

    Google Scholar 

  110. R. Gregory, Nucl. Phys. B 467, 159 (1996) [arXiv:hep-th/9510202].

    MATH  ADS  MathSciNet  Google Scholar 

  111. C. Charmousis, R. Emparan and R. Gregory, JHEP 0105, 026 (2001) [arXiv:hep-th/0101198].

    ADS  MathSciNet  Google Scholar 

  112. C. Charmousis and U. Ellwanger, JHEP 0402, 058 (2004) [arXiv:hep-th/0402019].

    ADS  MathSciNet  Google Scholar 

  113. S. C. Davis, AIP Conf. Proc. 736, 147 (2005) [arXiv:hep-th/0410075].

    ADS  Google Scholar 

  114. S. C. Davis, Phys. Rev. D 72, 024026 (2005) [arXiv:hep-th/0410065].

    ADS  Google Scholar 

  115. S. C. Davis, arXiv:hep-th/0408139.

    Google Scholar 

  116. B. Bertotti, L. Iess and P. Tortora, A test of general relativity using radio links with the Cassini spacecraft, Nature 425, 374 (2003).

    ADS  Google Scholar 

  117. S. Mukohyama, Y. Sendouda, H. Yoshiguchi and S. Kinoshita, JCAP 0507, 013 (2005) [arXiv:hep-th/0506050].

    ADS  MathSciNet  Google Scholar 

  118. M. Peloso, L. Sorbo and G. Tasinato, Phys. Rev. D 73, 104025 (2006) [arXiv:hep-th/0603026].

    ADS  MathSciNet  Google Scholar 

  119. E. Papantonopoulos, A. Papazoglou and V. Zamarias, JHEP 0703, 002 (2007) [arXiv:hep-th/0611311].

    ADS  MathSciNet  Google Scholar 

  120. C. P. Burgess, D. Hoover and G. Tasinato, JHEP 0709, 124 (2007) [arXiv:0705.3212 [hep-th]].

    ADS  Google Scholar 

  121. F. Mueller-Hoissen and R. Sippel, Class. Quant. Grav. 5, 1473 (1988).

    ADS  Google Scholar 

  122. R. Kerner, C. R. Acad. Sc. Paris, t. 304, Série II, n˚ 12, 1987.

    Google Scholar 

  123. P. Kanti, N. E. Mavromatos, J. Rizos, K. Tamvakis and E. Winstanley, Dilatonic black holes in higher curvature string gravity, Phys. Rev. D 54, 5049 (1996) [hep-th/9511071].

    ADS  MathSciNet  Google Scholar 

  124. G. Esposito-Farese, Scalar-tensor theories and cosmology and tests of a quintessence-Gauss-Bonnet coupling, gr-qc/0306018.

    Google Scholar 

  125. G. Esposito-Farese, Tests of scalar-tensor gravity, AIP Conf. Proc. 736, 35 (2004) [[gr-qc/0409081].

    ADS  Google Scholar 

  126. L. Amendola, C. Charmousis and S. C. Davis, JCAP 0710, 004 (2007) [0704.0175 [astro-ph]].

    Google Scholar 

  127. L. Amendola, C. Charmousis and S. C. Davis, Constraints on Gauss-Bonnet gravity in dark energy cosmologies, JCAP 0612, 020 (2006) [hep-th/0506137].

    ADS  Google Scholar 

  128. T. Koivisto and D. F. Mota, Cosmology and astrophysical constraints of Gauss-Bonnet dark energy, Phys. Lett. B 644, 104 (2007) [astro-ph/0606078].

    ADS  MathSciNet  Google Scholar 

  129. T. Koivisto and D. F. Mota, Gauss-Bonnet quintessence: Background evolution, large scale structure and cosmological constraints, Phys. Rev. D 75, 023518 (2007) [hep-th/0609155].

    ADS  Google Scholar 

  130. B. M. Leith and I. P. Neupane, Gauss-Bonnet cosmologies: Crossing the phantom divide and the transition from matter dominance to dark energy, hep-th/0702002.

    Google Scholar 

  131. L. Amendola, C. Charmousis and S. C. Davis, arXiv:0801.4339 [gr-qc].

    Google Scholar 

  132. B. Cuadros-Melgar, E. Papantonopoulos, M. Tsoukalas and V. Zamarias, arXiv:0804.4459 [hep-th].

    Google Scholar 

  133. R. Gregory and R. Laflamme, Phys. Rev. Lett. 70, 2837 (1993) [arXiv:hep-th/9301052].

    MATH  ADS  MathSciNet  Google Scholar 

  134. C. Charmousis and R. Gregory, Class. Quant. Grav. 21, 527 (2004) [arXiv:gr-qc/0306069].

    MATH  ADS  MathSciNet  Google Scholar 

  135. C. Charmousis, D. Langlois, D. Steer and R. Zegers, JHEP 0702, 064 (2007) [arXiv:gr-qc/0610091].

    ADS  MathSciNet  Google Scholar 

  136. R. Emparan and H. S. Reall, Phys. Rev. D 65, 084025 (2002) [arXiv:hep-th/0110258].

    ADS  MathSciNet  Google Scholar 

  137. M. Beroiz, G. Dotti and R. J. Gleiser, Phys. Rev. D 76, 024012 (2007) [arXiv:hep-th/0703074].

    ADS  MathSciNet  Google Scholar 

  138. R. J. Gleiser and G. Dotti, Phys. Rev. D 72, 124002 (2005) [arXiv:gr-qc/0510069].

    ADS  MathSciNet  Google Scholar 

  139. G. Dotti and R. J. Gleiser, Phys. Rev. D 72, 044018 (2005) [arXiv:gr-qc/0503117].

    ADS  MathSciNet  Google Scholar 

  140. G. Dotti and R. J. Gleiser, Class. Quant. Grav. 22, L1 (2005) [arXiv:gr-qc/0409005].

    MATH  ADS  MathSciNet  Google Scholar 

  141. M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, arXiv:0802.3318 [hep-th]. M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, arXiv:0712.0805 [hep-th].

    Google Scholar 

  142. S. Deser and B. Tekin, Phys. Rev. D 75, 084032 (2007) [arXiv:gr-qc/0701140].

    ADS  MathSciNet  Google Scholar 

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  1. LPT, Université de Paris-Sud, Bât. 210, 91405 Orsay CEDEX, France

    C. Charmousis

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  1. Dept. of Physics, National Technical University, Zografou Campus, 157 80 Athens, Greece

    Eleftherios Papantonopoulos

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Charmousis, C. (2009). Higher Order Gravity Theories and Their Black Hole Solutions. In: Papantonopoulos, E. (eds) Physics of Black Holes. Lecture Notes in Physics, vol 769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88460-6_8

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