Abstract
We comment on the recently introduced Gauss-Bonnet gravity in four dimensions. We argue that it does not make sense to consider this theory to be defined by a set of D → 4 solutions of the higher-dimensional Gauss-Bonnet gravity. We show that a well-defined D → 4 limit of Gauss-Bonnet Gravity is obtained generalizing a method employed by Mann and Ross to obtain a limit of the Einstein gravity in D = 2 dimensions. This is a scalar-tensor theory of the Horndeski type obtained by dimensional reduction methods. By considering simple spacetimes beyond spherical symmetry (Taub-NUT spaces) we show that the naive limit of the higher-dimensional theory to D = 4 is not well defined and contrast the resultant metrics with the actual solutions of the new theory.
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References
D. Glavan and C. Lin, Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime, Phys. Rev. Lett. 124 (2020) 081301 [arXiv:1905.03601] [INSPIRE].
A. Kumar and R. Kumar, Bardeen black holes in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.13104 [INSPIRE].
P.G.S. Fernandes, Charged Black Holes in AdS Spaces in 4D Einstein Gauss-Bonnet Gravity, Phys. Lett. B 805 (2020) 135468 [arXiv:2003.05491] [INSPIRE].
R. Kumar and S.G. Ghosh, Rotating black holes in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.08927 [INSPIRE].
A. Kumar and S.G. Ghosh, Hayward black holes in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.01131 [INSPIRE].
S.-L. Li, P. Wu and H. Yu, Stability of the Einstein Static Universe in 4D Gauss-Bonnet Gravity, arXiv:2004.02080 [INSPIRE].
T. Kobayashi, Effective scalar-tensor description of regularized Lovelock gravity in four dimensions, arXiv:2003.12771 [INSPIRE].
D.D. Doneva and S.S. Yazadjiev, Relativistic stars in 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.10284 [INSPIRE].
S.G. Ghosh and S.D. Maharaj, Radiating black holes in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.09841 [INSPIRE].
D. Malafarina, B. Toshmatov and N. Dadhich, Dust collapse in 4D Einstein-Gauss-Bonnet gravity, Phys. Dark Univ. 30 (2020) 100598 [arXiv:2004.07089] [INSPIRE].
A. Casalino, A. Colleaux, M. Rinaldi and S. Vicentini, Regularized Lovelock gravity, arXiv:2003.07068 [INSPIRE].
R.A. Konoplya and A. Zhidenko, Black holes in the four-dimensional Einstein-Lovelock gravity, Phys. Rev. D 101 (2020) 084038 [arXiv:2003.07788] [INSPIRE].
B. Eslam Panah and K. Jafarzade, 4D Einstein-Gauss-Bonnet AdS Black Holes as Heat Engine, arXiv:2004.04058 [INSPIRE].
R.A. Konoplya and A.F. Zinhailo, Grey-body factors and Hawking radiation of black holes in 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.02248 [INSPIRE].
S.-W. Wei and Y.-X. Liu, Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space, Phys. Rev. D 101 (2020) 104018 [arXiv:2003.14275] [INSPIRE].
S.A. Hosseini Mansoori, Thermodynamic geometry of the novel 4D Gauss Bonnet AdS Black Hole, arXiv:2003.13382 [INSPIRE].
C.-Y. Zhang, P.-C. Li and M. Guo, Greybody factor and power spectra of the Hawking radiation in the novel 4D Einstein-Gauss-Bonnet de-Sitter gravity, arXiv:2003.13068 [INSPIRE].
D.V. Singh and S. Siwach, Thermodynamics and P − v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity, arXiv:2003.11754 [INSPIRE].
K. Hegde, A. Naveena Kumara, C.L.A. Rizwan, K.M. Ajith and M.S. Ali, Thermodynamics, Phase Transition and Joule Thomson Expansion of novel 4D Gauss Bonnet AdS Black Hole, arXiv:2003.08778 [INSPIRE].
R.A. Konoplya and A.F. Zinhailo, Quasinormal modes, stability and shadows of a black hole in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.01188 [INSPIRE].
Y.-P. Zhang, S.-W. Wei and Y.-X. Liu, Spinning test particle in four-dimensional Einstein-Gauss-Bonnet Black Hole, arXiv:2003.10960 [INSPIRE].
C.-Y. Zhang, S.-J. Zhang, P.-C. Li and M. Guo, Superradiance and stability of the novel 4D charged Einstein-Gauss-Bonnet black hole, arXiv:2004.03141 [INSPIRE].
S.-W. Wei and Y.-X. Liu, Testing the nature of Gauss-Bonnet gravity by four-dimensional rotating black hole shadow, arXiv:2003.07769 [INSPIRE].
M. Guo and P.-C. Li, The innermost stable circular orbit and shadow in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.02523 [INSPIRE].
X.-H. Jin, Y.-X. Gao and D.-J. Liu, Strong gravitational lensing of a 4-dimensional Einstein-Gauss-Bonnet black hole in homogeneous plasma, arXiv:2004.02261 [INSPIRE].
M. Heydari-Fard, M. Heydari-Fard and H.R. Sepangi, Bending of light in novel 4D Gauss-Bonnet-de Sitter black holes by Rindler-Ishak method, arXiv:2004.02140 [INSPIRE].
C. Liu, T. Zhu and Q. Wu, Thin Accretion Disk around a four-dimensional Einstein-Gauss-Bonnet Black Hole, arXiv:2004.01662 [INSPIRE].
S.U. Islam, R. Kumar and S.G. Ghosh, Gravitational lensing by black holes in 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.01038 [INSPIRE].
R. Roy and S. Chakrabarti, A study on black hole shadows in asymptotically de Sitter spacetimes, arXiv:2003.14107 [INSPIRE].
A. Naveena Kumara, C.L.A. Rizwan, K. Hegde, M.S. Ali and K.M. Ajith, Rotating 4D Gauss-Bonnet black hole as particle accelerator, arXiv:2004.04521 [INSPIRE].
A.K. Mishra, Quasinormal modes and Strong Cosmic Censorship in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.01243 [INSPIRE].
M. Gurses, T.C. Sisman and B. Tekin, Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?, arXiv:2004.03390 [INSPIRE].
W.-Y. Ai, A note on the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.02858 [INSPIRE].
F.-W. Shu, Vacua in novel 4D Einstein-Gauss-Bonnet Gravity: pathology and instability?, arXiv:2004.09339 [INSPIRE].
H. Lü and Y. Pang, Horndeski Gravity as D → 4 Limit of Gauss-Bonnet, arXiv:2003.11552 [INSPIRE].
R.B. Mann and S.F. Ross, The D → 2 limit of general relativity, Class. Quant. Grav. 10 (1993) 1405 [gr-qc/9208004] [INSPIRE].
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].
K. Van Acoleyen and J. Van Doorsselaere, Galileons from Lovelock actions, Phys. Rev. D 83 (2011) 084025 [arXiv:1102.0487] [INSPIRE].
C. Charmousis, From Lovelock to Horndeski‘s Generalized Scalar Tensor Theory, Lect. Notes Phys. 892 (2015) 25 [arXiv:1405.1612] [INSPIRE].
C. Charmousis, B. Gouteraux and E. Kiritsis, Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography, JHEP 09 (2012) 011 [arXiv:1206.1499] [INSPIRE].
H. Maeda and N. Dadhich, Matter without matter: Novel Kaluza-Klein spacetime in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 75 (2007) 044007 [hep-th/0611188] [INSPIRE].
F. Müller-Hoissen, Nonminimal Coupling From Dimensional Reduction of the Gauss-Bonnet Action, Phys. Lett. B 201 (1988) 325 [INSPIRE].
W.-H. Huang, Kaluza-Klein Reduction of Gauss-Bonnet Curvature, Phys. Lett. B 203 (1988) 105 [INSPIRE].
H.H. Soleng and O. Gron, Modification of the Coulomb potential from Kaluza-Klein model with a Gauss-Bonnet term in the action, Annals Phys. 240 (1995) 432 [gr-qc/9409060] [INSPIRE].
G.W. Gibbons and C.A.R. Herdeiro, Born-Infeld theory and stringy causality, Phys. Rev. D 63 (2001) 064006 [hep-th/0008052] [INSPIRE].
S. Nojiri and S.D. Odintsov, Novel cosmological and black hole solutions in Einstein and higher-derivative gravity in two dimensions, Europhys. Lett. 130 (2020) 10004 [arXiv:2004.01404] [INSPIRE].
R.B. Mann, A. Shiekh and L. Tarasov, Classical and Quantum Properties of Two-dimensional Black Holes, Nucl. Phys. B 341 (1990) 134 [INSPIRE].
A.E. Sikkema and R.B. Mann, Gravitation and Cosmology in Two-dimensions, Class. Quant. Grav. 8 (1991) 219 [INSPIRE].
R.B. Mann, S.M. Morsink, A.E. Sikkema and T.G. Steele, Semiclassical gravity in (1 + 1)-dimensions, Phys. Rev. D 43 (1991) 3948 [INSPIRE].
R.B. Mann, Lower dimensional black holes, Gen. Rel. Grav. 24 (1992) 433 [INSPIRE].
R.B. Mann, M.S. Morris and S.F. Ross, Properties of asymptotically flat two-dimensional black holes, Class. Quant. Grav. 10 (1993) 1477 [hep-th/9202068] [INSPIRE].
D. Christensen and R.B. Mann, The Causal structure of two-dimensional space-times, Class. Quant. Grav. 9 (1992) 1769 [hep-th/9203050] [INSPIRE].
J.P.S. Lemos and P.M. Sa, The Two-dimensional analog of general relativity, Class. Quant. Grav. 11 (1994) L11 [gr-qc/9310041] [INSPIRE].
J.P.S. Lemos, Two-dimensional black holes and planar general relativity, Class. Quant. Grav. 12 (1995) 1081 [gr-qc/9407024] [INSPIRE].
S. Mignemi, Black holes in generalized dilaton gravity in two-dimensions, Annals Phys. 245 (1996) 23 [hep-th/9411153] [INSPIRE].
J.R. Mureika and P. Nicolini, Aspects of noncommutative (1 + 1)-dimensional black holes, Phys. Rev. D 84 (2011) 044020 [arXiv:1104.4120] [INSPIRE].
A.M. Frassino, R.B. Mann and J.R. Mureika, Lower-Dimensional Black Hole Chemistry, Phys. Rev. D 92 (2015) 124069 [arXiv:1509.05481] [INSPIRE].
D. Hansen and N. Yunes, Applicability of the Newman-Janis Algorithm to Black Hole Solutions of Modified Gravity Theories, Phys. Rev. D 88 (2013) 104020 [arXiv:1308.6631] [INSPIRE].
Y. Tomozawa, Quantum corrections to gravity, arXiv:1107.1424 [INSPIRE].
G. Cognola, R. Myrzakulov, L. Sebastiani and S. Zerbini, Einstein gravity with Gauss-Bonnet entropic corrections, Phys. Rev. D 88 (2013) 024006 [arXiv:1304.1878] [INSPIRE].
M.H. Dehghani and R.B. Mann, NUT-charged black holes in Gauss-Bonnet gravity, Phys. Rev. D 72 (2005) 124006 [hep-th/0510083] [INSPIRE].
M.H. Dehghani and S.H. Hendi, Taub-NUT/bolt black holes in Gauss-Bonnet-Maxwell gravity, Phys. Rev. D 73 (2006) 084021 [hep-th/0602069] [INSPIRE].
S.H. Hendi and M.H. Dehghani, Taub-NUT Black Holes in Third order Lovelock Gravity, Phys. Lett. B 666 (2008) 116 [arXiv:0802.1813] [INSPIRE].
P. Bueno, P.A. Cano, R.A. Hennigar and R.B. Mann, NUTs and bolts beyond Lovelock, JHEP 10 (2018) 095 [arXiv:1808.01671] [INSPIRE].
G. Dotti, J. Oliva and R. Troncoso, Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns, Phys. Rev. D 76 (2007) 064038 [arXiv:0706.1830] [INSPIRE].
R.A. Konoplya and A. Zhidenko, BTZ black holes with higher curvature corrections in the 3D Einstein-Lovelock theory, arXiv:2003.12171 [INSPIRE].
P.G.S. Fernandes, P. Carrilho, T. Clifton and D.J. Mulryne, Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions, arXiv:2004.08362 [INSPIRE].
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Hennigar, R.A., Kubizňák, D., Mann, R.B. et al. On taking the D → 4 limit of Gauss-Bonnet gravity: theory and solutions. J. High Energ. Phys. 2020, 27 (2020). https://doi.org/10.1007/JHEP07(2020)027
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DOI: https://doi.org/10.1007/JHEP07(2020)027