Abstract
In this work we study a more restricted class of quasi-topological gravity theories where the higher curvature terms have no contribution to the equation of motion on general static spherically symmetric metric where gttgrr ≠ constant. We construct such theories up to quintic order in Riemann tensor and observe an important property of these theories: the higher order term in the Lagrangian vanishes identically when evaluated on the most general non-stationary spherically symmetric metric ansatz. This not only signals the higher terms could only have non-trivial effects when considering perturbations, but also makes the theories quasi-topological on a much wider range of metrics. As an example of the holographic effects of such theories, we consider a general Einstein-scalar theory and calculate it’s holographic shear viscosity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.J. Gross and J.H. Sloan, The quartic effective action for the heterotic string, Nucl. Phys. B 291 (1987) 41 [INSPIRE].
M.T. Grisaru and D. Zanon, σ model superstring corrections to the Einstein-Hilbert action, Phys. Lett. B 177 (1986) 347 [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].
A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035 [arXiv:1004.2055] [INSPIRE].
X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007 [arXiv:0911.3160] [INSPIRE].
X.O. Camanho and J.D. Edelstein, Causality in AdS/CFT and Lovelock theory, JHEP 06 (2010) 099 [arXiv:0912.1944] [INSPIRE].
P. Bueno, P.A. Cano, V.S. Min and M.R. Visser, Aspects of general higher-order gravities, Phys. Rev. D 95 (2017) 044010 [arXiv:1610.08519] [INSPIRE].
D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498 [INSPIRE].
D. Lovelock, Divergence-free tensorial concomitants, Aeq. Math. 4 (1970) 127.
R.C. Myers and B. Robinson, Black holes in quasi-topological gravity, JHEP 08 (2010) 067 [arXiv:1003.5357] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035 [arXiv:1004.2055] [INSPIRE].
J. Oliva and S. Ray, A new cubic theory of gravity in five dimensions: black hole, Birkhoff’s theorem and C-function, Class. Quant. Grav. 27 (2010) 225002 [arXiv:1003.4773] [INSPIRE].
M.H. Dehghani et al., Black holes in quartic quasitopological gravity, Phys. Rev. D 85 (2012) 104009 [arXiv:1109.4708] [INSPIRE].
J. Ahmed, R.A. Hennigar, R.B. Mann and M. Mir, Quintessential quartic quasi-topological quartet, JHEP 05 (2017) 134 [arXiv:1703.11007] [INSPIRE].
A. Cisterna, L. Guajardo, M. Hassaine and J. Oliva, Quintic quasi-topological gravity, JHEP 04 (2017) 066 [arXiv:1702.04676] [INSPIRE].
R.A. Hennigar, D. Kubizňák and R.B. Mann, Generalized quasitopological gravity, Phys. Rev. D 95 (2017) 104042 [arXiv:1703.01631] [INSPIRE].
P. Bueno, P.A. Cano and R.A. Hennigar, (Generalized) quasi-topological gravities at all orders, Class. Quant. Grav. 37 (2020) 015002 [arXiv:1909.07983] [INSPIRE].
P. Bueno and P.A. Cano, Einsteinian cubic gravity, Phys. Rev. D 94 (2016) 104005 [arXiv:1607.06463] [INSPIRE].
R.A. Hennigar and R.B. Mann, Black holes in Einsteinian cubic gravity, Phys. Rev. D 95 (2017) 064055 [arXiv:1610.06675] [INSPIRE].
P. Bueno and P.A. Cano, Four-dimensional black holes in Einsteinian cubic gravity, Phys. Rev. D 94 (2016) 124051 [arXiv:1610.08019] [INSPIRE].
P. Bueno, P.A. Cano and A. Ruipérez, Holographic studies of Einsteinian cubic gravity, JHEP 03 (2018) 150 [arXiv:1802.00018] [INSPIRE].
M. Mir, R.A. Hennigar, J. Ahmed and R.B. Mann, Black hole chemistry and holography in generalized quasi-topological gravity, JHEP 08 (2019) 068 [arXiv:1902.02005] [INSPIRE].
M. Mir and R.B. Mann, On generalized quasi-topological cubic-quartic gravity: thermodynamics and holography, JHEP 07 (2019) 012 [arXiv:1902.10906] [INSPIRE].
P.A. Cano, Á.J. Murcia, A. Rivadulla Sánchez and X. Zhang, Higher-derivative holography with a chemical potential, JHEP 07 (2022) 010 [arXiv:2202.10473] [INSPIRE].
P. Bueno, P.A. Cano, J. Moreno and Á. Murcia, All higher-curvature gravities as generalized quasi-topological gravities, JHEP 11 (2019) 062 [arXiv:1906.00987] [INSPIRE].
P. Bueno et al., Generalized quasi-topological gravities: the whole shebang, Class. Quant. Grav. 40 (2023) 015004 [arXiv:2203.05589] [INSPIRE].
Y.-Z. Li, H.-S. Liu and H. Lu, Quasi-topological Ricci polynomial gravities, JHEP 02 (2018) 166 [arXiv:1708.07198] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
C. Martinez, R. Troncoso and J. Zanelli, Exact black hole solution with a minimally coupled scalar field, Phys. Rev. D 70 (2004) 084035 [hep-th/0406111] [INSPIRE].
H. Dykaar, R.A. Hennigar and R.B. Mann, Hairy black holes in cubic quasi-topological gravity, JHEP 05 (2017) 045 [arXiv:1703.01633] [INSPIRE].
N. Caceres et al., Quadratic gravity and conformally coupled scalar fields, JHEP 04 (2020) 157 [arXiv:2001.01478] [INSPIRE].
T. Padmanabhan and D. Kothawala, Lanczos-Lovelock models of gravity, Phys. Rept. 531 (2013) 115 [arXiv:1302.2151] [INSPIRE].
P. Bueno et al., Aspects of three-dimensional higher curvatures gravities, Class. Quant. Grav. 39 (2022) 125002 [arXiv:2201.07266] [INSPIRE].
S.A. Fulling, R.C. King, B.G. Wybourne and C.J. Cummins, Normal forms for tensor polynomials. 1: the Riemann tensor, Class. Quant. Grav. 9 (1992) 1151 [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427–R3431 [gr-qc/9307038] [INSPIRE].
N. Deruelle, M. Sasaki, Y. Sendouda and D. Yamauchi, Hamiltonian formulation of f(Riemann) theories of gravity, Prog. Theor. Phys. 123 (2010) 169 [arXiv:0908.0679] [INSPIRE].
M.J. Duff, Observations on conformal anomalies, Nucl. Phys. B 125 (1977) 334 [INSPIRE].
C. Imbimbo, A. Schwimmer, S. Theisen and S. Yankielowicz, Diffeomorphisms and holographic anomalies, Class. Quant. Grav. 17 (2000) 1129 [hep-th/9910267] [INSPIRE].
Y.-Z. Li, H. Lu and J.-B. Wu, Causality and a-theorem constraints on Ricci polynomial and Riemann cubic gravities, Phys. Rev. D 97 (2018) 024023 [arXiv:1711.03650] [INSPIRE].
L. Li, On thermodynamics of AdS black holes with scalar hair, Phys. Lett. B 815 (2021) 136123 [arXiv:2008.05597] [INSPIRE].
M.F. Paulos, Transport coefficients, membrane couplings and universality at extremality, JHEP 02 (2010) 067 [arXiv:0910.4602] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2301.00235
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Chen, F. Quasi-topological gravities on general spherically symmetric metric. J. High Energ. Phys. 2023, 55 (2023). https://doi.org/10.1007/JHEP03(2023)055
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2023)055