Holographic entanglement entropy and the first law of thermodynamics are believed to decode the gravity theory in the bulk. In particular, assuming the Ryu-Takayanagi (RT) [Phys. Rev. Lett. 96, 181602 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.181602] formula holds for ball-shaped regions on the boundary around conformal field theory vacuum states implies [J. High Energy Phys. 08 (2017) 057JHEPFG1029-847910.1007/JHEP08(2017)057] a bulk gravity theory equivalent to Einstein gravity through second-order perturbations. In this paper, we show that the same assumptions can also give rise to second-order Lovelock gravity. Specifically, we generalize the procedure in [J. High Energy Phys. 08 (2017) 057JHEPFG1029-847910.1007/JHEP08(2017)057] to show that the arguments there also hold for Lovelock gravity by proving through second-order perturbation theory, the entropy calculated using the Wald formula [Phys. Rev. D 48, R3427 (1993)PRVDAQ0556-282110.1103/PhysRevD.48.R3427] in Lovelock also obeys an area law (at least up to second order). Since the equations for second-order perturbations of Lovelock gravity are different in general from the second-order perturbation of the Einstein-Hilbert action, our work shows that the holographic area law cannot determine a unique bulk theory even for second-order perturbations assuming only RT on ball-shaped regions. It is anticipated that RT on all subregions is expected to encode the full nonlinear Einstein equations on asymptotically anti-de Sitter spacetimes.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)