2017

Action Growth in $f\left(R\right)$ Gravity

Wang, Peng, Yang, Haitang, Ying, Shuxuan

Understand

Inspired by the recent "Complexity = Action" conjecture, we use the approach proposed by Lehner et al.

to calculate the rate of the action of the WheelerDeWitt patch at late times for static uncharged and charged black holes in $f\left( R\right) $ gravity.
Our results have the same expressions in terms of the mass, charge, and electrical potentials at the horizons of black holes as in Einstein's gravity.
In the context of $f\left( R\right) $ gravity, the Lloyd bound is saturated for uncharged black holes but violated for charged black holes near extremality.

Built on

P. G. Bergmann, “Comments on the scalar tensor theory,” Int. J. Theor. Phys. 1
1968
Earlier work this paper cites.
S. Lloyd, “Ultimate physical limits to computation,” Nature 406
2000
Earlier work this paper cites.
M. Hassaine and C. Martinez, “Higher-dimensional black holes with a conformally invariant Maxwell source,” Phys. Rev. D 75
2007
Earlier work this paper cites.
J. Watrous, “Quantum computational complexity,” in Encyclopedia of Complexity and Systems Science, ed., R. A. Meyers (2009) 7174–7201, arXiv:0804.3401 [quant-ph]
Original
2009
Earlier work this paper cites.
S. Capozziello, M. De Laurentis and V. Faraoni, “A Bird’s eye view of f(R)-gravity,” Open Astron. J. 3
Original
2010
Earlier work this paper cites.
A. De Felice and S. Tsujikawa, “f(R) theories,” Living Rev. Rel. 13
Original
2010
Earlier work this paper cites.
L. Pogosian and A. Silvestri, “The pattern of growth in viable f(R) cosmologies,” Phys. Rev. D 77
Original
2010
Earlier work this paper cites.

Similar

S. Capozziello and M. De Laurentis, “Extended Theories of Gravity,” Phys. Rept. 509
Original
2011
Cited alongside, same era.
S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models,” Phys. Rept. 505
Original
2011
Cited alongside, same era.
T. Moon, Y. S. Myung and E. J. Son, “f(R) black holes,” Gen. Rel. Grav. 43
Original
2011
Cited alongside, same era.
A. de la Cruz-Dombriz, A. Dobado and A. L. Maroto, “Black Holes in f(R) theories,” Phys. Rev. D 80
Original
2011
Cited alongside, same era.
T. J. Osborne, “Hamiltonian complexity,” Reports on Progress in Physics 75
Original
2012
Cited alongside, same era.
A. Sheykhi, “Higher-dimensional charged f ⁡ ( R ) f(R) black holes,” Phys. Rev. D 86
Original
2012
Cited alongside, same era.
D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” Phys. Rev. D 90
Original
2014
Cited alongside, same era.
L. Susskind and Y. Zhao, “Switchbacks and the Bridge to Nowhere,” arXiv:1408.2823 [hep-th]
Original
Cited in the paper.
J. Couch, W. Fischler and P. H. Nguyen, “Noether Charge, Black Hole Volume, and Complexity,” arXiv:1610.02038 [hep-th]
Original
Cited in the paper.
W. J. Pan and Y. C. Huang, “Holographic complexity and action growth in massive gravities,” arXiv:1612.03627 [hep-th]
Original
Cited in the paper.
M. Alishahiha, A. Faraji Astaneh, A. Naseh and M. H. Vahidinia, “On Complexity for Higher Derivative Gravities,” arXiv:1702.06796 [hep-th]
Original
Cited in the paper.
R. G. Cai, M. Sasaki and S. J. Wang, “Action growth of charged black holes with a single horizon,” arXiv:1702.06766 [gr-qc]
Original
Cited in the paper.

Then

S. Gharibian, Y. Huang, Z. Landau, and S. W. Shin, “Quantum hamiltonian complexity,” Foundations and Trends in Theoretical Computer Science 10
Original
2015
Later among the works it cites.
A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116
Original
2016
Later among the works it cites.
A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Complexity, action, and black holes,” Phys. Rev. D 93
Original
2016
Later among the works it cites.
L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch. Phys. 64
Original
2016
Later among the works it cites.
L. Susskind, “Entanglement is not enough,” Fortsch. Phys. 64
Original
2016
Later among the works it cites.
L. Lehner, R. C. Myers, E. Poisson and R. D. Sorkin, “Gravitational action with null boundaries,” Phys. Rev. D 94
Original
2016
Later among the works it cites.
R. G. Cai, S. M. Ruan, S. J. Wang, R. Q. Yang and R. H. Peng, “Action growth for AdS black holes,” JHEP 1609
Original
2016
Later among the works it cites.

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