Built on

P. C. Vaidya, “The External Field of a Radiating Star in General Relativity,” Curr. Sci. 12
1943
Earlier work this paper cites.
P. C. Vaidya, “The gravitational field of a radiating star,” Indian Acad. Sci. (Math. Sci.) (1951) 33
1951
Earlier work this paper cites.
B. F. Schutz, “Perfect fluids in general relativity: velocity potentials and a variational principle,” Phys. Rev. D 2̱ (1970) 2762, PhysRevD.2.2762
1970
Earlier work this paper cites.
J. D. Bekenstein, “Black holes and the second law,” Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
J. W. York, Jr., “Role of conformal three geometry in the dynamics of gravitation,” Phys. Rev. Lett. 28
1972
Earlier work this paper cites.
J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7
1973
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Action Integrals and Partition Functions in Quantum Gravity,” Phys. Rev. D 15
1977
Earlier work this paper cites.
R. D. Sorkin, “1983 paper on entanglement entropy: ‘On the Entropy of the Vacuum outside a Horizon’,” Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. II, pp. 734-736, gr-qc/1402.3589
Original
1983
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
J. D. Brown, “Action functionals for relativistic perfect fluids,” Class. Quant. Grav. 10
1993
Earlier work this paper cites.
G. Hayward, “Gravitational action for space-times with nonsmooth boundaries,” Phys. Rev. D 47
1993
Earlier work this paper cites.
D. Brill and G. Hayward, “Is the gravitational action additive?,” Phys. Rev. D 50
1994
Earlier work this paper cites.
O. Coussaert and M. Henneaux, “Supersymmetry of the (2+1) black holes,” Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
J. Bicak and K. V. Kuchar, “Null dust in canonical gravity,” Phys. Rev. D56
1997
Earlier work this paper cites.
A. Wang and Y. Wu, “Generalized Vaidya solutions,” Gen. Rel. Grav. 31
1999
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O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large N field theories, string theory and gravity,” Phys. Rept. 323
2000
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S. Lloyd, “Ultimate physical limits to computation,” Nature 406 (2000), no. 6799, 1047-1054, quant-ph/9908043
2000
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S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
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S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP 0608
2006
Earlier work this paper cites.
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, “Null energy condition and superluminal propagation,” JHEP 0603
2006
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V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
Original
2007
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J. Watrous, “Quantum Computational Complexity,” pp 7174-7201 in Encyclopedia of Complexity and Systems Science
Original
2009
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S. Bhattacharyya and S. Minwalla, “Weak Field Black Hole Formation in Asymptotically AdS Spacetimes,” JHEP 0909
Original
2009
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M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Earlier work this paper cites.
S. R. Das, T. Nishioka and T. Takayanagi, “Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT,” JHEP 1007
Original
2010
Earlier work this paper cites.
J. Abajo-Arrastia, J. Aparicio and E. Lopez, “Holographic Evolution of Entanglement Entropy,” JHEP 1011
Original
2010
Earlier work this paper cites.

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L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch. Phys. 64
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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
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A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Complexity, action, and black holes,” Phys. Rev. D 93
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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
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L. Lehner, R. C. Myers, E. Poisson and R. D. Sorkin, “Gravitational action with null boundaries,” Phys. Rev. D 94

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2018

Holographic Complexity in Vaidya Spacetimes I

Chapman, Shira, Marrochio, Hugo, Myers, Robert C.

Understand

We examine holographic complexity in time-dependent Vaidya spacetimes with both the complexity$=$volume (CV) and complexity$=$action (CA) proposals.

We focus on the evolution of the holographic complexity for a thin shell of null fluid, which collapses into empty AdS space and forms a (one-sided) black hole.
In order to apply the CA approach, we introduce an action principle for the null fluid which sources the Vaidya geometries, and we carefully examine the contribution of the null shell to the action.
Further, we find that adding a particular counterterm on the null boundaries of the Wheeler-DeWitt patch is essential if the gravitational action is to properly describe the complexity of the boundary state.

Built on

P. C. Vaidya, “The External Field of a Radiating Star in General Relativity,” Curr. Sci. 12
1943
Earlier work this paper cites.
P. C. Vaidya, “The gravitational field of a radiating star,” Indian Acad. Sci. (Math. Sci.) (1951) 33
1951
Earlier work this paper cites.
B. F. Schutz, “Perfect fluids in general relativity: velocity potentials and a variational principle,” Phys. Rev. D 2̱ (1970) 2762, PhysRevD.2.2762
1970
Earlier work this paper cites.
J. D. Bekenstein, “Black holes and the second law,” Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
J. W. York, Jr., “Role of conformal three geometry in the dynamics of gravitation,” Phys. Rev. Lett. 28
1972
Earlier work this paper cites.
J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7
1973
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Action Integrals and Partition Functions in Quantum Gravity,” Phys. Rev. D 15
1977
Earlier work this paper cites.
R. D. Sorkin, “1983 paper on entanglement entropy: ‘On the Entropy of the Vacuum outside a Horizon’,” Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. II, pp. 734-736, gr-qc/1402.3589
Original
1983
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
J. D. Brown, “Action functionals for relativistic perfect fluids,” Class. Quant. Grav. 10
1993
Earlier work this paper cites.
G. Hayward, “Gravitational action for space-times with nonsmooth boundaries,” Phys. Rev. D 47
1993
Earlier work this paper cites.
D. Brill and G. Hayward, “Is the gravitational action additive?,” Phys. Rev. D 50
1994
Earlier work this paper cites.
O. Coussaert and M. Henneaux, “Supersymmetry of the (2+1) black holes,” Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
J. Bicak and K. V. Kuchar, “Null dust in canonical gravity,” Phys. Rev. D56
1997
Earlier work this paper cites.
A. Wang and Y. Wu, “Generalized Vaidya solutions,” Gen. Rel. Grav. 31
1999
Earlier work this paper cites.
O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large N field theories, string theory and gravity,” Phys. Rept. 323
2000
Earlier work this paper cites.
S. Lloyd, “Ultimate physical limits to computation,” Nature 406 (2000), no. 6799, 1047-1054, quant-ph/9908043
2000
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP 0608
2006
Earlier work this paper cites.
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, “Null energy condition and superluminal propagation,” JHEP 0603
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
Original
2007
Earlier work this paper cites.
J. Watrous, “Quantum Computational Complexity,” pp 7174-7201 in Encyclopedia of Complexity and Systems Science
Original
2009
Earlier work this paper cites.
S. Bhattacharyya and S. Minwalla, “Weak Field Black Hole Formation in Asymptotically AdS Spacetimes,” JHEP 0909
Original
2009
Earlier work this paper cites.
M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Earlier work this paper cites.
S. R. Das, T. Nishioka and T. Takayanagi, “Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT,” JHEP 1007
Original
2010
Earlier work this paper cites.
J. Abajo-Arrastia, J. Aparicio and E. Lopez, “Holographic Evolution of Entanglement Entropy,” JHEP 1011
Original
2010
Earlier work this paper cites.