Built on

G. Compere and D. Marolf, “Setting the boundary free in AdS/CFT,” Class. Quant. Grav. 25
Original
1902
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.
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.
J. W. York, Jr., “Boundary terms in the action principles of general relativity", Foundations of Physics, 16, No. 3, 1986, 249-257
1986
Earlier work this paper cites.
J. D. Brown and J. W. York, Jr., “The Microcanonical functional integral. 1. The Gravitational field,” Phys. Rev. D 47
1993
Earlier work this paper cites.
M. Banados and F. Mendez, “A Note on covariant action integrals in three-dimensions,” Phys. Rev. D 58
1998
Earlier work this paper cites.

Similar

M. Henningson and K. Skenderis, “The Holographic Weyl anomaly,” JHEP 9807
1998
Cited alongside, same era.
V. Balasubramanian and P. Kraus, “A Stress tensor for Anti-de Sitter gravity,” Commun. Math. Phys. 208
1999
Cited alongside, same era.
S. de Haro, S. N. Solodukhin and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,” Commun. Math. Phys. 217
2001
Cited alongside, same era.
P. Mora, R. Olea, R. Troncoso and J. Zanelli, “Finite action principle for Chern-Simons AdS gravity,” JHEP 0406
2004
Cited alongside, same era.
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2006
Cited alongside, same era.

Then

S. Detournay, D. Grumiller, F. Scholler and J. Simon, “Variational principle and one-point functions in three-dimensional flat space Einstein gravity,” Phys. Rev. D 89
Original
2014
Later among the works it cites.
K. S. Kiran, C. Krishnan and A. Raju, “3D gravity, Chern–Simons and higher spins: A mini introduction,” Mod. Phys. Lett. A 30
Original
2015
Later among the works it cites.
C. Krishnan, A. Raju and P. N. B. Subramanian, “Dynamical boundary for anti–de Sitter space,” Phys. Rev. D 94
Original
2016
Closest in time.
K. Parattu, S. Chakraborty, B. R. Majhi and T. Padmanabhan, “A Boundary Term for the Gravitational Action with Null Boundaries,” Gen. Rel. Grav. 48
Original
2016
Closest in time.
C. Krishnan, K. V. P. Kumar and A. Raju, “An alternative path integral for quantum gravity,” JHEP 1610

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2016

A Neumann Boundary Term for Gravity

Krishnan, Chethan, Raju, Avinash

Understand

The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well defined, but no such general term seems to be known for Neumann boundary conditions.

In this paper, we view Neumann {\em not} as fixing the normal derivative of the metric ("velocity") at the boundary, but as fixing the functional derivative of the action with respect to the boundary metric ("momentum").
This leads directly to a new boundary term for gravity: the trace of the extrinsic curvature with a specific dimension-dependent coefficient.
In three dimensions this boundary term reduces to a "one-half" GHY term noted in the literature previously, and we observe that our action translates precisely to the Chern-Simons action with no extra boundary terms.

Built on

G. Compere and D. Marolf, “Setting the boundary free in AdS/CFT,” Class. Quant. Grav. 25
Original
1902
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.
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.
J. W. York, Jr., “Boundary terms in the action principles of general relativity", Foundations of Physics, 16, No. 3, 1986, 249-257
1986
Earlier work this paper cites.
J. D. Brown and J. W. York, Jr., “The Microcanonical functional integral. 1. The Gravitational field,” Phys. Rev. D 47
1993
Earlier work this paper cites.
M. Banados and F. Mendez, “A Note on covariant action integrals in three-dimensions,” Phys. Rev. D 58
1998
Earlier work this paper cites.

Similar

M. Henningson and K. Skenderis, “The Holographic Weyl anomaly,” JHEP 9807
1998
Cited alongside, same era.
V. Balasubramanian and P. Kraus, “A Stress tensor for Anti-de Sitter gravity,” Commun. Math. Phys. 208
1999
Cited alongside, same era.
S. de Haro, S. N. Solodukhin and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,” Commun. Math. Phys. 217
2001
Cited alongside, same era.
P. Mora, R. Olea, R. Troncoso and J. Zanelli, “Finite action principle for Chern-Simons AdS gravity,” JHEP 0406
2004
Cited alongside, same era.
O. Miskovic and R. Olea, “On boundary conditions in three-dimensional AdS gravity,” Phys. Lett. B 640
2006
Cited alongside, same era.