Robin Gravity

Krishnan, Chethan; Maheshwari, Shubham; Subramanian, P. N. Bala

doi:10.1088/1742-6596/883/1/012011

Cited by 26 publications

(27 citation statements)

References 6 publications

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“…Comment added: After this preprint appeared on the arXiv, more work has been done developing this set of ideas further. These include [19] which studies a semi-classical path integral with Neumann boundary conditions and uses it to reproduce the thermodynamics of horizons, [14] that applies this boundary term in the context of the AdS/CFT correspondence, and [20] which does a slight generalization of the Neumann boundary term to allow Robin boundary conditions for general relativity. A paper [21] that discusses the conditions under which Neumann boundary conditions lead to normalizable fluctuations in AdS and explores its connection to conformal gravity on the boundary, is about to appear.…”

Section: Discussionmentioning

confidence: 99%

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A Neumann boundary term for gravity

2017

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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 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. In four dimensions the boundary term vanishes, giving a natural Neumann interpretation to the standard Einstein-Hilbert action without boundary terms. We argue that in light of AdS/CFT, ours is a natural approach for defining a "microcanonical" path integral for gravity in the spirit of the (pre-AdS/CFT) work of Brown and

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Section: Discussionmentioning

confidence: 99%

“…Holding the normal derivative fixed is not a covariant notion in a generic spacetime, whereas our approach is. Our approach can also be understood in terms of a Legendre transform as we will explore in various contexts in [19,14,20,21].…”

Section: Introductionmentioning

confidence: 99%

A Neumann boundary term for gravity

2017

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“…[21]. A covariant implementation of the initial Robin condition requires an extra boundary term [47], which was also discussed in Ref. [9].…”

Section: Implications For Cosmologymentioning

confidence: 97%

Lessons for quantum cosmology from anti–de Sitter black holes

2020

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Gravitational physics is arguably better understood in the presence of a negative cosmological constant than a positive one, yet there exist strong technical similarities between the two settings. These similarities can be exploited to enhance our understanding of the more speculative realm of quantum cosmology, building on robust results regarding anti-de Sitter black holes describing the thermodynamics of holographic quantum field theories. To this end, we study four-dimensional gravitational path integrals in the presence of a negative cosmological constant and with minisuperspace metrics. We put a special emphasis on boundary conditions and integration contours. The Hawking-Page transition is recovered, and we find that below the minimum temperature required for the existence of black holes the corresponding saddle points become complex. When the asymptotic anti-de Sitter space is cut off at a finite distance, additional saddle points contribute to the partition function, albeit in a very suppressed manner. These findings have direct consequences for the no-boundary proposal in cosmology, because the anti-de Sitter calculation can be brought into one-to-one correspondence with a path integral for de Sitter space with Neumann conditions imposed at the nucleation of the Universe. Our results lend support to recent implementations of the no-boundary proposal focusing on momentum conditions at the "big bang."

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“…It was shown in [16] that the Robin problem for gravity in 4 dimensions is obtained from the boundary term…”

Section: The Final Hubble Rate As a Boundary Conditionmentioning

confidence: 99%

No-boundary prescriptions in Lorentzian quantum cosmology

2019

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We analyse the impact of various boundary conditions on the (minisuperspace) Lorentzian gravitational path integral. In particular we assess the implications for the Hartle-Hawking no-boundary wavefunction. It was shown recently that when this proposal is defined as a sum over compact metrics, problems arise with the stability of fluctuations. These difficulties can be overcome by an especially simple implementation of the no-boundary idea: namely to take the Einstein-Hilbert action at face value while adding no boundary term. This prescription simultaneously imposes an initial Neumann boundary condition for the scale factor of the universe and, for a Bianchi IX spacetime, Dirichlet conditions for the anisotropies. Another way to implement the no-boundary wavefunction is to use Robin boundary conditions. A sub-class of Robin conditions allows one to specify the Hubble rate on the boundary hypersurface, and we highlight the surprising aspect that specifying the final Hubble rate (rather than the final size of the universe) significantly alters the off-shell structure of the path integral. The conclusion of our investigations is that all current working examples of the no-boundary wavefunction force one to abandon the notion of a sum over compact and regular geometries, and point to the importance of an initial Euclidean momentum.

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Robin Gravity

Cited by 26 publications

References 6 publications

A Neumann boundary term for gravity

A Neumann boundary term for gravity

Lessons for quantum cosmology from anti–de Sitter black holes

No-boundary prescriptions in Lorentzian quantum cosmology

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