On the continuum limit of Benincasa–Dowker–Glaser causal set action

Machet, Ludovico; Wang, Jinzhao

doi:10.1088/1361-6382/abc274

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…It states the continuum limit of the BD action, evaluated on a causal set generated from sprinkling on a compact region with null boundaries, is proportional to the Einstein-Hilbert action plus a joint term proportional to its co-dimension 2 volume. This conjecture is recently verified for causal diamonds in perturbative regimes [18,19]. Here we consider the region X with more complex joints than the simple lightcone-light-cone intersection.…”

Section: S[c] = S[x] + S[y] (43)mentioning

confidence: 54%

On the horizon entropy of a causal set

Machet¹,

Wang²

2021

Class. Quantum Grav.

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We discuss how to define a kinematical horizon entropy on a causal set. We extend a recent definition of horizon molecules to a setting with a null hypersurface crossing the horizon. We argue that, as opposed to the spacelike case, this extension fails to yield an entropy local to the hypersurface-horizon intersection in the continuum limit when the causal set approximates a curved spacetime. We then investigate the entropy defined via the spacetime mutual information between two regions of a causal diamond truncated by a causal horizon, and find it does limit to the area of the intersection.

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Section: S[c] = S[x] + S[y] (43)mentioning

confidence: 54%

On the horizon entropy of a causal set

Machet¹,

Wang²

2021

Class. Quantum Grav.

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Section: Entropy From Smimentioning

confidence: 56%

On the horizon entropy of a causal set

Machet,

Wang

2020

Preprint

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We discuss how to define a kinematical horizon entropy on a causal set. We extend a recent definition of horizon molecules to a setting with a null hypersurface crossing the horizon. We argue that, as opposed to the spacelike case, this extension fails to yield an entropy local to the hypersurface-horizon intersection in the continuum limit when the causal set approximates a curved spacetime. We then investigate the entropy defined via the Spacetime Mutual Information between two regions of a causal diamond truncated by a causal horizon, and find it does limit to the area of the intersection.

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“…I thank Ludovico Machet and Jinzhao Wang for sharing with me their calculations of the mean of the discrete random action of Riemann normal neighbourhoods which stimulated this work. The results on causal intervals are a special case of their general result on Riemann normal neighbourhoods in all dimensions [24]. We have used different methods both of which can be useful in future work and have agreed to publish both sets of calculations.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Boundary contributions in the causal set action

Dowker

2021

Class. Quantum Grav.

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Evidence is provided for a conjecture that, in the continuum limit, the mean of the causal set action of a causal set sprinkled into a globally hyperbolic Lorentzian spacetime, M, of finite volume equals the Einstein Hilbert action of M plus the volume of the co-dimension 2 intersection of the future boundary with the past boundary. We give the heuristic argument for this conjecture and analyse some examples in 2 dimensions and one example in 4 dimensions.

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On the continuum limit of Benincasa–Dowker–Glaser causal set action

Cited by 7 publications

References 12 publications

On the horizon entropy of a causal set

On the horizon entropy of a causal set

On the horizon entropy of a causal set

Boundary contributions in the causal set action

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