Boundary terms for causal sets

Buck, Michel; Dowker, Fay; Jubb, Ian; Surya, Sumati

doi:10.1088/0264-9381/32/20/205004

Cited by 25 publications

(72 citation statements)

References 21 publications

(54 reference statements)

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“…Our methods of probing ACD can be applied to causal set theory. For example, ACD is used to test the boundary term contribution in the causal set action [9]. It turns out that in Minkowski spacetime, the BDG causal set action [10] evaluated in ACD contributes an amount proportional to the edge area.…”

Section: Discussionmentioning

confidence: 99%

“…The GCD is the one used by Feynman to interpret Einstein equation and recently used by Jacobson to derive Einstein equation from entanglement equilibrium [2,7]. The ACD is perhaps the most standard causal diamond and it is a natural object to consider in causal set theory [3][4][5][9][10][11]. Its geometric properties are investigated in different contexts by Gibbons and Solodukhin [1,30,31].…”

Section: U a < L A T E X I T S H A 1 _ B A S E 6 4 = " E P O L S R X mentioning

confidence: 99%

“…The causal diamond setup also plays an important role in the study of quantum gravity. It has been used in causal set theory [3][4][5][9][10][11], holography [12][13][14] and cosmology [15,16]. In most applications, however, the geometry of the small causal diamond is resolved at the order of Ricci curvature.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, the standard notion of causal diamond usually refers to the Alexandrov interval. ACD already receives a lot of attention in earlier works [1,3,4,9]. However, none of the investigations on ACD extends to higher order of perturbations, in particular, the leading order in vacuum.…”

Section: Introductionmentioning

confidence: 99%

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Geometry of small causal diamonds

Wang

2019

Phys. Rev. D

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The geometry of small causal diamonds is systematically studied, based on three distinct constructions that are common in the literature, namely the geodesic ball, the Alexandrov interval and the lightcone cut. The causal diamond geometry is calculated perturbatively using Riemann normal coordinate expansion up to the leading order in both vacuum and non-vacuum. We provide a collection of results including the area of the codimension-two edge, the maximal hypersurface volume and their isoperimetric ratio for each construction, which will be useful for any applications involving the quantitative properties of causal diamonds. In particular, by solving the dynamical equations of the expansion and the shear on the lightcone, we find that intriguingly only the lightcone cut construction yields an area deficit proportional to the Bel-Robinson superenergy density W in four dimensional spacetime, but such a direct connection fails to hold in any other dimension. We also compute the volume of the Alexandrov interval causal diamond in vacuum, which we believe is important but missing from the literatures. Our work complements and extends the earlier works on the causal diamond geometry by Gibbons and Solodukhin [1], Jacobson, Senovilla and Speranza [2] and others [3][4][5]. Some potential applications of our results in mathematical general relativity and quantum gravity are discussed.

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Section: Discussionmentioning

confidence: 99%

Section: U a < L A T E X I T S H A 1 _ B A S E 6 4 = " E P O L S R X mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Geometry of small causal diamonds

Wang

2019

Phys. Rev. D

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“…by counting something on the causal set. Following the procedure given in [14,15], we can get close to extracting the first order correction using the following causal set random variable:…”

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confidence: 99%

Horizon molecules in causal set theory

et al. 2019

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We propose a new definition of "horizon molecules" in Causal Set Theory following pioneering work by Dou and Sorkin. The new concept applies for any causal horizon and its intersection with any spacelike hypersurface. In the continuum limit, as the discreteness scale tends to zero, the leading behaviour of the expected number of horizon molecules is shown to be the area of the horizon in discreteness units, up to a dimension dependent factor of order one. We also determine the first order corrections to the continuum value, and show how such corrections can be exploited to obtain further geometrical information about the horizon and the spacelike hypersurface from the causal set. 1 arXiv:1909.08620v1 [gr-qc] 18 Sep 2019 7 Entropy 31 Appendices 32 A I − (M − + ) ∩ M − − = I − (J ) 32 B Determining the set of independent scalars 32 8 References 36 a (d) H to get an estimate for the horizon area of a causal set. In the continuum limit the expectation value of the associated random variable was the horizon area, which is proportional to the first term in the small l expansion of J dV J I (d) 1 (q; l, τ ) = a (d) n J dV J + l J dV J b

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The Causal Set Approach to the Problem of Quantum Gravity

Dowker,

Surya

2024

Handbook of Quantum Gravity

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Boundary terms for causal sets

Cited by 25 publications

References 21 publications

Geometry of small causal diamonds

Geometry of small causal diamonds

Horizon molecules in causal set theory

The Causal Set Approach to the Problem of Quantum Gravity

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