Geometry of small causal diamonds

Wang, Jinzhao

doi:10.1103/physrevd.100.064020

Cited by 14 publications

(14 citation statements)

References 33 publications

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“…However, the vacuum limit (12) is not proportional to the BR superenergy Q in any dimensions n > 4. Note that the area of the lightcone cut S l itself has a deficit due to curvature that is proportional to Q 0 in four dimensions [15], but it is not proportional to Q in higher dimensions [31]. Here, we see the behaviour of the QLM is in line with the area deficit.…”

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confidence: 53%

Local gravitational energy in higher dimensions

Wang

2019

Preprint

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In general relativity, the local gravitational energy is best characterised by the quasilocal mass. The small sphere limit of quasilocal mass provides us the most local notion of gravitational energy. In four dimensions, the limits were shown be the stress tensor in non-vacuum and the Bel-Robinson tensor in vacuum. We study the local gravitational energy in higher dimensions through the lens of the small sphere limits of various quasilocal mass proposals which can be appropriately generalised beyond four dimensions, and report a new quantity W which potentially characterises the local gravitational energy content in vacuum. We find that the limits at presence of matter yield the stress tensor as expected, but the vacuum limits are not proportional to the Bel-Robinson superenergy Q in dimensions n > 4. The result defies the role of the Bel-Robinson superenergy as characterising the gravitational energy in higher dimensions, albeit the fact that it uniquely generalises. More surprisingly, W replace the Bel-Robinson superenergy Q in all three quasilocal mass proposals that we study. However, W cannot be directly interpreted as a local gravitational energy because of its non-positivity. The physical meaning of W awaits more evidence from investigating other quasilocal masses in higher dimensions.Introduction.-The gravitational field itself carries energy, but it is tricky to locally describe it in general relativity. It is well know that the equivalence principle forbids a covariant stress tensor characterising the energy content of the gravitational field [1]. Nevertheless, there is no obstruction in giving nonlocal prescriptions and the quasilocal mass (QLM) is such an attempt. Over the past half-century, QLM is an ongoing research subject studied by both physicists and mathematicians [2][3][4][5][6][7][8][9][10][11][12]. Nevertheless, QLM is rarely studied in dimensions beyond four.

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confidence: 53%

Local gravitational energy in higher dimensions

Wang

2019

Preprint

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“…The presence of inhomogeneities is reflected in the appearance of shear terms in (21) and (24). It is stressed again, that, due to the conservation law (25), the so generated 1-parameter family of density and equationof-state parameters (ρ(z), w(z)) does not describe the evolution of a FLRW-fluid with redshift in general, but rather reinterprets the given inhomogeneous geometry with a RW-bias. Thirdly, the monotonicity of the Hawking energy along the lightcone is applied to FLRW-spacetimes to derive bounds (28) & (29) on w(z) and ρ(z), which are in particular relevant for redshifts beyond the turnaround of the area distance.…”

Section: Discussionmentioning

confidence: 99%

“…The differential equation ( 18) links the area to the matter content in an exact way, in contrast to the expansions of the area about Minkowski space, for instance about the lightcone vertex or within the causal diamond construction as discussed in [24,25]. However, these expansions are recovered from (18) for a general affine parameter λ by solving it in a series expansion in the respective regime.…”

Section: A Link Between Area and Matter Contentmentioning

confidence: 99%

Applications of the Hawking Energy in Inhomogeneous Cosmology

Stock

2020

Preprint

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The past lightcone of an observer in a cosmological spacetime is the unique geometric structure directly linked to observations. After general properties of the Hawking energy along slices of the past lightcone were studied in [1], the present work continues along this path by providing explicit cosmological applications of the Hawking energy associated with a lightcone. Firstly, it is shown that amongst all two-dimensional non-trapped spheres with equal area and average matter density, a shear-free matter distribution maximizes the Hawking energy for sufficiently high densities. Secondly, a Robertson-Walker-reference slice is constructed for every lightcone slice based on area and energy. Thirdly, the implications of the monotonicity of the energy down the lightcone are explored, arriving at two new bounds on the cosmic fluid's density and equation-of-state parameter.

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“…1 for a deeper analysis of GLCDs, see, e.g., [29][30][31]. 2 We remember that this interpretation, as are all interpretations, is not free of controversy.…”

Section: Conflicts Of Interestmentioning

confidence: 95%

Quantum Gravity Phenomenology from the Thermodynamics of Spacetime

Alonso-Serrano

Liška

2022

Universe

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This work is based on the formalism developed in the study of the thermodynamics of spacetime used to derive Einstein equations from the proportionality of entropy within an area. When low-energy quantum gravity effects are considered, an extra logarithmic term in the area is added to the entropy expression. Here, we present the derivation of the quantum modified gravitational dynamics from this modified entropy expression and discuss its main features. Furthermore, we outline the application of the modified dynamics to cosmology, suggesting the replacement of the Big Bang singularity with a regular bounce.

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Geometry of small causal diamonds

Cited by 14 publications

References 33 publications

Local gravitational energy in higher dimensions

Local gravitational energy in higher dimensions

Applications of the Hawking Energy in Inhomogeneous Cosmology

Quantum Gravity Phenomenology from the Thermodynamics of Spacetime

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