Outer entropy equals Bartnik-Bray inner mass and the gravitational ant conjecture

Wang, Jinzhao

doi:10.1103/physrevd.102.066009

Cited by 4 publications

(3 citation statements)

References 88 publications

(232 reference statements)

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“…Recently, Wang [31] noted that the concept of outer entropy due to Engelhardt and Wall [10] in the context of the AdS/CFT correspondence is essentially the same concept as Bray's inner Bartnik mass [2]. The former was formulated from the perspective of the AdS/CFT correspondence for asymptotically hyperbolic manifolds while the latter was formulated from a purely geometric perspective for asymptotically flat manifolds.…”

Section: Engelhardt-wall Outer Entropy and Bray's Inner Bartnik Massmentioning

confidence: 99%

Fill-ins with scalar curvature lower bounds and applications to positive mass theorems

McCormick

2024

Ann Glob Anal Geom

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Given a constant C and a smooth closed $$(n-1)$$ ( n - 1 ) -dimensional Riemannian manifold $$(\Sigma , g)$$ ( Σ , g ) equipped with a positive function H, a natural question to ask is whether this manifold can be realised as the boundary of a smooth n-dimensional Riemannian manifold with scalar curvature bounded below by C and boundary mean curvature H. That is, does there exist a fill-in of $$(\Sigma ,g,H)$$ ( Σ , g , H ) with scalar curvature bounded below by C? We use variations of an argument due to Miao and the author (Int Math Res Not 7:2019, 2019) to explicitly construct fill-ins with different scalar curvature lower bounds, where we permit the fill-in to contain another boundary component provided it is a minimal surface. Our main focus is to illustrate the applications of such fill-ins to geometric inequalities in the context of general relativity. By filling in a manifold beyond a boundary, one is able to obtain lower bounds on the mass in terms of the boundary geometry through positive mass theorems and Penrose inequalities. We consider fill-ins with both positive and negative scalar curvature lower bounds, which from the perspective of general relativity corresponds to the sign of the cosmological constant, as well as a fill-in suitable for the inclusion of electric charge.

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Section: Engelhardt-wall Outer Entropy and Bray's Inner Bartnik Massmentioning

confidence: 99%

Fill-ins with scalar curvature lower bounds and applications to positive mass theorems

McCormick

2024

Ann Glob Anal Geom

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“…[28], S (outer) [χ ] can be used to define a quasilocal mass M (outer) [χ ] by setting the outer entropy equal to the Bekenstein-Hawking entropy of a black hole of mass M (outer) [χ ] (see related discussion of the Bartnik-Bray inner mass in Refs. [30,31]). That is, M (outer) [χ ] is the mass of the largest black hole that can be fit inside χ while keeping the external geometry fixed.…”

Section: Outer Entropymentioning

confidence: 99%

Exploration of a singular fluid spacetime

Remmen

2021

Gen Relativ Gravit

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We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter $$w=p/\rho $$ w = p / ρ , there exist static, spherically-symmetric solutions with density profile $$\propto 1/r^2$$ ∝ 1 / r 2 , with the constant of proportionality fixed to be a special function of w. Like black holes, singular isothermal spheres possess a fixed mass-to-radius ratio independent of size, but no horizon cloaking the curvature singularity at $$r=0$$ r = 0 . For $$w=1$$ w = 1 , these solutions can be constructed from a homogeneous dilaton background, where the metric spontaneously breaks spatial homogeneity. We study the perturbative structure of these solutions, finding the radial modes and tidal Love numbers, and also find interesting properties in the geodesic structure of this geometry. Finally, connections are discussed between these geometries and dark matter profiles, the double copy, and holographic entropy, as well as how the swampland distance conjecture can obscure the naked singularity.

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“…(see related discussion of the Bartnik-Bray inner mass in Refs. [30,31]). That is, M (outer) [χ] is the mass of the largest black hole that can be fit inside χ while keeping the external geometry fixed.…”

Section: Outer Entropymentioning

confidence: 99%

Exploration of a Singular Fluid Spacetime

Remmen

2021

Preprint

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We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter w = p/ρ, there exist static, spherically-symmetric solutions with density profile ∝ 1/r 2 , with the constant of proportionality fixed to be a special function of w. Like black holes, singular isothermal spheres possess a fixed mass-to-radius ratio independent of size, but no horizon cloaking the curvature singularity at r = 0. For w = 1, these solutions can be constructed from a homogeneous dilaton background, where the metric spontaneously breaks spatial homogeneity. We study the perturbative structure of these solutions, finding the radial modes and tidal Love numbers, and also find interesting properties in the geodesic structure of this geometry. Finally, connections are discussed between these geometries and dark matter profiles, the double copy, and holographic entropy, as well as how the swampland distance conjecture can obscure the naked singularity.

show abstract

Outer entropy equals Bartnik-Bray inner mass and the gravitational ant conjecture

Cited by 4 publications

References 88 publications

Fill-ins with scalar curvature lower bounds and applications to positive mass theorems

Fill-ins with scalar curvature lower bounds and applications to positive mass theorems

Exploration of a singular fluid spacetime

Exploration of a Singular Fluid Spacetime

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