Buchdahl limit for d-dimensional spherical solutions with a cosmological constant

The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity. These results follow rigorously from the Buchdahl inequalities in four-dimensional de Sitter space. In this work, we obtain the generalized Buchdahl inequalities in arbitrary space-time dimensions with = 0 and consider both the de Sitter and the anti-de Sitter cases. The dependence on D, the number of space-time dimensions, of the minimum and maximum masses for stable spherical objects is explicitly obtained. The analysis is then extended to the case of dark energy satisfying an arbitrary linear barotropic equation of state. The Jeans instability of barotropic dark energy is also investigated, for arbitrary D, in the framework of a simple Newtonian model with and without viscous dissipation, and we determine the dispersion relation describing the dark energy-matter condensation process, along with estimates of the corresponding Jeans mass (and radius). Finally, the quantum mechanical implications of the mass limits are investigated, and we show that the existence of a minimum mass scale naturally leads to a model in which dark energy is composed of a 'sea' of quantum particles, each with an effective mass proportional to 1/4 .

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“…(9) and (13) in Eq. (7), we obtain the TOV equation in arbitrary space-time dimensions, in the presence of a cosmological constant, as…”

Section: Introductionmentioning

confidence: 99%

The minimum mass of a spherically symmetric object in D-dimensions, and its implications for the mass hierarchy problem

et al. 2015

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“…In [18] this is generalised to include a non-zero cosmological constant where it is found (rewritten into our notation)…”

Section: Matter Models and Previous Resultsmentioning

confidence: 99%

“…The higher dimensional Buchdahl inequality for a perfect fluid was derived in [17], and is given byM 6) whereM is related to the mass of the fluid. In [18] this bound is generalised to include a non-zero cosmological constant, generalising the inequality found in [7]. An inequality for d-dimensional charged spheres was also derived in [13].…”

Section: Introductionmentioning

confidence: 91%

“…In four dimensions this corresponds to the Newtonian mass as no metric terms are included. If the source is compact, then the exterior solution is found by setting the energy density and pressure to zero in the Einstein field equations (5.6)-(5.8) and is given by d-dimensional Reissner-Nordström-de Sitter solution; first derived in [19,20] 18) where Λ is the cosmological constant. The constants µ and Θ are related to the total mass and charge; M and Q respectively, by…”

Section: Equations For D-dimensional Anisotropic Fluid Spherementioning

confidence: 99%

“…Now, since the variables lie in the set U 1 , we have that 18) and so w 2 is decreasing whenever v 2 ≥ 0. Thus…”

Section: Dominant Energy In the Tangential Directionmentioning

confidence: 99%

See 2 more Smart Citations

Buchdahl type inequalities in d dimensions

Wright¹

2015

Class. Quantum Grav.

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Spherically symmetric anisotropic static compact solutions to the Einstein equations in dimension d ≥ 4 are considered. Various matter models are examined and upper bounds on the ratio of the gravitational mass to the radius in these different models are obtained, and saturation of these bounds are proven. Bounds are also generalised in the presence of a non-zero charge and a positive cosmological constant. These bounds are then used to find the maximum of the gravitational redshift at the surface of the object.

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Buchdahl’s inequality in five dimensional Gauss–Bonnet gravity

Wright¹

2016

Gen Relativ Gravit

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The Buchdahl limit for static spherically symmetric isotropic stars is generalised to the case of five dimensional Gauss-Bonnet gravity. Our result depends on the sign of the Gauss-Bonnet coupling constant α. When α > 0, we find, unlike in general relativity, that the bound is dependent on the stellar structure, in particular the central energy density and we find that stable stellar structures can exist arbitrarily close to the black hole horizon. Thus stable stars can exist with extra mass in this theory compared to five dimensional general relativity. For α < 0 it is found that the Buchdahl bound is more restrictive than the general relativistic case.

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Buchdahl limit for d-dimensional spherical solutions with a cosmological constant

Cited by 41 publications

References 15 publications

The minimum mass of a spherically symmetric object in D-dimensions, and its implications for the mass hierarchy problem

The minimum mass of a spherically symmetric object in D-dimensions, and its implications for the mass hierarchy problem

Buchdahl type inequalities in d dimensions

Buchdahl’s inequality in five dimensional Gauss–Bonnet gravity

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