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

Burikham, Piyabut; Cheamsawat, Krai; Harkó, Tiberiu; Lake, Matthew J.

doi:10.1140/epjc/s10052-015-3673-5

Cited by 25 publications

(74 citation statements)

References 70 publications

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“…Hence, it is clear that, if the fundamental quanta of space-time are fermionic, universal expansion can also be viewed as a result of their continuous pair-production. Such a view is consistent with the model of particulate dark energy proposed in [48][49][50][51][52].…”

supporting

confidence: 90%

“…both hold, independently of Eqs. (48) and (51). We denote the position and momentum uncertainties by ∆ g x ′i = σ i g and ∆ g p ′ j =σ gj , respectively, when |g| 2 is chosen to be a Gaussian function.…”

Section: A Basicsmentioning

confidence: 99%

“…In addition, using these values, Eqs. (48), (51) and (56) may be Taylor expanded to first order to yield the GUP, EUP and EGUP, respectively, expressed in terms of ∆ ψ x ′i and ∆ ψ p ′ j . As discussed in the Introduction, the GUP implements a minimum length scale of the order of the Planck length ∼ l Pl , but no minimum momentum scale, whereas the EUP implements a minimum momentum of the order of the de Sitter momentum ∼ m dS c, but no minimum length.…”

Section: A Basicsmentioning

confidence: 99%

“…(115) takes a form analogous to Eqs. (48) and (51), but with additional cross terms, i.e., terms that are generated by operators that do not act on one subspace of the composite state |Ψ = |ψ ⊗ |g (88) alone.…”

Section: Generalised Algebra and Gursmentioning

confidence: 99%

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Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry

2020

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We derive generalised uncertainty relations (GURs) for orbital angular momentum and spin in the recently proposed smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum, and recovers both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP), previously proposed in the quantum gravity literature, within a single formalism. In this paper, we investigate the consequences of these results for particles with extrinsic and intrinsic angular momentum, and obtain generalisations of the canonical so(3) and su(2) algebras. We find that, although SO(3) symmetry is preserved on three-dimensional slices of an enlarged phase space, corresponding to a superposition of background geometries, individual subcomponents of the generalised generators obey nontrivial subalgebras. These give rise to GURs for orbital angular momentum while leaving the canonical commutation relations intact except for a simple rescaling, → + β. The value of the new parameter, β ≃ × 10 −61 , is determined by the ratio of the dark energy density to the Planck density and its existence is required by the presence of both minimum length and momentum uncertainties. Here, we assume the former to be of the order of the Planck length and the latter to be of the order of the de Sitter momentum ∼ √ Λ, where Λ is the cosmological constant, which is consistent with the existence of a finite cosmological horizon. In the smeared-space model, and β are interpreted as the quantisation scales for matter and geometry, respectively, and a quantum state vector is associated with the spatial background. We show that this also gives rise to a rescaled Lie algebra for generalised spin operators, together with associated subalgebras that are analogous to those for orbital angular momentum. Remarkably, consistency of the algebraic structure requires the quantum state associated with the background space to be fermionic. However, this is no way contradicts the standard result that the graviton is expected to be a spin-2 boson. (We explain why, at length, in the text.) Finally, the modified spin algebra leads to GURs for spin measurements. The potential implications of these results for cosmology and high-energy physics, and for the description of spin and angular momentum in relativistic theories of quantum gravity, are briefly discussed. Contents

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confidence: 90%

Section: A Basicsmentioning

confidence: 99%

Section: A Basicsmentioning

confidence: 99%

Section: Generalised Algebra and Gursmentioning

confidence: 99%

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Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry

2020

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“…Note that in the field of static spherically symmetric fluid spheres, an important bound on the massradius ratio for stable general relativistic stars was obtained in Buchdahl (1959), given by 2GM/c 2 R ≤ 8/9, where M is the mass of the star as measured by its external gravitational field, and R is the boundary radius of the star. The Buchdahl bound was generalized to include the presence of the cosmological constant as well as higher dimensions and electromagnetic fields in (Mak et al 2000;Burikham et al 2015Burikham et al , 2016a.…”

Section: Introductionmentioning

confidence: 99%

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state

Harkó

Mak

2016

Astrophys Space Sci

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Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state T. Harko 1,2 • M. K. Mak 3Abstract Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n = 1, and for the indexes n = 1/2 and n = 1/5, respectively. The case of n = 3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven

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Isotropic uncharged model with compactness and stable configurations

Prasad

Kumar

2021

Arab. J. Math.

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In this study we have obtained a new exact model for relativistic stellar object by solving Einstein’s field equation with help of Buchdahl metric. The model is capable to represent some known compact stars like Her X-1,4U 1538-52 and SAX J1808.4-3658. The model satisfies the regularity, casuality, stability and energy conditions. Using the Tolman–Oppenheimer–Volkoff equations, we explore the hydrostatic equilibrium for an uncharged case. We have also compared these conditions with graphical representations that provide strong evidences for more realistic and viable models.

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

Cited by 25 publications

References 70 publications

Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry

Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state

Isotropic uncharged model with compactness and stable configurations

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