Perfect Fluids From High Power Sigma-Models

Slobodeanu, Radu

doi:10.1142/s0219887811005919

Cited by 13 publications

(21 citation statements)

References 41 publications

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“…Secondly, in the subspace of spherically symmetric solutions we may define a kind of EoS p = p(ρ), because both ρ and p are functions of r. We find numerically that a simple power law p = aρ b (21) reproduces this EoS with a high precision. Here, however, a and b are not universal constants.…”

Section: Bps Skyrmions Coupled To Gravitymentioning

confidence: 85%

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BPS Skyrmions as neutron stars

et al. 2015

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The BPS Skyrme model has been demonstrated already to provide a physically intriguing and quantitatively reliable description of nuclear matter. Indeed, the model has both the symmetries and the energy-momentum tensor of a perfect fluid, and thus represents a field theoretic realization of the "liquid droplet" model of nuclear matter. In addition, the classical soliton solutions together with some obvious corrections (spin-isospin quantization, Coulomb energy, proton-neutron mass difference) provide an accurate modeling of nuclear binding energies for heavier nuclei. These results lead to the rather natural proposal to try to describe also neutron stars by the BPS Skyrme model coupled to gravity. We find that the resulting self-gravitating BPS Skyrmions provide excellent results as well as some new perspectives for the description of bulk properties of neutron stars when the parameter values of the model are extracted from nuclear physics. Specifically, the maximum possible mass of a neutron star before black-hole formation sets in is a few solar masses, the precise value depending on the precise values of the model parameters, and the resulting neutron star radius is of the order of 10 km.Comment: 15 pages, 4 figures, Latex, 2 figures added, discussion extended and improved, references added; published versio

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Section: Bps Skyrmions Coupled To Gravitymentioning

confidence: 85%

“…(4)) (12) which is the energy-momentum tensor of a perfect fluid (the perfect-fluid property of the term L 6 alone, as well as its coupling to gravity, have already been discussed in [21]), (13) where the four-velocity u ρ , energy density ρ and pressure p are…”

Section: Bps Skyrmions Coupled To Gravitymentioning

confidence: 99%

BPS Skyrmions as neutron stars

et al. 2015

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“…ϕ * h = λ 2 g H ) critical point of the action functional M |dϕ| r vol g . The corresponding Euler-Lagrange equations are given precisely by (8), while (9) is an identity fulfilled by any horizontally conformal submersion (for more details see [31]). …”

Section: 2mentioning

confidence: 99%

“…[13,14]. In particular, it turns out [31] that a shear-free relativistic perfect fluid with linear equation of state (U, p = r− 3 3 ρ, ρ = λ r ) (r = 0) is determined by a (locally defined) horizontally conformal submersion which is a critical point of the action functional, i.e. an rharmonic morphism ( [21]) with 1-dimensional timelike fibres tangent to U and dilation λ.…”

Section: Introductionmentioning

confidence: 99%

Shear-free perfect fluids with linear equation of state

Slobodeanu¹

2014

Class. Quantum Grav.

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Abstract. We prove that shear-free perfect fluid solutions of Einstein's field equations must be either expansion-free or non-rotating (as conjectured by Ellis and Treciokas) for all linear equations of state p = wρ except for w ∈ − IntroductionFor the Einstein field equations with perfect fluid sources, an important insight into the structure of solutions can be obtained under two fairly general and observationally defensible assumptions: the equation of state for the pressure p and energy density ρ is barotropic (i.e. p = p(ρ)) and the flow is shear-free (i.e. fluid's velocity is a transversally conformal vector). While the former restriction is specific to isoentropic fluids, the latter is essentially a kinematic condition of isotropy. In cosmology, the shear-free condition expresses the isotropy of the relative recessional motion of the galaxies (but allows the red shift and the cosmic microwave background radiation to be anisotropic) and is a common feature of standard spacetimes, such as the FRW and Gödel models. In kinetic theory this characterizes [35] the velocity of collision-dominated gases with isotropic distribution function, under the Einstein-Boltzmann equations.The first result indicating the nature of solutions in this context was stated by Gödel ([12]): a shear-free dust fluid (i.e. p = 0, in particular a congruence of timelike geodesics) in a spatially homogeneous spacetime of type IX cannot both expand and rotate. This contrasts Newtonian cosmology where expanding and rotating (shear-free) solutions exist and can avoid the singularity formation [24]. Gödel's result was later proved [15] to remain true without symmetry assumptions and it can be seen as a timelike analogue of the Goldberg-Sachs theorem [18]. After proving that the same conclusion holds for radiation fluids (i.e. p = If the velocity vector field of a self-gravitating barotropic perfect fluid (p + ρ = 0 and p = p(ρ)) is shear-free, then either the expansion or the rotation of the fluid vanishes.2010 Mathematics Subject Classification. 53B30, 53C43, 53Z05, 83C55.

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“…(For an alternative characterization of E 4 and its stress tensor, which avoids using the lie group structure of the target space, see [21].) A Skyrme field ϕ : M → N is restricted E 4 -critical if and only if div S F is exact, and hence, if and only if div (ϕ * ω · ϕ * ω) is exact.…”

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confidence: 99%

Near BPS skyrmions and restricted harmonic maps

Speight

2015

Journal of Geometry and Physics

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Motivated by a class of near BPS Skyrme models introduced by Adam, Sánchez-Guillén and Wereszczyński, the following variant of the harmonic map problem is introduced: a map ϕ : (M, g) → (N, h) between Riemannian manifolds is restricted harmonic if it locally extremizes E 2 on its SDiff(M ) orbit, where SDiff(M ) denotes the group of volume preserving diffeomorphisms of (M, g), and E 2 denotes the Dirichlet energy. It is conjectured that near BPS skyrmions tend to restricted harmonic maps in the BPS limit. It is shown that ϕ is restricted harmonic if and only if ϕ * h has exact divergence, and a linear stability theory of restricted harmonic maps is developed, from which it follows that all weakly conformal maps are stable restricted harmonic. Examples of restricted harmonic maps in every degree class R 3 → SU (2) and R 2 → S 2 are constructed. It is shown that the axially symmetric BPS skyrmions on which all previous analytic studies of near BPS Skyrme models have been based, are not restricted harmonic, casting doubt on the phenomenological predictions of such studies. The problem of minimizing E 2 for ϕ : R k → N over all linear volume preserving diffeomorphisms is solved explicitly, and a deformed axially symmetric family of Skyrme fields constructed which are candidates for approximate near BPS skyrmions at low baryon number. The notion of restricted harmonicity is generalized to restricted F -criticality where F is any functional on maps (M, g) → (N, h) which is, in a precise sense, geometrically natural. The case where F is a linear combination of E 2 and E 4 , the usual Skyrme term, is studied in detail, and it is shown that inverse stereographic projection R 3 → S 3 ≡ SU (2) is stable restricted F -critical for every such F .

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Perfect Fluids From High Power Sigma-Models

Abstract: Certain critical points of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyze from a differential geometric perspective this correspondence extended to general barotropic fluids.

Cited by 13 publications

References 41 publications

BPS Skyrmions as neutron stars

BPS Skyrmions as neutron stars

Shear-free perfect fluids with linear equation of state

Near BPS skyrmions and restricted harmonic maps

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