Slowly rotating homogeneous stars and the Heun equation

Petroff, David

doi:10.1088/0264-9381/24/5/003

Cited by 7 publications

(3 citation statements)

References 24 publications

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“…Such differential equations are known in the mathematics literature as Heun's equations [36,60]. They arise in a variety of physical contexts, for instance as eigenvalue equations in the background of the Kerr-Newman-de Sitter black hole [61], of large AdS black holes in five dimensions [62], of the toric Sasaki-Einstein manifolds L a,b,c [63], or in the study of RG flows between 2D CFTs [64] and of slowly-rotating homogeneous stars [65] (for more physics applications see the references in [36,66]). Heun's equation is the next in the series of canonical Fuchsian equations on the Riemann sphere, after the hypergeometric equation which has three regular singular points.…”

Section: Heun's Equationmentioning

confidence: 99%

Spin-2 spectrum of defect theories

Bachas

Estes

2011

J. High Energ. Phys.

178

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We study spin-2 excitations in the background of the recently-discovered type-IIB solutions of D'Hoker et al. These are holographically-dual to defect conformal field theories, and they are also of interest in the context of the Karch-Randall proposal for a string-theory embedding of localized gravity. We first generalize an argument by Csaki et al to show that for any solution with four-dimensional anti-de Sitter, Poincaré or de Sitter invariance the spin-2 excitations obey the massless scalar wave equation in ten dimensions. For the interface solutions at hand this reduces to a Laplace-Beltrami equation on a Riemann surface with disk topology, and in the simplest case of the supersymmetric Janus solution it further reduces to an ordinary differential equation known as Heun's equation. We solve this equation numerically, and exhibit the spectrum as a function of the dilaton-jump parameter ∆φ. In the limit of large ∆φ a nearly-flat linear-dilaton dimension grows large, and the Janus geometry becomes effectively five-dimensional. We also discuss the difficulties of localizing four-dimensional gravity in the more general backgrounds with NS5-brane or D5-brane charge, which will be analyzed in detail in a companion paper.

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Section: Heun's Equationmentioning

confidence: 99%

Spin-2 spectrum of defect theories

Bachas

Estes

2011

J. High Energ. Phys.

178

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“…The HT formalism has been applied to various tabulated EOSs for NSs, since their pioneering work [38] and more recently by [39]. In the context of solutions to Einstein's equations for compact objects, the HT perturbative method has been applied to uniform density configurations [41][42][43] and polytropic fluid spheres [44,45]. Slowly rotating T-VII models, to the first order in Ω, were considered by [23,26].…”

Section: Introductionmentioning

confidence: 99%

Slowly rotating Tolman VII solution

Posada

Stuchlík

2023

Class. Quantum Grav.

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We present a model of a slowly rotating Tolman VII (T-VII) fluid sphere, at second order in the angular velocity. The structure of this configuration is obtained by integrating numerically the Hartle-Thorne equations for slowly rotating relativistic masses. We consider a sequence of models where we vary the parameter R/Rs, where R is the radius of the configuration and Rs is its Schwarzschild radius, representing an adiabatic and quasi-stationary contraction by progressively reducing the radius while keeping the angular momentum and gravitational mass constant. We determined the moment of inertia I, mass quadrupole moment Q, and the ellipticity ε, for various configurations. Similarly to previous results for Maclaurin and polytropic spheroids, in slow rotation, we found a change in the behaviour of the ellipticity when R/Rs reaches a certain critical value. Based on our analysis for the T-VII solution, we found variations of O(10)% in the I-C and Q-C relations, and O(1)% variation in the I-Q relation, with respect to the universal fittings proposed for realistic neutron stars. Our results suggest that the T-VII solution can be considered a rather good approximation for the description of the interior of neutron stars.

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“…One possibility includes improving the analytic results presented here. For example, one could try a different expansion in ξ or C for the Love-C relation, such as that in [56] for constant density stars. One could then try to construct a more accurate inversion of the relation, so that an accurate, analytic I-Love relation can be derived.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Analytic I-Love-C relations for realistic neutron stars

Jiang,

Yagi

2020

Preprint

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Recent observations of neutron stars with radio, X-rays and gravitational waves have begun to constrain the equation of state for nuclear matter beyond the nuclear saturation density. To one's surprise, there exist approximate universal relations connecting certain bulk properties of neutron stars that are insensitive to the underlying equation of state and having important applications on probing fundamental physics including nuclear and gravitational physics. To date, analytic works on universal relations for realistic neutron stars are lacking, which may lead to a better understanding of the origin of the universality. Here, we focus on the universal relations between the compactness (C), the moment of inertia (I), and the tidal deformability (related to the Love number), and derive analytic, approximate I-Love-C relations. To achieve this, we construct slowlyrotating/tidally-deformed neutron star solutions analytically starting from an extended Tolman VII model that accurately describes non-rotating realistic neutron stars, which allows us to extract the moment of inertia and the tidal deformability on top of the compactness. We solve the field equations analytically by expanding them about the Newtonian limit and keeping up to 6th order in the stellar compactness. Based on these analytic solutions, we can mathematically demonstrate the O(10%) equation-of-state variation in the I-C and Love-C relations and the O(1%) variation in the I-Love relation that have previously been found numerically. Our new analytic relations agree more accurately with numerical results for realistic neutron stars (especially the I-C and Love-C ones) than the analytic relations for constant density stars derived in previous work. Our results provide a mathematical explanation of the amount of universality for realistic neutron stars in the above universal relations.

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Slowly rotating homogeneous stars and the Heun equation

Cited by 7 publications

References 24 publications

Spin-2 spectrum of defect theories

Spin-2 spectrum of defect theories

Slowly rotating Tolman VII solution

Analytic I-Love-C relations for realistic neutron stars

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