Can rigidly rotating polytropes be sources of the Kerr metric?

Martín, Jesús Izquierdo; Molina, Alfred; Ruiz, E.

doi:10.1088/0264-9381/25/10/105019

Cited by 14 publications

(25 citation statements)

References 15 publications

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“…3 Proposition 2 Let (V 0 , g) with Σ 0 be the static and spherically symmetric background matched spacetime as described in Proposition 1, and assume that (20) is satisfied. Let it be perturbed to first order by K (1)± plus Q ± 1 and T ± 1 so that (18), (19), (21), (22) hold. Consider the second order metric perturbation tensor K (2)± as defined in (9) at either side, plus two unknown functionsQ ± 2 (τ, ϑ) and two unknown vectors…”

Section: Second Order Matchingmentioning

confidence: 99%

Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass

Reina

Vera

2015

Class. Quantum Grav.

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Hartle's model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in General Relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no convective motions and rigid rotation. That interior is matched across its surface to an asymptotically flat vacuum exterior. Perturbations are taken to second order around a static and spherically symmetric background configuration. Apart from the explicit assumptions, the perturbed configuration is constructed upon some implicit premises, in particular the continuity of the functions describing the perturbation in terms of some background radial coordinate. In this work we revisit the model within a modern general and consistent theory of perturbative matchings to second order, which is independent of the coordinates and gauges used to describe the two regions to be joined. We explore the matching conditions up to second order in full. The main particular result we present is that the radial function m 0 (in the setting of the original work) of the second order perturbation tensor, contrary to the original assumption, presents a jump at the surface of the star, which is proportional to the value of the energy density of the background configuration there. As a consequence, the change in mass δM needed by the perturbed configuration to keep the value of the central energy density unchanged must be amended. We also discuss some subtleties that arise when studying the deformation of the star.

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Section: Second Order Matchingmentioning

confidence: 99%

Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass

Reina

Vera

2015

Class. Quantum Grav.

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“…These stars are modeled by stationary, axisymmetric perfect fluid spacetimes and one would expect that they are-in analogy to the static case-glued to a Kerr vacuum exterior. This is surprisingly not the case [18,52], but if a rotating star collapses to a black hole, it is expected that the exterior region is approximately Kerr [5,35,57,64,77,80]. Remark 1.10 (Other matter fields).…”

Section: Geometric Interpretation: Our Resultsmentioning

confidence: 99%

On the Asymptotic Behavior of Static Perfect Fluids

Andersson

Burtscher

2019

Ann. Henri Poincaré

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Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the latter case, the matter extends globally with the density approaching zero at infinity. The asymptotic behavior largely depends on the equation of state of the fluid and is still poorly understood. While a few such unbounded solutions are known to be asymptotically flat with finite ADM mass, the vast majority are not. We provide a full geometric description of the asymptotic behavior of static spherically symmetric perfect fluid solutions with linear equations of state and polytropic-type equations of state with index n > 5. In order to capture the asymptotic behavior, we introduce a notion of scaled quasi-asymptotic flatness, which encompasses the notion of asymptotic conicality. In particular, these spacetimes are asymptotically simple.

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“…As in our previous work [12,13,14,15] on the rigid rotation problem, here we introduce a post-Minkowskian parameter, λ, and a dimensionless rotation parameter, Ω = λ −1/2 ωr 0 , where r 0 is the radius of the source in the nonrotation limit. Then we can rewrite (12) as:…”

Section: Approximation Schemementioning

confidence: 99%

“…If we assume that the metric components are continuous on the matching surface, then we can use their exterior expressions given by (14) to make (9) into a true equation for this surface. So we can search for a parametric form of the matching surface up to zero order in λ and up to order Ω 4 0 by making the following assumption:…”

Section: Matching Surface and Energy-momentum Tensormentioning

confidence: 99%

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An approximate global solution of Einstein’s equations for a differentially rotating compact body

Molina

Ruiz

2017

Gen Relativ Gravit

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We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought of as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic coordinates. Interior and exterior solutions are matched, in the sense described by Lichnerowicz, on the surface of zero pressure, to obtain a global solution. The resulting metric depends on four arbitrary constants: mass density; rotational velocity at r = 0; a parameter that accounts for the change in rotational velocity through the star; and the star radius in the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined in terms of these four parameters. PACS number(s) 04.40.Nr, 04.20.Jb

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Can rigidly rotating polytropes be sources of the Kerr metric?

Cited by 14 publications

References 15 publications

Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass

Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass

On the Asymptotic Behavior of Static Perfect Fluids

An approximate global solution of Einstein’s equations for a differentially rotating compact body

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