A mass shell with flat interior cannot rotate rigidly

Pfister, Herbert; Braun, Kerstin

doi:10.1088/0264-9381/3/3/008

Cited by 25 publications

(30 citation statements)

References 4 publications

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“…This is another interesting and fundamental situation apart from the gravastar. Therefore, similar but not the same situations have been so far considered by several authors, e.g., [19,20,21,22]. The quadrupole metric perturbations for the interior spacetime of the thin shell, given in (16) and (17), vanish in the limit of L → ∞.…”

Section: Slowly Rotating Thin Shells With Isotropic Pressure: Limit Osupporting

confidence: 56%

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Slowly rotating thin shell gravastars

Uchikata

Yoshida

2015

Class. Quantum Grav.

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Abstract. We construct the solutions of slowly rotating gravastars with a thin shell. In the zero-rotation limit, we consider the gravastar composed of a de Sitter core, a thin shell, and Schwarzschild exterior spacetime. The rotational effects are treated as small axisymmetric and stationary perturbations. The perturbed internal and external spacetimes are matched with a uniformly rotating thin shell. We assume that the angular velocity of the thin shell, Ω, is much smaller than the Keplerian frequency of the nonrotating gravastar, Ω k . The solutions within an accuracy up to the second order of Ω/Ω k are obtained. The thin shell matter is assumed to be described by a perfect fluid and to satisfy the dominant energy condition in the zero-rotation limit. In this study, we assume that the equation of state for perturbations is the same as that of the unperturbed solution. The spherically symmetric component of the energy density perturbations, δσ 0 , is assumed to vanish independently of the rotation rate. Based on these assumptions, we obtain many numerical solutions and investigate properties of the rotational corrections to the structure of the thin shell gravastar.

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Section: Slowly Rotating Thin Shells With Isotropic Pressure: Limit Osupporting

confidence: 56%

“…With perturbation approaches, as mentioned before, self-gravitating slowly rotating thin shells were studied by several authors, e.g., [19,20,21,22]. De la Cruz and Israel [20] and Pfister and Braun [21] obtained slowly rotating thin shells very similar to those discussed in this subsection.…”

Section: Slowly Rotating Thin Shells With Isotropic Pressure: Limit Omentioning

confidence: 84%

Slowly rotating thin shell gravastars

Uchikata

Yoshida

2015

Class. Quantum Grav.

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“…This correlated to the result obtained by Cohen [8]. Orwig [9] and Pfister and Braun [10] further analyzed shells with a flat interior. They determined that the local inertial frames are "dragged" by the shell when the shell radius approaches the gravitational radius.…”

Section: Introductionsupporting

confidence: 85%

A spinning shell around a Kerr black hole in a slow rotation approximation

Siegl¹

2010

Gen Relativ Gravit

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This paper explores a thin shell of ideal fluid surrounding a Kerr black hole assuming a slow rotation and retaining only first order terms of expansion in angular momentum. It is shown that a physically feasible shell rotates rigidly in this approximation and that the interior black hole mass is constrained by other parameters of the system. Furthermore, it is shown that the local inertial frames are "dragged" by the shell as the shell radius approaches the gravitational radius, which is similar to results of studies considering a flat interior.

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“…Furthermore, it turns out (Pfister, & Braun, 1986) that in order ω 3 the flatness of the interior space-time can only be maintained if the shell material rotates differentially, ω S = ω(1 + ω 2 e 2 P 2 (cos θ)), with a constant e 2 , and with corresponding corrections in higher (odd) orders ω 2n+1 . Surprisingly, the flatness condition enforces a prolate form of the shell: invariant equatorial circumference smaller than the invariant polar circumference.…”

Section: Introductionmentioning

confidence: 99%

On the history of the so-called Lense-Thirring effect

Pfister

2007

Gen Relativ Gravit

122

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Some historical documents, especially the Einstein-Besso manuscript from 1913, an extensive notebook by Hans Thirring from 1917, and a correspondence between Thirring and Albert Einstein in the year 1917 reveal that most of the merit of the so-called Lense-Thirring effect of general relativity belongs to Einstein. Besides this "central story" of the effect, we comment shortly on some type of prehistory, with contributions by Ernst Mach, Benedikt and Immanuel Friedlaender, and August Föppl, and we follow the later history of the problem of a correct centrifugal force inside a rotating mass shell which was resolved only relatively recently. We also shortly comment on recent possibilities to confirm the so-called Lense-Thirring effect, and the related Schiff effect, experimentally.

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A mass shell with flat interior cannot rotate rigidly

Cited by 25 publications

References 4 publications

Slowly rotating thin shell gravastars

Slowly rotating thin shell gravastars

A spinning shell around a Kerr black hole in a slow rotation approximation

On the history of the so-called Lense-Thirring effect

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