Critical collapse of an axisymmetric ultrarelativistic fluid in 
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Bourg, Patrick; Gundlach, Carsten

doi:10.1103/physrevd.104.104017

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…In (2 + 1) spacetime, a negative cosmological constant is to guarantee not only hydrostatic equilibrium [42] (the pressure is monotonically decreasing) but also permit a black hole solution of Bañados-Teitelboim-Zanelli (BTZ) [43]. The dynamical process of dust collapse [44], critical collapse of scalar field [45][46][47], and ultra-relativistic fluid [48,49] into a BTZ hole have been shown to be possible. Nevertheless, in this note, we are more interested in the condition triggering the dynamical instability of a monatomic fluid disk in the hydrodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

On the Dynamical Instability of Monatomic Fluid Spheres in (N + 1)-Dimensional Spacetime

Feng

2023

Astronomy

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In this note, I derive the Chandrasekhar instability of a fluid sphere in (N + 1)-dimensional Schwarzschild–Tangherlini spacetime and take the homogeneous (uniform energy density) solution for illustration. Qualitatively, the effect of a positive (negative) cosmological constant tends to destabilize (stabilize) the sphere. In the absence of a cosmological constant, the privileged position of (3 + 1)-dimensional spacetime is manifest in its own right. As it is, the marginal dimensionality in which a monatomic ideal fluid sphere is stable but not too stable to trigger the onset of gravitational collapse. Furthermore, it is the unique dimensionality that can accommodate stable hydrostatic equilibrium with a positive cosmological constant. However, given the current cosmological constant observed, no stable configuration can be larger than 1021M⊙. On the other hand, in (2 + 1) dimensions, it is too stable to collapse either in the context of Newtonian Gravity (NG) or Einstein’s General Relativity (GR). In GR, the role of negative cosmological constant is crucial not only to guarantee fluid equilibrium (decreasing monotonicity of pressure) but also to have the Bañados–Teitelboim–Zanelli (BTZ) black hole solution. Owing to the negativeness of the cosmological constant, there is no unstable configuration for a homogeneous fluid disk with mass 0<M≤0.5 to collapse into a naked singularity, which supports the Cosmic Censorship Conjecture. However, the relativistic instability can be triggered for a homogeneous disk with mass 0.5<M≲0.518 under causal limit, which implies that BTZ holes of mass MBTZ>0 could emerge from collapsing fluid disks under proper conditions. The implicit assumptions and implications are also discussed.

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Section: Introductionmentioning

confidence: 99%

On the Dynamical Instability of Monatomic Fluid Spheres in (N + 1)-Dimensional Spacetime

Feng

2023

Astronomy

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“…In (2+1) spacetime, a negative cosmological constant is to guarantee not only hydrostatic equilibrium [42] (the pressure is monotonically decreasing) but also permit a black hole solution of Bañados-Teitelboim-Zanelli (BTZ) [43]. The dynamical process of dust collapse [44], critical collapse of scalar field [45][46][47] and ultra-relativistic fluid [48,49] into a BTZ hole have been shown possible. Nevertheless, in this note we are more interested in the condition triggering the dynamical instability of a monatomic fluid disk in the hydrodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

On the Dynamical Instability of Monatomic Fluid Spheres in (N+1)-dimensional Spacetime

Feng

2022

Preprint

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In this note, I derive the Chandrasekhar instability of a fluid sphere in (N + 1)-dimensional Schwarzschild-Tangherlini spacetime and take the homogeneous (uniform energy density) solution for illustration. Qualitatively, the effect of positive (negative) cosmological constant tends to destabilize (stabilize) the sphere. In the absence of cosmological constant, the privileged position of (3+1)-dimensional spacetime is manifest in its own right. As it is the marginal dimensionality in which a monatomic ideal fluid sphere is stable but not too stable to trigger the onset of gravitational collapse. Furthermore, it is the unique dimensionality that can accommodate stable hydrostatic equilibrium with positive cosmological constant. However, given the current cosmological constant observed no stable configuration can be larger than 1021 M⦿. On the other hand, in (2+1) dimensions it is too stable to collapse either in the context of Newtonian Gravity (NG) or Einstein's General Relativity (GR). In GR, the role of negative cosmological constant is crucial not only to guarantee fluid equilibrium (decreasing monotonicity of pressure) but also to have the Bañados-Teitelboim-Zanelli (BTZ) solution. Owing to the negativeness of the cosmological constant, there is no unstable configuration for a homogeneous fluid disk with mass 0 < M ≤ 0.5 to collapse into a naked singularity, which supports the Cosmic Censorship Conjecture. However, the relativistic instability can be triggered for a homogeneous disk with mass 0.5 < M ≲ 0.518 under causal limit, which implies that BTZ holes of mass MBTZ > 0 could emerge from collapsing fluid disks under proper conditions. The implicit assumptions and implications are also discussed.

show abstract

“…In (2+1) spacetime, a negative cosmological constant is to guarantee not only hydrostatic equilibrium [35] (the pressure is monotonically decreasing) but also permit a black hole solution of Bañados-Teitelboim-Zanelli (BTZ) [36]. The dynamical process of dust collapse [37], critical collapse of scalar field [38][39][40] and ultra-relativistic fluid [41,42] into a BTZ hole have been shown possible. Nevertheless, in this note we are more interested in the condition triggering the dynamical instability of a monatomic fluid disk in the hydrodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

On the Dynamical Instability of Monatomic Fluid Spheres in (N+1)-dimensional Spacetime

Feng¹

2021

Preprint

View full text Add to dashboard Cite

In this note, I derive the Chandrasekhar instability of a fluid sphere in (N +1)-dimensional Schwarzschild-Tangherlini spacetime and take the homogeneous (uniform energy density) solution for illustration. Qualitatively, the effect of positive (negative) cosmological constant tends to destabilize (stabilize) the sphere. In the absence of cosmological constant, the privileged position of (3+1)-dimensional spacetime is manifest in its own right. As it is the marginal dimensionality in which a monatomic ideal fluid sphere is stable but not too stable to trigger the onset of gravitational collapse. Furthermore, it is the unique dimensionality that can accommodate stable hydrostatic equilibrium with positive cosmological constant. However, given the current cosmological constant observed no stable configuration can be larger than 10 20 M ⊙ . On the other hand, in (2+1) dimensions it is too stable to collapse either in the context of Newtonian Gravity (NG) or Einstein's General Relativity (GR). In GR, the role of negative cosmological constant is crucial not only to guarantee fluid equilibrium (decreasing monotonicity of pressure) but also to have the Bañados-Teitelboim-Zanelli (BTZ) solution. Owing to the negativeness of the cosmological constant, there is no unstable configuration for a homogeneous fluid disk with mass 0 < M ≤ 0.5 to collapse into a naked singularity, which supports the Cosmic Censorship Conjecture. However, the relativistic instability can be triggered for a homogeneous disk with mass 0.5 < M ≲ 0.518 under causal limit, which implies that BTZ holes of mass M BTZ > 0 could emerge from collapsing fluid disks under proper conditions. The implicit assumptions and implications are also discussed.

show abstract

Critical collapse of an axisymmetric ultrarelativistic fluid in 2+1 dimensions

Cited by 4 publications

References 15 publications

On the Dynamical Instability of Monatomic Fluid Spheres in (N + 1)-Dimensional Spacetime

On the Dynamical Instability of Monatomic Fluid Spheres in (N + 1)-Dimensional Spacetime

On the Dynamical Instability of Monatomic Fluid Spheres in (N+1)-dimensional Spacetime

On the Dynamical Instability of Monatomic Fluid Spheres in (N+1)-dimensional Spacetime

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