Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres

Andréasson, Håkan

doi:10.1007/s00220-008-0690-3

Cited by 240 publications

(222 citation statements)

References 26 publications

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“…By relaxing these assumptions and considering any static solution of the spherically symmetric Einstein equations for which the energy density ρ ≥ 0 and the radial and tangential pressures, p ≥ 0 and p T , satisfy the condition p + 2 p T ≤ ρc 2 , > 0, one can obtain the relation sup r >0 [2G M(r )/c 2 r ] ≤ [(1 + 2 ) 2 − 1]/(1 + 2 ) 2 [5]. These bounds were generalized to the case of charged compact general relativistic objects in [6]. Bounds on M/R for static objects with a positive cosmological constant > 0 were obtained in [7], where it was shown that the relation G M/c 2 R ≤ 2/9 − R 2 /3 + (2/9) √ 1 + 3 R 2 holds if the energy conditions listed above are satisfied.…”

Section: Introductionmentioning

confidence: 92%

“…The physical implications of the existence of a minimum mass (in D = 4) were investigated in [15]. An especially important result is that the ratio l 4 Pl / , where l Pl is the reduced Planck length and is the four-dimensional cosmological constant, is numerically of the same order of magnitude as r 6 e , where r e ≈ 2.818 × 10 −13 cm denotes the classical electron radius. This suggests the identification of in terms of fundamental physical constants as …”

Section: Introductionmentioning

confidence: 99%

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The minimum mass of a spherically symmetric object in D-dimensions, and its implications for the mass hierarchy problem

et al. 2015

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The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity. These results follow rigorously from the Buchdahl inequalities in four-dimensional de Sitter space. In this work, we obtain the generalized Buchdahl inequalities in arbitrary space-time dimensions with = 0 and consider both the de Sitter and the anti-de Sitter cases. The dependence on D, the number of space-time dimensions, of the minimum and maximum masses for stable spherical objects is explicitly obtained. The analysis is then extended to the case of dark energy satisfying an arbitrary linear barotropic equation of state. The Jeans instability of barotropic dark energy is also investigated, for arbitrary D, in the framework of a simple Newtonian model with and without viscous dissipation, and we determine the dispersion relation describing the dark energy-matter condensation process, along with estimates of the corresponding Jeans mass (and radius). Finally, the quantum mechanical implications of the mass limits are investigated, and we show that the existence of a minimum mass scale naturally leads to a model in which dark energy is composed of a 'sea' of quantum particles, each with an effective mass proportional to 1/4 .

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

The minimum mass of a spherically symmetric object in D-dimensions, and its implications for the mass hierarchy problem

et al. 2015

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“…whereas the upper bound of the mass-radius of a charged sphere was generalized by Andréasson [50] as follows:…”

Section: Generalized Tov Equation For Solution Imentioning

confidence: 99%

Spherically symmetric charged compact stars

Maurya

Gupta

Ray³

et al. 2015

Eur. Phys. J. C

131

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In this article we consider the static spherically symmetric metric of embedding class 1. When solving the Einstein-Maxwell field equations we take into account the presence of ordinary baryonic matter together with the electric charge. Specific new charged stellar models are obtained where the solutions are entirely dependent on the electromagnetic field, such that the physical parameters, like density, pressure etc. do vanish for the vanishing charge. We systematically analyze altogether the three sets of Solutions I, II, and III of the stellar models for a suitable functional relation of ν(r ). However, it is observed that only the Solution I provides a physically valid and well-behaved situation, whereas the Solutions II and III are not well behaved and hence not included in the study. Thereafter it is exclusively shown that the Solution I can pass through several standard physical tests performed by us. To validate the solution set presented here a comparison has also been made with that of the compact stars, like R X J 1856 − 37, Her X − 1, P S R 1937 + 21, P S R J 1614 − 2230, and P S R J 0348 + 0432, and we have shown the feasibility of the models.

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“…The upper bound of the mass of charged sphere was generalized by Andréasson [191] and one proved that…”

Section: Elementary Criteria For Physical Acceptabilitymentioning

confidence: 99%

Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling

Murad

Fatema

2015

Eur. Phys. J. C

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In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein-Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30.

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Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres

Cited by 240 publications

References 26 publications

The minimum mass of a spherically symmetric object in D-dimensions, and its implications for the mass hierarchy problem

The minimum mass of a spherically symmetric object in D-dimensions, and its implications for the mass hierarchy problem

Spherically symmetric charged compact stars

Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling

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