Convection and cracking stability of spheres in general relativity
Abstract In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or overturning) for isotropic and anisotropic relativist...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-10-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-018-6365-0 |
| Summary: | Abstract In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or overturning) for isotropic and anisotropic relativistic spheres. We show that a density profile $$\rho (r)$$ ρ(r) , monotonous, decreasing and concave , i.e. $$\rho ' < 0$$ ρ′<0 and $$\rho '' < 0$$ ρ′′<0 , will be stable against convection, if the radial sound velocity monotonically decreases outward. We also studied the cracking instability scenarios and found that isotropic models can be unstable, when the reaction of the pressure gradient is neglected, i.e. $$\delta \mathcal {R}_p = 0$$ δRp=0 ; but if it is considered, the instabilities may vanish and this result is valid, for both isotropic and anisotropic matter distributions. |
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| ISSN: | 1434-6044 1434-6052 |