# The Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity.

@article{Chandrasekhar1964TheDI, title={The Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity.}, author={Subrahmanyan Chandrasekhar}, journal={The Astrophysical Journal}, year={1964}, volume={140}, pages={417-433} }

ABSTRACT In this paper the theory of the infinitesimal, baryon-number conserving, adiabatic, radial oscillations of a gas sphere is developed in the framework of general relativity. A variational base for determining the characteristic frequencies of oscillation is established. It provides a convenient method for obtaining sufficient conditions for the occurrence of dynamical instability. The principal result of the analysis is the demonstration that the Newtonian lower limit f, for the ratio…

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## References

SHOWING 1-2 OF 2 REFERENCES

An Introduction to the Study of Stellar Structure

- PhysicsNature
- 1939

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since…

Fluid Mechanics (London

- 1959