# 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…

## 578 Citations

### Dynamical instability of gaseous sphere in the Reissner–Nordström limit

- Physics, Environmental Science
- 2015

In this paper, we study the dynamical instability of gaseous sphere under radial oscillations approaching the Reissner–Nordström limit. For this purpose, we derive linearized perturbed equation of…

### A variational principle for the axisymmetric stability of rotating relativistic stars

- Physics
- 2016

It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar–Friedman–Schutz (CFS) instability. However,…

### Dynamical instability of shear-free collapsing star in extended teleparallel gravity

- Physics
- 2015

We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model…

### Stability of general relativistic gaseous masses and variational principles

- Physics
- 1969

The Einstein field equations for a self-gravitating fluid that obeys an equation of state of the formp=p(w),p the pressure andw the energy density may be derived from a variational principle. The…

### Dynamical instability of fluid spheres in the presence of a cosmological constant

- Physics
- 2005

The equations describing the adiabatic, small radial oscillations of general relativistic stars are generalized to include the effects of a cosmological constant. The generalized eigenvalue equation…

### The stability of the equilibrium of supermassive and superdense stars

- Physics
- 1970

The second variation of the mass-energy (by constant baryon number) is analysed to inquire into the stability of the equilibrium for a spherical mass under the action of its own gravitation. The…

### Stability of the charged spherical dissipative collapse in f(R) gravity

- Physics
- 2013

We analyse the dynamical instability of the charged isotropic spherical symmetric matter distribution which collapses non-adiabatically in Carrol–Duvvuri–Trodden–Turner (CDTT) f ( R ) model…

### Conditions for equilibrium of perfect fluids in the scalar-tensor theories

- Physics
- 1993

AbstractWe have determined the first and second order radial and time symmetric variations of the mass-energy of spherically symmetric isentropic perfect fluids in the framework of the scalar-tensor…

### On the radial stability of ultra-compact Schwarzschild stars beyond the Buchdahl limit

- PhysicsClassical and Quantum Gravity
- 2019

In this paper we used the theory of adiabatic radial oscillations developed by Chandrasekhar to study the conditions for dynamical stability of constant energy-density stars, or Schwarzschild stars,…

## 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