Gravitational instability of finite isothermal spheres in general relativity. Analogy with neutron stars
Laboratoire de Physique Quantique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France Institute for Theoretical Physics, University of California, Santa Barbara, California CA93106, USA
Corresponding author: chavanis@irsamc2.ups-tlse.fr
Received:
29
August
2001
Accepted:
10
October
2001
We investigate the effects of relativity on the gravitational
instability of finite isothermal gaseous spheres. In the first part of
the paper, we treat the gravitational field within the framework of
Newtonian mechanics but we allow the speed of the particles to be
close to the velocity of light so that special relativity must be
taken into account. In the second part of the paper, we study the full
general relativistic problem for a gas described by an equation of
state 
such that the pressure is proportional to the
energy density (“isothermal” distribution). For 
, this
equation of state describes the core of neutron stars. The
mass-density diagram displays some damped oscillations and there
exists a critical value of mass-energy above which no equilibrium
state is possible. We show analytically that the mass peaks are
associated with new modes of instability. These results are strikingly
similar to those obtained by Antonov (1962) and Lynden-Bell & Wood (1968)
for a classical isothermal
gas. Our study completes the analogy between isothermal spheres and
neutron stars investigated by Yabushita (1974).
Key words: hydrodynamics, instabilities / relativity / stars: neutron
© ESO, 2002