Neutron Stars 1: Equation of State and Structure

When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

On Continued Gravitational Contraction

There is a wide range of fundamental physical problems directly related to how pulsars function. Some of these are independent of the specific pulsar mechanism. Others relate directly to the physics of the pulsar and already shed some light on the properties of matter at high density (\ensuremath{\sim}${10}^{15}$ g/cc) and in strong magnetic fields (\ensuremath{\sim}${10}^{12}$ G). Pulsars are assumed to be rotating neutron stars surrounded by strong magnetic fields and energetic particles. It is somewhere within this "magnetosphere" that the pulsar action is expected to take place. Currently there has been considerable difficulty in formulating an entirely self-consistent theory of the magnetospheric behavior and there may be rapid revisions in the near future, which is all the more surprising since many of the issues involve "elementary" problems in electromagnetism. One interesting discovery is that charge-separated plasmas apparently can support stable static discontinuities.

Theory of pulsar magnetospheres

The exact nonstationary solution for the variation of the magnetic field in the Schwarzschild metric with a given spherically symmetric flow is obtained. Initially a homogeneous magnetic field increases with time, changing into a quasi-radial field. On the assumption of equipartition between the magnetic and kinetic energies of a falling gas, in the relativistic case, estimates of the stationary field and the intensity of synchrotron radiation are presented. A considerable part of the radiation is formed in the relativistic regionr≲(2.5 to 7.7)r

 g
 (r

 g
 is the gravitational radius of a black hole). Estimates are made for radiation from the relativistic region in the case of disc type accretion.

The Accretion of Matter by a Collapsing Star in the Presence of a Magnetic Field

Dense baryon matter calculations with realistic potentials

Pulsars are presently believed to be rotating neutron stars with frozen-in magnetic fields. Because of the high density of neutron stars, general relativistic effects are important since they effect both the structure and stability of such stars. Besides this, the magnetic field outside the star is also affected. Instead of falling of asr
(2+l) as in flat space, it is shown that each magnetic multipole varies as a hypergeometric function of radius. A closed form of these hypergeometric functions is given in terms of Legendre functions of the second kind. If the mass of a neutron star exceeds about 2.4m
⊙, the star becomes unstable and coliapses. For a quasistatically collapsing body, it is shown that the magnetic field seen by a distant observer vanishes as the radius approaches the gravitational radius.

Gravitational collapse of magnetic neutron stars

A new series of neutron star models has been computed. The equation of state used included the effects of nuclear dissolution, nuclear forces, and the presence of hyperons. The nuclear forces were introduced through use of a generalized form of the Levinger-SimmonsVα andVγ potentials. The maximum stable masses obtained were 2.28 and 2.37M⊙, respectively. Details are given of the structure of the outer layers which are expected to be crystalline. Expressions are given for the angular momentum and rotational energy of a neutron star and the relevant moment of inertia is tabulated for the models.

Neutron star models including the effects of hyperon formation

ONE or more planets may be orbiting the pulsar in the Crab Nebula. Richards et al.1 inferred the presence of a planet from the sinusoidal behaviour of the residuals in the pulse arrival time data of NP 0532 after the first and second derivatives of the pulsar period had been removed. The sinusoidal character of the residuals has, however, been queried2,3. Michel4 has attributed the period discontinuity observed last autumn5,6 (the so-called “glitch”) to a planet in a highly eccentric orbit sweeping close to the pulsar. And the Princeton group7 have tentatively fitted their pulse arrival time residuals by invoking three planets!

Physical sciences: planet, pulsar, "glitch" and wisp.

Closed anisotropic cosmological models.

THIRRING'S solution for a rotating mass shell is frequently used to illustrate the appearance of centrifugal and Coriolis force in general relativity In the equations of motion of test particles within the shell, terms appear which are of second order in the shell angular velocity, ω These terms are conventionally identified with “centrifugal force”, yet they do bear the relationship to “Coriolis force” that one would expect from Mach's principle The resolution of this paradox has an important bearing on the foundations of general relativity because, to resolve it, some authors have taken the extreme position that either general relativity or Mach's principle must be abandoned In this communication we resolve the paradox without abandoning either

Jeffrey M. Cohen

Papers

Gravitational collapse of magnetic neutron stars

Neutron star models including the effects of hyperon formation

Physical sciences: planet, pulsar, "glitch" and wisp.

Closed anisotropic cosmological models.

Centrifugal force and general relativity.