Relativistic Figures of Equilibrium

Abstract

Ever since Newton introduced his theory of gravity, many famous physicists and mathematicians have worked on the problem of determining the properties of rotating bodies in equilibrium, such as planets and stars. In recent years, neutron stars and black holes have become increasingly important, and observations by astronomers and modelling by astrophysicists have reached the stage where rigorous mathematical analysis needs to be applied in order to understand their basic physics. This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It begins by presenting basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case, using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge. org/9780521863834.

On the multipole moments of a rigidly rotating fluid body

“…The associated multipole moments were derived shortly thereafter by Kleinwächter et al [14], see also [15]. Figure 4 shows that in this case the conjecture is true for n = 2 .…”

Gyromagnetic factor of rotating disks of electrically charged dust in general relativity

“…Note that within the Newton-Raphson scheme, one must solve a linear system involving the Jacobian matrixĴ = ∂ F /∂ X. As detailed in [29], this linear system is solved with the iterative BiCGStab method, with a pre-conditioner based on a finite difference representation of the algebraic system of equations.…”

“…with δ(ζ) the Dirac delta and σ P (ρ) the proper surface mass density [29]. The disk's coordinate radius ρ 0 sets the length scale of the system.…”

“…To this end, we make use of a (pseudo-)spectral method, whose algorithm is based on the one described in [29]. This paper has the following structure: section II introduces the physical model.…”

Do triaxial supramassive compact stars exist?

“…This led to historical mathematical studies including Poincaré's bifurcation theory [2]. A generalization of the Maclaurin spheroids, and other stationary axisymmetric equilibriums, to the case of relativistic gravity have been fully investigated in [3]. From a point of view of relativistic astrophysics, it is also important to include compressibility of the fluid; realistic neutron stars are modeled as axisymmetric and uniformly rotating configurations associated with equations of state (EOSs) of high density nuclear matter (see e.g.…”