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17000 results

Page 83 of 850

  • 2 - General Relativity

  • Jürgen Schaffner-Bielich, Goethe-Universität Frankfurt Am Main
  • Book:
    Compact Star Physics
    Published online:
    17 August 2020
    Print publication:
    27 August 2020, pp 8-37

  • Summary

    The basic principles of general relativity are reviewed, in particular the different forms of the equivalence principle: the weak, Einstein, and strong equivalence principles. The concept of a metric is introduced within special relativity. The Einstein equations are derived in an heurisitic manner including the Christoffel symbols, the Ricci tensor, and the Ricci scalar. The Schwarzschild as the solution of Einstein‘s equation in vacuum are explicitly derived. The notion of the energy–momentum tensor, as the source term of the Einstein equations, is discussed in terms of the four-momentum of particles. For bulk matter, the definition of an ideal fluid is given. The conservation of the energy–momentum tensor in curved space-time is discussed. The Einstein equations are solved for a sphere of an ideal fluid to arrive at the Tolman–Oppenheimer–Volkoff equations, the central equations for the investigation of compact stars. Finally the analytically known solution for a sphere of an incompressible fluid, the Schwarzschild solution, is derived and used to set the Buchdahl limit on the compactness of a compact star.

Compact Star Physics
  • Jürgen Schaffner-Bielich
  • Published online:
    17 August 2020
    Print publication:
    27 August 2020
  • This self-contained introduction to compact star physics explains important concepts from areas such as general relativity, thermodynamics, statistical mechanics, and nuclear physics. Containing many tested exercises, and written by an international expert in the research field, the book provides important insights on the basic concepts of compact stars, discusses white dwarfs, neutron stars, quark stars and exotic compact stars. Included are sections on astrophysical observations of compact stars, and present and future terrestrial experiments related to compact stars physics, as the study of exotic nuclei and relativistic heavy-ion collisions. Major developments in the field such as the discovery of massive neutron stars, and a discussion of the recent gravitational wave measurement of a neutron star merger are also presented. This book is ideal for graduate students and researchers working on the physics of compact stars, general relativity and nuclear physics.

  • 8 - Algorithmic Regularization

  • Seppo Mikkola, University of Turku, Finland
  • Book:
    Gravitational Few-Body Dynamics
    Published online:
    06 April 2020
    Print publication:
    16 April 2020, pp 173-210

  • Summary

    The gravitational field of a black hole differs significantly from the point-mass field that is normally used in N-Body simulations. The additional terms needed are called Post-Newtonian ones and abbreviated as PN-terms. They depend in addition of coordinates also on velocities. Thus the methods discussed in Section~\ref{v-dependence} must be used in numerical integration. An other problem is that the orbital elements of two-body motions cannot any more be evaluatedin the same way as in the Newtonian point-mass dynamics. Finally one must remember that black holes rotate and form a so called Kerr-hole that produce a fielddiffering from the non-rotating one and the rotation, the black hole spin, changes due to interactions withother bodies. These complexities is discussed and formulae given in this short chapter

Page 83 of 850