ABSTRACT
This chapter describes the stellar structure equations of non-rotating, spherically symmetric objects in the framework of Albert Einstein’s general theory of relativity. For non-rotating stars the metric functions are particularly simple because they depend on the time and radial coordinate only. The chapter demonstrates that the explicitly for the energy-momentum tensor of a perfect fluid. Stellar bodies that are in hydrostatic equilibrium are not automatically stable against oscillations about their equilibrium configurations or other types of vibration, such as torsional or octupole eigenmodes. A simple but efficient method to adequately analyze the vibrational and seismological properties of compact stars performing non-radial oscillations was developed by Bastrukov et al. Association of non-radial oscillations and the elastodynamic behavior of superdense stellar matter with observed phenomena may be pulsar glitches. The discovery of elastic properties of macroscopic nuclear matter constitutes one of the major landmarks in the development of laboratory nuclear physics.
