Noname manuscript No. (will be inserted by the editor) Rotating Stars in Relativity Vasileios Paschalidis Nikolaos Stergioulas · Received: date / Accepted: date Abstract Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densi- ties and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is re- viewed in this updated article. The sections on equilibrium properties and on nonaxisymmetric oscillations and instabilities in f-modes and r-modes have been updated. Several new sections have been added on equilibria in modi- fied theories of gravity, approximate universal relationships, the one-arm spiral instability, on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativ- ity including both hydrodynamic and magnetohydrodynamic studies of these objects. Keywords Relativistic stars · Rotation · Stability · Oscillations · Magnetic fields · Numerical relativity Vasileios Paschalidis Theoretical Astrophysics Program, Departments of Astronomy and Physics, University of Arizona, Tucson, AZ 85721, USA Department of Physics, Princeton University Princeton, NJ 08544, USA E-mail:
[email protected] http://physics.princeton.edu/~vp16/ Nikolaos Stergioulas Department of Physics, Aristotle University of Thessaloniki Thessaloniki, 54124, Greece E-mail:
[email protected] http://www.astro.auth.gr/~niksterg arXiv:1612.03050v2 [astro-ph.HE] 30 Nov 2017 2 Vasileios Paschalidis, Nikolaos Stergioulas The article has been substantially revised and updated. New Section 5 and various Subsections (2.3 { 2.5, 2.7.5 { 2.7.7, 2.8, 2.10-2.11,4.5.7) have been added.