The role of General Relativity in the evolution of Low Mass X-ray   Binaries
  We study the evolution of Low Mass X-ray Binaries (LMXBs) and of millisecond binary radio pulsars (MSPs), with numerical simulations that keep into account the evolution of the companion, of the binary system and of the neutron star. According to general relativity, when energy is released, the system loses gravitational mass. Moreover, the neutron star can collapse to a black hole if its mass exceeds a critical limit, that depends on the equation of state. These facts have some interesting consequences: 1) In a MSP the mass-energy is lost with a specific angular momentum that is smaller than the one of the system, resulting in a positive contribution to the orbital period derivative. If this contribution is dominant and can be measured, we can extract information about the moment of inertia of the neutron star, since the energy loss rate depends on it. Such a measurement can therefore help to put constraints on the equation of state of ultradense matter. 2) In LMXBs below the bifurcation period (\sim 18 h), the neutron star survives the period gap only if its mass is smaller than the maximum non-rotating mass when the companion becomes fully convective and accretion pauses. Therefore short period (P < 2h) millisecond X-ray pulsar like SAX J1808.4-3658 can be formed only if either a large part of the accreting matter has been ejected from the system, or the equation of state of ultradense matter is very stiff. 3) In Low Mass X-ray binaries above the bifurcation period, the mass-energy loss lowers the mass transfer rate. As side effect, the inner core of the companion star becomes 1% bigger than in a system with a non-collapsed primary. Due to this difference, the final orbital period of the system becomes 20% larger than what is obtained if the mass-energy loss effect is not taken into account. 
Giuseppe Lavagetto, Luciano Burderi, Francesca D'Antona, Tiziana Di   Salvo, Rosario Iaria and Natale Renato Robba