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Register a new userThe Shapiro Conjecture: Prompt or Delayed Collapse in the head-on collision of neutron stars?
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We study the question of prompt vs. delayed collapse in the head-on collision of two neutron stars. We show that the prompt formation of a black hole is possible, contrary to a conjecture of Shapiro which claims that collapse is delayed until after neutrino cooling. We discuss the insight provided by Shapiros conjecture and its limitation. An understanding of the limitation of the conjecture is provided in terms of the many time scales involved in the problem. General relativistic simulations in the Einstein theory with the full set of Einstein equations coupled to the general relativistic hydrodynamic equations are carried out in our study.
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We found type I critical collapses of compact objects modeled by a polytropic equation of state (EOS) with polytropic index $Gamma=2$ without the ultra-relativistic assumption. The object is formed in head-on collisions of neutron stars. Further we showed that the critical collapse can occur due to a change of the EOS, without fine tuning of initial data. This opens the possibility that a neutron star like compact object, not just those formed in a collision, may undergo a critical collapse in processes which slowly change the EOS, such as cooling.
It has been conjectured that in head-on collisions of neutron stars (NSs), the merged object would not collapse promptly even if the total mass is higher than the maximum stable mass of a cold NS. In this paper, we show that the reverse is true: even if the total mass is {it less} than the maximum stable mass, the merged object can collapse promptly. We demonstrate this for the case of NSs with a realistic equation of state (the Lattimer-Swesty EOS) in head-on {it and} near head-on collisions. We propose a ``Prompt Collapse Conjecture for a generic NS EOS for head on and near head-on collisions.
We perform hydrodynamical simulations of neutron-star mergers for a large sample of temperature-dependent, nuclear equations of state, and determine the threshold mass above which the merger remnant promptly collapses to form a black hole. We find that, depending on the equation of state, the threshold mass is larger than the maximum mass of a non-rotating star in isolation by between 30 and 70 per cent. Our simulations also show that the ratio between the threshold mass and maximum mass is tightly correlated with the compactness of the non-rotating maximum-mass configuration. We speculate on how this relation can be used to derive constraints on neutron-star properties from future observations.
We evaluate how much energy can be converted into gravitational radiation in head-on collision of black holes. We estimate it by the area theorem of black hole horizon incorporating merging entropy of colliding black holes from a viewpoint of black hole thermodynamics. Then we obtain an upper bound of energy ratio of the gravitational radiation which is smaller than the upper bound originally derived by Hawking. The fact that this estimation is not inconsistent with the results of both numerical investigations in low- and high-energy head-on collision implies that thermodynamics of coalescing black holes requires the contribution of the merging entropy.
We prove a generalization of the Shapiro-Shapiro conjecture on Wronskians of polynomials, allowing the Wronskian to have complex conjugate roots. We decompose the real Schubert cell according to the number of real roots of the Wronski map, and define an orientation of each connected component. For each part of this decomposition, we prove that the topological degree of the restricted Wronski map is given as an evaluation of a symmetric group character. In the case where all roots are real, this implies that the restricted Wronski map is a topologically trivial covering map; in particular, this gives a new proof of the Shapiro-Shapiro conjecture.
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