1. MICHAEL ROTONDO* R. RUFFINI*°^ S-S. XUE*° *DEPARTMENT OF PHYSICS AND ICRA, UNIVERSITY OF ROME “SAPIENZA” °ICRANET, PESCARA ^ICRANET,UNIVERSITY OF NICE “SOPHIA ANTIPOLIS” THIRD STUECKELBERG MEETING JULY 11 2008, PESCARA, ITALY

2. The energy source as crucial factor in the understanding of astrophysical phenomena

3. Some astrophysical open problems The problem of the almost known equations of state for neutron stars which are not able to reproduce the observations in millisecond binary pulsars The problem of explaining the energetics of the emission of the remnant during the collapse to a neutron star The problem of formation of the supercritical fields during the collapse to a black hole It is our opinion that the solution of these problems could find their natural explanation from a yet unexplored field : the electro-dynamical structure of a neutron star. In this work we outline a few crucial ideas of how a Thomas-Fermi approach to neutron stars can indeed represent an important step in identify this crucial feature.

4. Thomas-Fermi model

5. White Dwarfs and Neutron Stars as Thomas-Fermi systems

7. The relativistic Thomas-Fermi equation

8. The essential role of the non-point-like nucleus

9. Electrodynamics of nuclear matter in bulk n, p, e

10. Electromagnetic components Proton component Poisson equation Electron component

11. The dimensionless Thomas-Fermi equation

12. The neutron component and the A-Np relation

13. Generalized A-Np relation and the penetration of electrons inside the core

14. The ultra-relativistic approximation

15. Coulomb potential energy and electric field

16. The electric field and the muon/pion production

17. Gravitational and electrodynamical stability

18. The inapplicability of the free test particle approximation

19. Neutral nuclear matter cores vs supercharged ones

20. Consequences for Neutron Stars

21. Different proton profiles

22. Conclusions 1- The requirement of beta decay equilibrium appears to be necessary for obtaining from first principles the phenomenological relations between A and Np adopted in superheavy nuclei. 2-The Thomas-Fermi equation is a good example of the possibility that collective effects of relativistic quantum statistics leads to electric fields in astrophysical situations with values much larger than the ones suggested by the test particle approximation. 3-The possibility of having stable massive cores describable based solely on gravitational, electromagnetic and weak interactions and relativistic quantum statistics opens a whole new scenario for the study of neutron star configurations close to their critical mass and the subsequent approach to process of gravitational collapse to a Kerr-Newman black hole.

23. References [1] J. Ferreirinho, R. Ruffini, L. Stella, Phys. Lett. B 91, (1980) 442. [2] R.Ruffini, M. Rotondo, S.S. Xue, Int. Journal of Modern Phys. D Vol. 16, No. 1 (2007) 1-9. [3] A.B. Migdal, D.N. Voskresenskii, V.S. Popov, Sov. Phys. JETP 45 (3), (1977) 436. [4] R.Rotondo, R. Ruffini, S.S.Xue, in the “Proceedings of the fourth Italian-Sino Workshop on Relativistic Astrophysics”, C.L. Bianco, S.S. Xue (eds.), AIP Conf. Proc. 966, 147 (2008). [5] B. Patricelli, R.Rotondo, R. Ruffini, in the “Proceedings of the fourth Italian-Sino Workshop on Relativistic Astrophysics”, C.L. Bianco, S.S. Xue (eds.), AIP Conf. Proc. 966, 143 (2008). [6] J. Madsen, Phys. Rev. Lett., Vol. 100, 151102 (2008). [7] R.Ruffini, M. Rotondo, S.S. Xue, submitted to Phys. Rev. Lett. (2008).