arXiv:1205.6915v1 [astro-ph.HE] 31 May 2012 Gravitational Waves versus Electromagnetic Emission in Gamma-Ray Bursts Jorge A. Rueda ∗ and Remo Ruffini † Dipartimento di Fisica and ICRA, Sapienza Universit` a di Roma, P.le Aldo Moro 5, I–00185 Rome, Italy and ICRANet, P.zza della Repubblica 10, I–65122 Pescara, Italy (Dated: June 1, 2012) The recent progress in the understanding the physical nature of neutron star equilibrium configu- rations and the first observational evidence of a genuinely Short Gamma-Ray Burst, GRB 090227B, allows to give an estimate of the gravitational waves versus electromagnetic emission in a Gamma- Ray Burst. We first recall that we have recently proved [1–3] how the consistent treatment of neutron star equilibrium con- figurations, taking into account the strong, weak, elec- tromagnetic, and gravitational interactions, implies the solution of the general relativistic Thomas-Fermi equa- tions, coupled with the Einstein-Maxwell system of equa- tions. This new set of equations supersed the tra- ditional Tolman-Oppenheimer-Volkoff (TOV) equations [4, 5], which impose the condition of local charge neu- trality throughout the configuration (see e.g. [6] and ref- erences therein). The solution of the Einstein-Maxwell-Thomas-Fermi coupled differential equations leads to a new structure of the star (see [1], for details): the positively charged core at supranuclear densities, ρ>ρ nuc ∼ 2.7 × 10 14 g cm −3 , is surrounded by an electron distribution of thick- ness  /(m e c) and, at lower densities ρ<ρ nuc , a neu- tral ordinary crust. The equilibrium condition given by the constancy of the particle Klein potentials leads to a discontinuity in the density at the core-crust transi- tion and, correspondingly, an overcritical electric field ∼ (m π /m e ) 2 E c , where E c = m 2 e c 3 /(e) ∼ 1.3 × 10 16 Volt/cm, develops in the boundary interface; see Fig. 1. In particular, the continuity of the electron Klein poten- tial leads to a decreasing of the electron chemical poten- tial µ e and density at the core-crust boundary interface. They reach values µ crust e <µ core e and ρ crust <ρ core at the edge of the crust, where global charge neutrality is achieved (see Fig. 1). We shall adopt some features of these neutron stars computed using the NL3 parameter- ization [7] of the phenomenological σ-ω-ρ nuclear model [8]; we refer to [1] for details. For each central density there exists an entire family of core-crust interface boundaries and, correspondingly, a family of crusts with different mass M crust and thick- ness ΔR crust . The larger ρ crust , the smaller the thickness of the core-crust interface, the peak of the electric field, and the larger the M crust and ΔR crust . The configuration with ρ crust = ρ drip ∼ 4.3 × 10 11 g/cm 3 separates neutron stars with and without inner crust. All the above new features lead to crusts with masses and thickness smaller than the ones obtained from the traditional TOV treat- ment. The mass-radius relation obtained in this case have been compared and contrasted with the one ob- FIG. 1: Upper panel: particle density profiles in the core-crust boundary interface, in units of cm −3 . Middle panel: electric field in the core-crust transition layer, in units of the critical field Ec. Lower panel: density profile inside a neutron star with central density ρ(0) ∼ 5ρnuc. We compare and contrast the structural differences between the solution obtained from the traditional TOV equations (locally neutral case) and the globally neutral solution presented in [1]. In this example the density at the edge of the crust is ρcrust = ρ drip =4.3 × 10 11 g/cm 3 and λσ = /(mσ c) ∼ 0.4 fm denotes the σ-meson Compton wavelength. tained from the locally neutral TOV approach; see Fig. 2 and [1] for details. In Fig. 2 we show how our new neutron star the- ory is in agreement with the most up-to-date strin- gent observational constraints to the mass-radius rela- tion of neutron stars, that are provided by the largest mass, the largest radius, the highest rotational frequency, and the maximum surface gravity, observed from pulsars [9]. They are imposed by the mass of PSR J1614-2230 M =1.97 ± 0.04M ⊙ [10], the lower limit to the radius of RX J1856-3754 [12] (dotted-dashed curve), the 716 Hz PSR J1748-2246ad [15] (dashed curve), and the sur- face gravity of the neutron star in the Low Mass X-Ray Binary X7 from which 90% confidence level contours of constant R ∞ can be extracted [13] (dotted curves); see