Neutrino trapping in braneworld extremely compact stars

Abstract

Extremely Compact Stars (ECS) contain trapped null geodesics. When such objects enter the evolution period admitting geodetical motion of neutrinos, certain part of neutrinos produced in their interior will be trapped influencing their neutrino luminosity and thermal evolution. We study neutrino trapping in the braneworld ECS, assuming uniform distribution of neutrino emissivity and massless neutrinos. We give the efficiency of the neutrino trapping effects in the framework of the simple model of the internal spacetime with uniform distribution of energy density, and external spacetime described by the Reissner-Nordstr\"om geometry characterized by the braneworld "tidal" parameter $b$. For $b < 0$ the external spacetime is of the black-hole type, while for $b > 0$ the external spacetime can be of both black-hole and naked-singularity type. Then the ECS surface radius $R$ can be located also above the unstable (outer) photon circular orbit. Such basically new types of the spacetimes strongly alter the trapping phenomena as compared to the standard case of $b = 0$. It is shown that the neutrino trapping effects are slightly lowered by the presence of physically more plausible case of $b < 0$, as compared to the standard internal Schwarzschild spacetime, while they can be magnified by positive tidal charges if $b < 1$ and lowered for $b > 1$. However, potential astrophysical relevance of the trapping phenomena is strongly enhanced for negative tidal charges enabling a significant enlargement of the ECS surface radius to values coherent with recent observations

Neutrino trapping in extremely compact objects described by the internal Schwarzschild-(anti-)de Sitter spacetimes

“…In the S(a)dS spacetimes the internal and external geometry are smoothly matched at the surface radius x, similarly to the case of Schwarzschild spacetimes (y = 0) and contrary to braneworld spacetimes [16,43], where the tidal effects of the bulk space are reflected by the "derivative jump" in the matching surface [13]. The ECS of the S(a)dS type are simply given by the condition…”

“…3 for details). Similarly to [52,43] we define two radii of ECS internal space that are relevant for the trapping effect. The "internal" radius r b(i) where the value of the internal effective potential is equal to its value at surface of the star, and the "external" radius r b(e) where the value of the internal effective potential is equal to the value of the external effective potential at r = 3.…”

“…3) may generally appear outside the ECS, being trapped by the strong gravitational field. Therefore, we divide the trapped neutrinos into two families, see [52,43]:…”

“…In the paper [43], we have studied the trapping effect in the braneworld ECS, using the uniform density model and the external field described by the Reissner-Nordström geometry with the tidal charge parameter b reflecting (tidal) effect of the bulk space on the ECS structure on the brane [13]. Such a model is a natural one and its properties were widely discussed in the recent literature [1,6,9,21,28,29,35,36,47].…”

“…Such a model is a natural one and its properties were widely discussed in the recent literature [1,6,9,21,28,29,35,36,47]. Due to the special braneworld matching conditions on the surface R of the braneworld compact stars, see [16,43] for details, their internal and external geometries are not smoothly matched (their derivatives differ at R), and the definition of ECS is more complex than in the case of internal Schwarzschild spacetimes; it depends on the value of the tidal charge b and it is not (always) directly related to the radius of the unstable photon circular orbit of the external spacetime (see [16,43] for details). We have considered negative (positive) tidal charges related to positive (negative) tension of the brane, demonstrating that for more realistic [11,13] negatively tidally charged spacetimes the surface of ECS overcomes the limit of R = 3G M/c 2 rising up significantly the possible relevance of trapping phenomena [43].…”