**Publication date:** Nov 2011

**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-

Nordström 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.

**Authors:**

Stuchlík, Zdeněk; Hladík, Jan; Urbanec, Martin;