{#SECogeoi}
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In terms of the tetrad formalism the metric (\[EQmetric\]) reads $$\mathrm{d} s^{2} = -[\omega^{(t)}]^{2}
                         +[\omega^{(r)}]^{2}
                         +[\omega^{(\theta)}]^{2}
                         +[\omega^{(\phi)}]^{2},$$ where $$\omega^{(t)}  = A(r)\,\mathrm{d} t,\quad
      \omega^{(r)}      = B(r)\,\mathrm{d} r,\quad
      \omega^{(\theta)} = r\,\mathrm{d} \theta,\quad
      \omega^{(\phi)}   = r\sin\theta\,\mathrm{d} \phi.$$ Since there is $e^{\mu}_{(\alpha)} = \left[\omega^{(\alpha)}_{\mu}\right]^{-1}$, the tetrad of 4-vectors is given by $$\vec{e}_{(t)}  = \frac{1}{A(r)} \frac{\partial}{\partial t},\quad
      \vec{e}_{(r)}      = \frac{1}{B(r)} \frac{\partial}{\partial r},\quad
      \vec{e}_{(\theta)} = \frac{1}{r}    \frac{\partial}{\partial \theta},\quad
      \vec{e}_{(\phi)}   = \frac{1}{r\sin\theta}\frac{\partial}{\partial \phi}.$$ Tetrad components of 4-momentum of a test particle or a photon are determined by the projections $p_{(\alpha)} = p_{\mu}e^{\mu}_{(\alpha)}$, $p^{(\alpha)} = p^{\mu}\omega_{\mu}^{(\alpha)}$ which give quantities measured by the local observers.

Null geodesics and effective potential {#SECngaep}
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We consider the period of evolution and cooling of ECS when their temperature falls down enough that the motion of neutrinos can be considered free, i.e., geodetical. We can assume this period starts at the moment when mean free path of neutrinos becomes to be comparable to the radius $R$, i.e., in hours after the gravitational collapse creating the compact object [@Gle:1992:PHYSR4:; @Gle:2000:CompactStars:; @Hae-Zdu:1986:NATURE:; @Web:1999:Pul:; @Sha-Teu:1983:BHWDNS:]. In fact, there are arguments that this condition starts to be fulfilled about 50 s after collapse to a proto-neutron star [@Lat-Pra:2007:PhysRep:; @Lat-Pra:2004:SCIENCE:]. Weak interaction of ultrarelativistic (massless) neutrinos 