The neutrino flavor oscillations in the static and spherically symmetric black-hole-like wormholes

Abstract We study the effects of neutrino lensing induced by a Damour–Solodukhin wormhole on the neutrino oscillation. We derive and calculate the flavour transition probabilities in the presence of Damour–Solodukhin factor $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> as a shift in the massive source to show that the neutrino flavour oscillation is also sensitive not only to the sign of difference between the squared masses but also to the individual mass of neutrinos in both the two-flavour and the three-flavour cases. As a consequence of parameter $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> within a region, a series of curves of probability function versus the azimuthal angle $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> with definite masses of neutrino can be plotted and their shapes resemble each other in the case of two-flavoured neutrinos and of three-flavoured ones. In view of the probability functions due to the wormhole, we reveal that the contribution of the factor $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> is novel. Based on our analytical and numerical discussions on the probability expressions, the difference of the neutrino flavour oscillation arising from the shift in the wormhole factor $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> is detectable. It is crucial that the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> as deviation from the black holes can change the shapes of the curves greatly, in the case of three-flavoured neutrinos in particular. The detailed comparisons can be made among our estimations depicted in the figures for neutrino oscillations and the measurements from the detector, which open a new window for judging whether the remote star as lens is black-hole-like wormhole or spherically symmetric black hole and further the wormhole factor $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> can be estimated.