Fermionic steering and its monogamy relations in Schwarzschild spacetime

Using two different types of quantification for quantum steering, we study the influence of Hawking radiation on quantum steering for fermionic fields in Schwarzschild spacetime. The degradation for the steering between physically accessible observers and the generation for the steering between physically accessible and inaccessible observers induced by Hawking radiation are studied. We also reveal the difference between the two types of quantification for steering, and find some monogamy relations between steering and entanglement. Furthermore, we show the different properties between fermionic steering and bosonic steering in Schwarzschild spacetime.