  Bipartite entanglement for states of a non-interacting bosonic or fermionic
field in the spacetime of a spherically symmetric black hole of
Einstein-Gauss-Bonnet gravity, is investigated. Although the initial state is
chosen to be maximally entangled as the Bell states, the Hawking-Unruh effect
causes the state to be mixed and the entanglement degrades, but with different
asymptotic behaviors for the fermionic and bosonic fields. The Gauss-Bonnet
term with positive $\alpha$ can play an anti-gravitation role and so this
causes to decrease the Hawking-Unruh effect and consequently reduces the
entanglement degradation. On the other hand, the suggested higher dimensions
for the spacetime, lead to more entanglement degradation by increasing the
dimension. There is a dramatic difference between the behaviors of the
entanglement in terms of the radius of the horizon for a five-dimensional black
hole and that for higher dimensional black holes.
