The invention relates to an electrical machine (1, 51), in particular an asynchronous machine, comprising a stator (2), a rotor (4) which is rotatably mounted about a rotation axis (3) and magnetically interacts with the stator (2) during operation of the electrical machine (1, 51), a shaft (5) on which the rotor (4) is fixed and which has an axial hole (6), and an inflow element (7, 47) which extends into the axial hole (6) such that a coolant (15), in particular a cooling liquid (15), can flow into the axial hole (6) from the inflow element (7, 47). The invention also relates to a cooling system (50) comprising an electrical machine (1, 51) and a coolant circuit (55) for transporting the coolant (15), in particular the cooling liquid (15), through the axial hole (6), and to a vehicle (61) comprising a cooling system (50).