To the best of my (limited) knowledge of theoretical physics you cannot rip a pair of virtual particles apart without investing enough energy to create another pair of virtual particles...
If Hawking Radiation is real, how can the gravity of an event horizon apply enough force to rip a pair of virtual particles apart without creating another pair of virtual particles in the process?
The particle-antiparticle view is just a pictorial simplification of the process that bears a lot of issues. It is meant as an illustration, but shouldn't be taken too seriously.
What actually happens in the process is that the very notion of particle is dependent on an observer and is not a fundamental notion in Physics. In the particular case of Hawking radiation, the notion of particle that exists in the spacetime before a star collapses into a black hole does not coincide with the notion of particle after the collapse has come to an equilibrium state in which the black hole is now stationary. As a consequence, a stationary observer sees creation of particles by the black hole, but that is due to the fact that the very notion of what is a particle has changed. I've given a more detailed description in this answer, which still attempts to not dive too deep into the math.
Hawking's original article in fact even states about the particle-antiparticle viewpoint that
It should be emphasized that these pictures of the mechanism responsible for thermal emission and area decrease are heuristic only and should not be taken too literally.
Hawking radiation is a prediction from a subject known as Quantum Field Theory in Curved Spacetime. As the name suggests, its fundamental objects are fields, not particles. In a few situations, it is convenient to interpret the field variables in terms of particles and it might lead to some intuition, but it is necessary to be careful and recall that the particle viewpoint is not fundamental, but rather a cartoonish illustration of the process meant to provide a bit more intuition.
The concept of virtual particles is a mathematical definition in the calculation of elementary particle interactions using quantum field theory with Feynman diagrams. One cannot "rip apart" virtual loops.
here is a simple virtual diagram
The virtual is called a photon because it has the quantum numbers of a photon but not the mass. It is useful to keep track of quantum number conservation laws that have to be obeyed at each vertex.
Here is a simplified diagram for Hawking radiation that gives rise to your misconception.
Figure 3: As explained in the text, when pairs of particles are created in the neighborhood of a black hole and one of them falls inside it, the other particle escapes as Hawking radiation
The virtual loops drawn are to illustrate that there is a lot of energy around the horizon of the black hole, represented by the virtual loops. These loops have the virtual particles which have four momenta. Hand waving , one can say that there is a probability one of the virtual particles to fall in the gravity well of the black hole, leaving a real particle with four momentum to go away taking the energy from the black hole. The link tries to clarify the misconceptions coming from this naive assumption.
