Gravitational potential energy plays a critical role in dictating the motion of comets. When a comet is far from the Sun, it possesses a high (less negative) gravitational potential energy and low kinetic energy. As it approaches the Sun, the gravitational potential energy decreases (becomes more negative), and the kinetic energy increases due to the Sun’s gravitational pull. This energy transformation governs the comet’s increase in speed as it nears the Sun. The interplay between gravitational potential energy and kinetic energy is essential in understanding the elliptical orbits of comets and their varying speeds along these orbits.

Yes, gravitational potential energy can be considered a form of stored energy. It’s the energy associated with an object due to its position within a gravitational field. In the context of Earth, for example, water stored at a height has gravitational potential energy that can be harnessed for generating electricity, as in hydroelectric power plants. In space, a spacecraft can utilise gravitational potential energy through gravitational assists or "slingshot" manoeuvres, where it gains kinetic energy and speed by passing close to a planet, "stealing" some of the planet’s orbital energy.

Gravitational potential energy is grounded in Newtonian physics, but it finds an intriguing extension and modification in Einstein’s theory of general relativity. In general relativity, gravity isn’t just a force between masses but is a curvature of spacetime caused by mass and energy. The concept of gravitational potential energy is still valid but becomes more complex and nuanced. It's related to the curvature of spacetime, and energy calculations involve tensors and the geometry of spacetime, marking a shift from the simplistic inverse-square law and offering a more comprehensive description of gravitational interactions, especially in extreme conditions like those near a black hole.

In scenarios involving multiple celestial bodies, like a moon orbiting a planet that orbits a star, the gravitational potential energy is calculated considering each pair of interacting bodies. Each pair contributes to the total gravitational potential energy of the system. For the moon, there's energy associated with its interaction with the planet and the star. For the planet, there's energy associated with the star and the moon. The total energy is the sum of these individual energies. This complex interplay of gravitational forces and energies is crucial in understanding the stability and dynamics of multi-body celestial systems.

The concept of gravitational potential energy is profoundly illustrated by black holes. These cosmic entities possess immense mass concentrated in a small volume, leading to extraordinarily high gravitational forces. Objects near a black hole have significantly large (more negative) gravitational potential energy due to the intense gravitational pull. The energy becomes infinitely negative as one approaches the event horizon, indicating an infinite amount of work is needed to "pull" the object back from this point. It underscores the idea that anything crossing the event horizon requires infinite energy to escape, thus getting inevitably drawn into the black hole.