From Magna Confractio Dimensionis.

When light (electromagnetic waves) in a vacuum goes from one point to another, it takes the shortest and most direct course. In classical physics, light is a ‘straight line’. However, under the effect of any given amount of gravity, light is ‘curved’; thus, in space (space-time) affected by gravity, the shortest course between two points is not a straight line, because light is not exempt from this ‘curvature of space-time’ (gravitational lensing). You can say that gravity causes the curving of space-time.

Objects with more energy than mass, especially astronomical bodies, draw in material and electromagnetic waves in their vicinity towards their centre of gravity; normally, this would not cause any special phenomena. However, when the mass of the object is ‘M’, the universal gravitational constant is ‘G’, and the speed of light is ‘c’,

rg=2GM/c2

once this relationship (function) is established within the radius ‘rg’ (the Schwarzschild radius), the effect becomes different. As the ‘distortion’ from gravity becomes too large, light is not simply ‘bent’, but ‘falls’ into the object’s centre. Illustrated three-dimensionally, this would like a ‘hole’ – ie. a black hole.

As it is divided by twice the speed of light, the value tends be quite small. For example, an object the size of the Moon will have about a Schwarzschild radius of about 0.11mm. Of course, the power of Gravity Magic is to create gravity where there are no objects with mass. To put it another way, Gravity Magic is the ability to warp space-time without a mass/object medium. Again, if the strength of the gravitational influence from the source is ‘F’, universal gravitational constant is ‘G’, the mass of the source is ‘M’, the mass being influenced by gravity is ‘m’, and the distance between the two is ‘r’,

F=GMm/r2

Under the effect of Gravity Magic, as there is gravity there, ‘F’ cannot equal 0. If the left side does not equal 0, then of course the right side cannot equal 0, so even without actual mass, ‘M’ can never equal 0.

As the value of ‘M’ increases under the effect of Gravity Magic, the Schwarzschild radius also increases. Gravity Magic does not require a large space to operate, but that ‘M’ becomes the required value for a black hole to be created.

In the centre of the black hole, as gravity is infinite, the warping of space-time becomes infinitely large, and density also becomes infinite. Due to this unique point, ‘traditional’ physics cannot be applied. Tamaki’s Artifact, *Encompandentia Infinitas*, has the ability to control a bounded space. This ability, coming from a time before general relativity or modern times, was designed in a different cultural background. Thus, while it can expand a bounded space with an infinitely large space-time within, concepts such as curvature of space-time and density of matter should not be assumed to exist.

Again, *Encompandentia Infinitas* uses a limited amount of mana to expand and control an infinitely large space. However, even without an infinite expanse, to control the infinitely large warping of space-time and density would require a large amount of mana. Opposing that, creating a black hole requires neither infinite gravity nor mana; you can naturally generate gravitational forces that can overwhelm even light. On the other hand, the great power and basis of *Encompandentia Infinitas* is ‘controlling infinity’; as long as there are no abnormalities in Tamaki’s mental state, the bounded space can be maintained.

Of course, this does not change the fact that there is a large difference in mana requirement between ‘using gravity magic to create a black hole’ and ‘maintaining a bounded space while there is a black hole inside it’. High-level gravity magic is the natural enemy of bounded space magic; you only need a micro-black hole appearing for an instant to break apart a bounded space.