Schwarzschild radius

Schwarzschild Radius, also called gravitational radius, distance that defines the size at which a spherical astronomical object such as a star becomes a black hole. A black hole is an object so dense that not even light can escape the pull of its gravitational force (seeGravitation). If an object collapses to within its Schwarzschild radius, it becomes a black hole. The radius is named after German astronomer Karl Schwarzschild, who derived the first model of a black hole in 1916.

Nothing, not even a particle moving at the speed of light, can escape the gravitational pull of a black hole. Therefore, the Schwarzschild radius is the largest radius that a body with a specific mass can have and still keep light from escaping. The formula for the Schwarzschild radius of a body is R_s = GM/c², where R_s is the Schwarzschild radius of the body, G is a constant known as the universal constant of gravitation, M is the mass of the object, and c is the speed of light.

To find the equation for the Schwarzschild radius of an object, Schwarzschild needed to know how massive a body has to be to keep light from escaping and how light behaves in such a strong gravitational field. French astronomer Pierre Laplace found the equation for escape velocity, or the speed an object needs to overcome the gravitational force of a body. Laplace noted in 1800 that the escape velocity would be greater than the speed of light for an object leaving a very small, dense body. German American physicist Albert Einstein explained how light behaves in a strong gravitational field in his general theory of relativity, published in 1916. In 1916 Karl Schwarzschild derived the first model of a black hole with help from the work of Laplace and Einstein.

The Schwarzschild radius of a black hole marks its event horizon, or the boundary past which light can enter but not escape. Astronomers believe that once an object collapses to within its Schwarzschild radius, it continues collapsing until it becomes a singularity, or a point with infinite density and a radius of zero.

The sun has a mass of 2×10³⁰ kg (4×10³⁰ lb) and a radius of about 700,000 km (about 400,000 mi). Its Schwarzschild radius is about 3 km (about 2 mi). If the sun were to collapse into a sphere with a radius of less than 3 km, light from the sun would be trapped and the sun would become a black hole. The sun, however, is not massive enough for it to collapse to this size and become a black hole (see Star: Evolution of Stars).

An object with a mass equal to that of the earth would have a Schwarzschild radius of about 3 mm (about 0.1 in). For an object with Mount Everest’s mass, the Schwarzschild radius is only about 1×10^-11 mm (4×10^-13 in). Some astronomers believe that any black hole smaller than this would be relatively unstable and would evaporate quickly, releasing gamma rays (see X Ray). Astronomers have speculated that the mysterious sources of celestial gamma ray bursts may be evaporating primordial black holes.

Old World (Mundus Vetus)

‘Mundus Vetus’. A term referring to our non-magical world which has given way to a culture different to that of Mundus Magicus.
The reason Earth is known as the ‘old’ world is similar to the reason why the Americas were referred to as the New World.
Most non-mage people calling our side ‘the real world’, mundus actualis is not exactly correct – in their own ways, they are both ‘real worlds’.

Western Magic

The style of magic based around the Europe’s cultural sphere of influence. With the spread of European culture and Christianity during the Age of Discovery, western-style magic has also spread throughout the world, with magical academies and similar institutions in many countries.

Closely conforming to the classic image of magicians, a western mage uses mana as energy, and requires spells, incantations, and catalysts to activate magic.

Unlike the amalgamation of ’schools’ that make up Eastern magic, such as Onmyoudou, Shinto, and Buddhism, there are no ’styles’ in Western magic. The two languages of incantation are Latin and Greek, with Latin being more common and Greek being solely used for High Ancient  – high-level magic.

However, as a mage can possess affinities, particular types of magic he excels in, the style of the caster differs based on these attributes. For example, if someone excels at the elements of wind and light, being able to turn wind into tornado barriers, and control all manners of gases using air as a medium. By comparison, while he would be able to solidify rock or metal, manipulate liquids, or control heat, he would find it difficult; these are the territories of earth, water, and fire mages, respectively.

Another point of note is the lack of ‘divine’ or holy magic or sorcery based on the power of Gods (such as those from the Greek, Scandinavian, or Celtic pantheons) due to the prohibitions of the Christian Church. Rather, most spells borrow and rely on the power of spirits.

Element

In modern science, the phenomenon of fire is the release of light and heat energy due to combustion. However, in classical elements, fire in itself is a “substance.” Magic is tied to a system of four elements, born from the world’s one ‘prime essense’, and from which forms the basis for all things in existence.

While magically-enabled fire or water are scientifically sound – for example, fire is a phenomenon, water is a liquid – they also ignore factors such as causation or physics, due to magic being born in a different age and cultural background. The substance called “fire” is simply a source of smoke, light, and heat, which burns everything in its surroundings. Regardless of any local conditions, “fire” will never lose these properties.

“Fire” will never burn out and can exist on water or in a complete vacuum; “water” will remain in liquid form regardless of temperature; “wind” will retain its designated velocity regardless of surrounding conditions; and “earth” will never change its physical composition.

However, it is entirely due to the stagnation within the magic societies that these beliefs continue to exist and prevail over modern science. It is quite possible, given time, and further interaction between the worlds of modern reality and classical magic, that even mages themselves will no longer be able to use magic in the future.

Incantation

The lines preceding the casting of a spell, which must be completed in their entirety for the magic to activate. The length of the incantation generally corresponds to the power of the spell itself – a spell with a short incantation has a weaker effect, and so on.

As noted, it is not the words that ‘activate’ a given magical phenomena, but the words themselves containing the power to enact or create those phenomena. In effect, what’s important is that the incantation is spoken correctly, and actually understanding the words is secondary.

Any spell which requires the caster’s name be cited in the incantation means the spell is commanding the power of a contracted, spiritually-powerful being.

Unincanted Spell
An incantation ’spoken’ internally, in the heart and mind that allows spells to be cast almost instantly. Thus it is possible to cast multiple spells at once, incanting one aloud while preparing another internally. However, it would be extremely difficult to use anything other than an incantation memorised to the point of being able to cast subconsciously.

The more capable the mage, the more powerful the spells he can cast without needing an actual incantation. Conversely, if a mage uses a full incantation for a spell which he is capable of casting unincanted, then the spell itself will become abnormally powerful.

Note that spells do exist which conditionally require a full incantation.

Activation Key
Particular to western magic, this is a specific type of incantation unique to each mage that precedes usage of magic – a password. Taking the ‘power of words’ further, the phrase doesn’t have to make sense or even be in a real language, as long as it feels ‘natural’ to the mage. It is considered a requirement for a proper mage and the setting of one’s activation key is a lengthy ritual.

Activation keys are spoken before the main incantation, but they can be skipped for simple spells. However, what exactly a “simple” spell is depends on the level of the mage; the more capable the mage, the more easily he will be able to cast powerful spells without needing his activation key.

Practe bigi nar is the general activation key used by novices before becoming full-fledged mages.

Focus

A tool possessing certain powers or symbols which assists in the invocation of magic. Most foci are staves, but other possibilities include rings, jewels, or books.

It is possible to cast magic without a focus – its purpose is to increase and stabilise the power output. As with activation keys, while novices will make use of simple wands, a customised focus is considered a requirement for a proper mage. However, it is not rare for high-class mages to dispose of foci entirely.