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General Relativity
General Relativity
In General Relativity, Albert Einstein expanded Newton’s inverse square law of gravity to include the curvature of spacetime. On the left of the equation is the curvature of space, on the right energy. This equation expresses the curvature of space and how it is effected by mass and energy. (Gμν is the Einsteinian curvature tensor of spacetime and Tμν is the energy-momentum tensor of matter in spacetime.)
The Schwarschild Radius
The Schwarschild Radius
Karl Schwarzschild applied Einstein’s equation to spherical objects, his equation now named the Schwarzchild metric. It revealed the existance of a radius where light could not escape the gravity of a ceratain mass, demonstrating the existence of black holes.
The Schwarschild Metric
The Schwarschild Metric
Kruska-Szekeres Coordinate Universe
Kruska-Szekeres Coordinate Universe
Kruskal–Szekeres coordinates extend the Schwarzschild metric across the event horizon, Not visible in standard coordinates, the transformation shows the full structure of Schwarzschild spacetime, revealing a spacetime diagram with four distinct regions.
Outside the event horizon ( r > 2M )
At the event horizon ( r = 2M )
Inside the event horizon ( r <2M )
Standard Schwarzschild coordinates break down at the event horizon — they become singular (the math blows up even though the spacetime is perfectly smooth there).
Kruskal–Szekeres coordinates fix that by reparametrizing the spacetime in a way that’s smooth across the horizon, letting you explore:
The black hole interior (future region)
The white hole interior (past region)
Two exterior universes (Region I and Region IV)
The Kerr Black Hole Metric in Boyer-Linquist Coordinates
The Kerr Black Hole Metric in Boyer-Linquist Coordinates
Most Black holes probably rotate. Boyer–Lindquist coordinates are a coordinate system used to express the Kerr metric, which describes the spacetime around an uncharged rotating black hole. They are the rotating black hole analog of the Kruska-Szekeres coordinates describing a non-rotaiting Schwarzschild black hole. Similar to a a Reissner-Nordström BH, the Kerr BH has two horizons: the Outer Event Horizon, located at the Schwarzschild event horizon, and an inner Cauchy Horizon, the point where all normal physics breaks down. Also of future interest is the area inbetween.
Morris-Thorne Wormhole Metric
Morris-Thorne Wormhole Metric
This is a python program to simulate a particle or traveler traversing a Kerr wormhole, with a time traveling outcome.
Python Traversable Kerr Wormhole with time travel:
Frame dragging increases on the outer edges of the Kerr wormhole, increasing time like curves.
Exotic Matter
Exotic Matter
As is evident from this diagram, when an observer crosses over the event horizon, r
and t switch roles (the Schwarzschild metric components
gtt and grr change sign). In (a), the Schwarzschild black
hole has a singularity at r = 0. In (b), the singularity is replaced by an initial time surface of the de Sitter
universe. In other words, the location r = 0 from the
viewpoint of an observer in the mother universe becomes
the initial time surface t = 0 for an observer in the baby
de Sitter universe. Hence all of the matter that will fall
into the black hole, eventually reaching the same place
(r = 0) but at different times will enter into the baby
universe at the same time (t = 0) but in different places. - P 2010
Why does it matter what happens inside a Kerr Black Hole? : We are in a Kerr Black Hole.
Slow rotation could cause alignments in large-scale structure of the universe, and explain the Axis of Evil. Ssuch rotation would cause the quadrupole and octupole modes in the CMB to align in the direction of the rotation axis — consistent with what’s observed.
A Kerr interior has a ring singularity and a weird causal structure — with paths to other regions of spacetime. Some speculative models try to match this to the structure of our universe — but it’s very hard to test observationall
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