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An example is the apparent (longitudinal) singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (i.e., jumping from longitude 0 to longitude 180 degrees). In ...
A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different frame. An example of this is the apparent singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the ...
The simplest example of a pinch point is the hypersurface defined by the equation = called Whitney umbrella. The pinch point (in this case the origin) is a limit of normal crossings singular points (the v {\displaystyle v} -axis in this case).
Consider a smooth real-valued function of two variables, say f (x, y) where x and y are real numbers.So f is a function from the plane to the line. The space of all such smooth functions is acted upon by the group of diffeomorphisms of the plane and the diffeomorphisms of the line, i.e. diffeomorphic changes of coordinate in both the source and the target.
In theoretical physics, a chronometric singularity (also called a temporal or horological singularity) is a point at which time cannot be measured or described. An example involves a time at a coordinate singularity, e.g. a geographical pole. Since time on Earth is measured through longitudes, and no unique longitude exists at a pole, time is ...
The Big Bang, for example, appears as a singularity in ordinary time but, when modelled with imaginary time, the singularity can be removed and the Big Bang functions like any other point in four-dimensional spacetime. Any boundary to spacetime is a form of singularity, where the smooth nature of spacetime breaks down.
American computer scientist and futurist Ray Kurzweil has long argued that the singularity would likely occur around the middle of the 21st century, and with the rise of AI, his predictions are ...
There is no coordinate singularity at the Schwarzschild radius (event horizon). The outgoing ones are simply the time reverse of ingoing coordinates (the time is the proper time along outgoing particles that reach infinity with zero velocity). The solution was proposed independently by Paul Painlevé in 1921 [1] and Allvar Gullstrand [2] in 1922.