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Penrose diagram of an infinite Minkowski universe, horizontal axis u, vertical axis v. In theoretical physics, a Penrose diagram (named after mathematical physicist Roger Penrose) is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity.
The Cauchy horizon inside a charged or rotating black hole might be an example of a weak singularity. Strong singularities: A strong singularity is one where tidal forces become infinite. In a strong singularity, any object would be destroyed by infinite tidal forces as it approaches the singularity.
The black hole event horizon bordering exterior region I would coincide with a Schwarzschild t-coordinate of + while the white hole event horizon bordering this region would coincide with a Schwarzschild t-coordinate of , reflecting the fact that in Schwarzschild coordinates an infalling particle takes an infinite coordinate time to reach the ...
Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory, as in the ultraviolet catastrophe , re-normalization , and instability of a hydrogen atom predicted by the Larmor formula .
Even after such symmetry reductions, the reduced system of equations is often difficult to solve. For example, the Ernst equation is a nonlinear partial differential equation somewhat resembling the nonlinear Schrödinger equation (NLS). But recall that the conformal group on Minkowski spacetime is the symmetry group of the Maxwell equations.
A particular form of the LQ problem that arises in many control system problems is that of the linear quadratic regulator (LQR) where all of the matrices (i.e., , , , and ) are constant, the initial time is arbitrarily set to zero, and the terminal time is taken in the limit (this last assumption is what is known as infinite horizon). The LQR ...
A cosmological horizon is a measure of the distance from which one could possibly retrieve information. [1] This observable constraint is due to various properties of general relativity, the expanding universe, and the physics of Big Bang cosmology. Cosmological horizons set the size and scale of the observable universe. This article explains a ...
A black hole event horizon is teleological in nature, meaning that it is determined by future causes. [14] [15] [16] More precisely, one would need to know the entire history of the universe and all the way into the infinite future to determine the presence of an event horizon, which is not possible for quasilocal observers (not even in principle).