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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 ...
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.
which is known as the discrete-time dynamic Riccati equation of this problem. The steady-state characterization of P, relevant for the infinite-horizon problem in which T goes to infinity, can be found by iterating the dynamic equation repeatedly until it converges; then P is characterized by removing the time subscripts from the dynamic equation.
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).
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 ...
While a system of 3 bodies interacting gravitationally is chaotic, a system of 3 bodies interacting elastically is not. [clarification needed] There is no general closed-form solution to the three-body problem. [1] In other words, it does not have a general solution that can be expressed in terms of a finite number of standard mathematical ...
A key tool used in the formulation and proof of the singularity theorems is the Raychaudhuri equation, which describes the divergence of a congruence (family) of geodesics. The divergence of a congruence is defined as the derivative of the log of the determinant of the congruence volume. The Raychaudhuri equation is
These tensor fields should obey any relevant physical laws (for example, any electromagnetic field must satisfy Maxwell's equations).Following a standard recipe which is widely used in mathematical physics, these tensor fields should also give rise to specific contributions to the stress–energy tensor. [1]