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Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events, as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational ...
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun.
Special relativity is defined in the absence of gravity. For practical applications, it is a suitable model whenever gravity can be neglected. Bringing gravity into play, and assuming the universality of free fall motion, an analogous reasoning as in the previous section applies: there are no global inertial frames. Instead there are ...
Given the covariant derivative, one can define the parallel transport of a vector v at a point P along a curve γ starting at P. For each point x of γ, the parallel transport of v at x will be a function of x, and can be written as v(x), where v(0) = v. The function v is determined by the requirement that the covariant derivative of v(x) along ...
The equivalence between inertia and gravity cannot explain tidal effects – it cannot explain variations in the gravitational field. [10] For that, a theory is needed which describes the way that matter (such as the large mass of the Earth) affects the inertial environment around it.
The Cauchy problem (sometimes called the initial value problem) is the attempt at finding a solution to a differential equation given initial conditions. In the context of general relativity , it means the problem of finding solutions to Einstein's field equations — a system of hyperbolic partial differential equations — given some initial ...
The time value of money means that money is worth more now than in the future because of its potential growth and earning power over time. In other words, receiving a dollar today is more valuable ...
The most commonly discussed aspect of the problem of time is the Frozen Formalism Problem. The non-relativistic equation of quantum mechanics includes time evolution: i ℏ ∂ ∂ t ψ ( t ) = H ψ ( t ) , {\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi (t)=H\psi (t),} where H {\displaystyle H} is an energy operator characterizing ...