In physics, curved spacetime is the mathematical model in which, with Einstein's theory of general relativity, gravity naturally arises, as opposed to...

field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory uses...

interpretation proved vital to the general theory of relativity, wherein spacetime is curved by mass and energy. Non-relativistic classical mechanics treats time...

Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved spacetime, a general Lorentzian...

quantum field theories in curved spacetime. These theories rely on general relativity to describe a curved background spacetime, and define a generalized...

physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may not be the...

of the curved 4-dimensional spacetime geometry around the star onto 3-dimensional space. A curve is a geodesic if the tangent vector of the curve at any...

where gravity is often visualized as curved spacetime. The Friedmann–Lemaître–Robertson–Walker metric is a curved metric which forms the current foundation...

implemented to include an algebraic version of quantum field theory in curved spacetime. Indeed, the viewpoint of local quantum physics is in particular suitable...

at that surface. After Hawking showed that quantum field theory in curved spacetime (without reference to the Einstein field equations) predicted that...

Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation...

Dirac equation in flat spacetime according to special relativity. It is possible to formulate the Dirac equation in curved spacetime. This article developed...

momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum...

ideal black body, as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same...

equations with special relativity manifest. Maxwell's equations in curved spacetime, commonly used in high-energy and gravitational physics, are compatible...

connects disparate points in spacetime. It may be visualized as a tunnel with two ends at separate points in spacetime (i.e., different locations, different...

time traces out a line or curve on a spacetime diagram, referred to as the object's world line. Each point in a spacetime diagram represents a unique...

extended, at least as a classical field theory, to curved spacetime. This arises similarly to the flat spacetime case, from coupling a free electromagnetic theory...

mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to...

Rohrlich (1963), Harry Lass (1963), and in relation to both flat and curved spacetime of general relativity by Wolfgang Rindler (1960, 1966). For details...

later when Einstein developed general relativity, which introduced a curved spacetime to incorporate gravity, the phrase "special relativity" was not used...

force field. With natural units this becomes Klein–Gordon equation on curved spacetime for a real scalar field ∇ a ∇ a Φ − m 2 Φ = 0 {\displaystyle \nabla...

}=0\,.} The electromagnetic wave equation is modified in two ways in curved spacetime, the derivative is replaced with the covariant derivative and a new...

manifestation of curved spacetime instead of being due to a force propagated between bodies. In Einstein's theory, energy and momentum distort spacetime in their...

flat Minkowski space, and not curved space nor GR. It is possible to formulate quantum field theory in curved spacetime, yet even this still cannot incorporate...

relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external,...

the universe. One major obstacle is that for quantum field theory in curved spacetime with a fixed metric, bosonic/fermionic operator fields supercommute...

proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight...

physics, Minkowski space (or Minkowski spacetime) (/mɪŋˈkɔːfski, -ˈkɒf-/) is the main mathematical description of spacetime in the absence of gravitation. It...

gravity supermultiplet. This is because mass is not well-defined in curved spacetimes, with P μ P μ {\displaystyle P_{\mu }P^{\mu }} no longer being a Casimir...