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A spherically symmetric spacetime is one that is invariant under rotations and taking the mirror image. A static spacetime is one in which all metric components are independent of the time coordinate t {\displaystyle t} (so that ∂ ∂ t g μ ν = 0 {\displaystyle {\tfrac {\partial }{\partial t}}g_{\mu \nu }=0} ) and the geometry of the ...
Thus, a static spacetime is a stationary spacetime satisfying this additional integrability condition. These spacetimes form one of the simplest classes of Lorentzian manifolds . Locally, every static spacetime looks like a standard static spacetime which is a Lorentzian warped product R × {\displaystyle \times } S with a metric of the form
The principle of local Lorentz covariance, which states that the laws of special relativity hold locally about each point of spacetime, lends further support to the choice of a manifold structure for representing spacetime, as locally around a point on a general manifold, the region 'looks like', or approximates very closely Minkowski space ...
Distinguishing these VSI spacetimes from Minkowski spacetime requires comparing non-polynomial invariants [1] or carrying out the full Cartan–Karlhede algorithm on non-scalar quantities. [2] [3] All VSI spacetimes are Kundt spacetimes. [4] An example with this property in four dimensions is a pp-wave.
De Sitter suggested that spacetime curvature might not be due solely to gravity [2] but he did not give any mathematical details of how this could be accomplished. In 1968 Henri Bacry and Jean-Marc Lévy-Leblond showed that the de Sitter group was the most general group compatible with isotropy, homogeneity and boost invariance. [3]
Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy , as expressed in the mass–energy equivalence formula E = m c 2 {\displaystyle E=mc^{2}} , where c {\displaystyle ...
Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects of spacetime.
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.