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  2. Exact solutions in general relativity - Wikipedia

    en.wikipedia.org/wiki/Exact_solutions_in_general...

    Noteworthy examples of vacuum solutions, electrovacuum solutions, and so forth, are listed in specialized articles (see below). These solutions contain at most one contribution to the energy–momentum tensor, due to a specific kind of matter or field. However, there are some notable exact solutions which contain two or three contributions ...

  3. Introduction to the mathematics of general relativity - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_the...

    For example, Christoffel symbols cannot be tensors themselves if the coordinates do not change in a linear way. In general relativity, one cannot describe the energy and momentum of the gravitational field by an energy–momentum tensor. Instead, one introduces objects that behave as tensors only with respect to restricted coordinate ...

  4. No-hair theorem - Wikipedia

    en.wikipedia.org/wiki/No-hair_theorem

    The no-hair theorem (which is a hypothesis) states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent externally observable classical parameters: mass, angular momentum, and electric charge.

  5. Mathematics of general relativity - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_general...

    The sources of any gravitational field (matter and energy) is represented in relativity by a type (0, 2) symmetric tensor called the energy–momentum tensor. It is closely related to the Ricci tensor. Being a second rank tensor in four dimensions, the energy–momentum tensor may be viewed as a 4 by 4 matrix.

  6. Two-body problem in general relativity - Wikipedia

    en.wikipedia.org/wiki/Two-body_problem_in...

    No exact solutions of the Kepler problem have been found, but an approximate solution has: the Schwarzschild solution. This solution pertains when the mass M of one body is overwhelmingly greater than the mass m of the other. If so, the larger mass may be taken as stationary and the sole contributor to the gravitational field.

  7. Solutions of the Einstein field equations - Wikipedia

    en.wikipedia.org/wiki/Solutions_of_the_Einstein...

    But if the exact solution is required or a solution describing strong fields, the evolution of the metric and the stress–energy tensor must be solved for together. To obtain solutions, the relevant equations are the above quoted EFE (in either form) plus the continuity equation (to determine evolution of the stress–energy tensor):

  8. Introduction to general relativity - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_general...

    In special relativity, parallel geodesics remain parallel. In a gravitational field with tidal effects, this will not, in general, be the case. If, for example, two bodies are initially at rest relative to each other, but are then dropped in the Earth's gravitational field, they will move towards each other as they fall towards the Earth's center.

  9. n-body problem - Wikipedia

    en.wikipedia.org/wiki/N-body_problem

    A prototypical example of a planetary problem is the Sun–Jupiter–Saturn system, where the mass of the Sun is about 1000 times larger than the masses of Jupiter or Saturn. [18] An approximate solution to the problem is to decompose it into n − 1 pairs of star–planet Kepler problems, treating interactions among the planets as perturbations.