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2. Mathematics of general relativity - Wikipedia

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

   Numerical relativity is the sub-field of general relativity which seeks to solve Einstein's equations through the use of numerical methods. Finite difference , finite element and pseudo-spectral methods are used to approximate the solution to the partial differential equations which arise.

3. Introduction to the mathematics of general relativity - Wikipedia

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

   The mathematics of general relativity is complicated. In Newton's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates, meaning that many problems in Newtonian mechanics may be solved by algebra alone.

4. Einstein field equations - Wikipedia

   en.wikipedia.org/wiki/Einstein_field_equations

   The nonlinearity of the EFE distinguishes general relativity from many other fundamental physical theories. For example, Maxwell's equations of electromagnetism are linear in the electric and magnetic fields , and charge and current distributions (i.e. the sum of two solutions is also a solution); another example is Schrödinger's equation of ...

5. General relativity - Wikipedia

   en.wikipedia.org/wiki/General_relativity

   General relativity has emerged as a highly successful model of gravitation and cosmology, which has so far passed many unambiguous observational and experimental tests. However, there are strong indications that the theory is incomplete. [210] The problem of quantum gravity and the question of the reality of spacetime singularities remain open ...

6. Solutions of the Einstein field equations - Wikipedia

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

   This reflects the fact that the system is gauge invariant (in general, absent some symmetry, any choice of a curvilinear coordinate net on the same system would correspond to a numerically different solution.) A "gauge fixing" is needed, i.e. we need to impose 4 (arbitrary) constraints on the coordinate system in order to obtain unequivocal ...

7. List of unsolved problems in physics - Wikipedia

   en.wikipedia.org/wiki/List_of_unsolved_problems...

   [2] [3] Another problem lies within the mathematical framework of the Standard Model itself—the Standard Model is inconsistent with that of general relativity, to the point that one or both theories break down under certain conditions (for example within known spacetime singularities like the Big Bang and the centres of black holes beyond the ...

8. Two-body problem in general relativity - Wikipedia

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

   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.

9. List of mathematical topics in relativity - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical...

   2 General relativity. 3 Cosmology. ... This is a list of mathematical topics in relativity, by Wikipedia page. ... horizon problem;