Non-exact solutions in general relativity explained

Non-exact solutions in general relativity are solutions of Albert Einstein's field equations of general relativity which hold only approximately. These solutions are typically found by treating the gravitational field,

g , as a background space-time, \gamma , (which is usually an exact solution) plus some small perturbation, h . Then one is able to solve the Einstein field equations as a series in h , dropping higher order terms for simplicity.

A common example of this method results in the linearised Einstein field equations. In this case we expand the full space-time metric about the flat Minkowski metric,

η _{\mu\nu} :g _{\mu\nu} = η _{\mu\nu} + h _{\mu\nu} + l{O}(h ^{2)} ,

and dropping all terms which are of second or higher order in

h .^[1]

See also

• Exact solutions in general relativity
• Linearized gravity
• Post-Newtonian expansion
• Parameterized post-Newtonian formalism
• Numerical relativity

Notes and References

1. Book: Sean M. Carroll. Spacetime and Geometry: An Introduction to General Relativity. 2004. Addison-Wesley Longman, Incorporated. 978-0-8053-8732-2. 274–279.