Math 2.0

Relativity and gravitational theory Definition

Alternatives to general relativity

Builds on General relativityEinstein field equationsLovelock's theoremParameterized post-Newtonian formalism

Definition

An alternative to general relativity is a classical theory of gravitation whose field equations or equations of motion differ from those of general relativity. Concretely, the theory departs from at least one of the following features of general relativity:

  1. the gravitational field is a Lorentzian metric gg on a four-dimensional manifold and there are no other gravitational fields;
  2. the metric obeys the Einstein field equations, possibly with a cosmological constant;
  3. the connection used to define curvature is the Levi-Civita connection of gg.

Remarks

By Lovelock's theorem, in four dimensions a local action for a metric alone with second-order field equations gives the Einstein field equations. So an alternative must add fields, allow higher derivatives, change the dimension or the connection, or give up locality. Example: Brans–Dicke theory adds a scalar field to the metric, so it breaks clause 1. Its predictions differ from those of general relativity by terms that vanish as its coupling constant grows. Non-example: writing the Einstein field equations in different coordinates, or in the ADM form, gives the same theory, so it is not an alternative. A metric theory is an alternative in which matter couples only to a single metric; such theories satisfy the Einstein equivalence principle and are compared through the parameterized post-Newtonian formalism.

Reading path

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Cosmological constant, concept, no evidence levelCosmological constantconceptEinstein field equations, concept, no evidence levelEinstein field equati…conceptEinstein tensor, concept, no evidence levelEinstein tensorconceptEinstein–Hilbert action, concept, no evidence levelEinstein–Hilbert acti…conceptGeneral relativity, concept, no evidence levelGeneral relativityconceptLorentzian manifold, concept, no evidence levelLorentzian manifoldconceptParameterized post-Newtonian formalism, concept, no evidence levelParameterized post-Ne…conceptTensor field, concept, no evidence levelTensor fieldconceptLovelock's theorem, statement, no evidence levelLovelock's theoremstatementAlternatives to general relativity, definition, no evidence levelAlternatives to gener…definition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Cosmological constant concept
  2. Einstein field equations concept
  3. Einstein tensor concept
  4. Einstein–Hilbert action concept
  5. General relativity concept
  6. Lorentzian manifold concept
  7. Parameterized post-Newtonian formalism concept
  8. Tensor field concept
  9. Lovelock's theorem statement
  10. Alternatives to general relativity definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Alternatives_to_general_relativity
About this page
TagRK6GB9B4MY
URIm2://RK6GB9B4MY
Kinddefinition
WritingW0 stub
MSC83D05
DefinesAlternatives to general relativity
UsesGeneral relativity, Einstein field equations, Lovelock's theorem, Parameterized post-Newtonian formalism
Changed3 November 2026

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