Alternatives to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition with Einstein's theory of general relativity. There have been many different attempts at constructing an ideal theory of gravity.^[1]

These attempts can be split into four broad categories based on their scope. In this article, straightforward alternatives to general relativity are discussed, which do not involve quantum mechanics or force unification. Other theories which do attempt to construct a theory using the principles of quantum mechanics are known as theories of quantized gravity. Thirdly, there are theories which attempt to explain gravity and other forces at the same time; these are known as classical unified field theories. Finally, the most ambitious theories attempt to both put gravity in quantum mechanical terms and unify forces; these are called theories of everything.

None of these alternatives to general relativity have gained wide acceptance. General relativity has withstood many tests,^[2][3] remaining consistent with all observations so far. In contrast, many of the early alternatives have been definitively disproven. However, some of the alternative theories of gravity are supported by a minority of physicists, and the topic remains the subject of intense study in theoretical physics.

Motivations

After general relativity, attempts were made either to improve on theories developed before general relativity, or to improve general relativity itself. Many different strategies were attempted, for example the addition of spin to general relativity, combining a general relativity-like metric with a spacetime that is static with respect to the expansion of the universe, getting extra freedom by adding another parameter. At least one theory was motivated by the desire to develop an alternative to general relativity that is free of singularities.

Experimental tests improved along with the theories. Many of the different strategies that were developed soon after general relativity were abandoned, and there was a push to develop more general forms of the theories that survived, so that a theory would be ready when any test showed a disagreement with general relativity.

By the 1980s, the increasing accuracy of experimental tests had all confirmed general relativity; no competitors were left except for those that included general relativity as a special case. Further, shortly after that, theorists switched to string theory which was starting to look promising, but has since lost popularity. In the mid-1980s a few experiments were suggesting that gravity was being modified by the addition of a fifth force (or, in one case, of a fifth, sixth and seventh force) acting in the range of a few meters. Subsequent experiments eliminated these.

Motivations for the more recent alternative theories are almost all cosmological, associated with or replacing such constructs as "inflation", "dark matter" and "dark energy". Investigation of the Pioneer anomaly has caused renewed public interest in alternatives to general relativity.^{[citation needed]}

Notation in this article

${\displaystyle c\;}$ is the speed of light, ${\displaystyle G\;}$ is the gravitational constant. "Geometric variables" are not used.

Latin indices go from 1 to 3, Greek indices go from 0 to 3. The Einstein summation convention is used.

${\displaystyle \eta _{\mu \nu }\;}$ is the Minkowski metric. ${\displaystyle g_{\mu \nu }\;}$ is a tensor, usually the metric tensor. These have signature (−,+,+,+).

Partial differentiation is written ${\displaystyle \partial _{\mu }\varphi \;}$ or ${\displaystyle \varphi _{,\mu }\;}$. Covariant differentiation is written ${\displaystyle \nabla _{\mu }\varphi \;}$ or ${\displaystyle \varphi _{;\mu }\;}$.

General relativity

For comparison with alternatives, the formulas of General Relativity^[4][5] are:

${\displaystyle \delta \int ds=0\,}$

${\displaystyle {ds}^{2}=g_{\mu \nu }\,dx^{\mu }\,dx^{\nu }\,}$

${\displaystyle R_{\mu \nu }={\frac {8\pi G}{c^{4}}}\left(T_{\mu \nu }-{\frac {1}{2}}g_{\mu \nu }T\right)\,}$

which can also be written

${\displaystyle T^{\mu \nu }={c^{4} \over 8\pi G}\left(R^{\mu \nu }-{\frac {1}{2}}g^{\mu \nu }R\right)\,.}$

The Einstein–Hilbert action for general relativity is:

${\displaystyle S=\frac{c^4}{16\mathrm{\pi <!--\; \pi \; -->}G}\int <!--\; \int \; -->R\sqrt{-<!--\; -\; -->g}}$Zdroj:https://en.wikipedia.org?pojem=Alternatives_to_general_relativity
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