Einstein-Ćther
Theories |

**In General** > s.a. hořava-lifshitz
gravity; modified general relativity.

* __Idea__: General
relativity coupled to a dynamical, unit timelike vector field *u*;
A generally covariant theory with a preferred vector field, or a preferred
frame.

* __Dynamics__: The
general form of the action is a sum of an Einstein-Hilbert term for the
metric and terms involving *u*; The leading ones are

*S*[*g*, *u*] = (16π*G*)^{–1}
∫ d^{4}*x* (–*g*)^{1/2}
[*R* + *c*_{1} (∇_{a}*u _{b}*)
(∇

but one can add terms with higher derivatives of *u* and/or
higher-order terms in the curvature; Stability and energy positivity imply
some inequalities for the coefficients *c _{i}*.

@

@

@

**Phenomenology** > s.a. black-hole
thermodynamics; horizons [universal
horizons]; positive-energy theorem.

* __Newtonian limit__:
The slow-motion, weak-field approximation can be made to agree with that
of general relativity, and in the limit one gets

*G*_{N}
= *G*/[1–(*c*_{1}+*c*_{4})/2]
.

* __Propagating modes__:
There are 5, two spin-2 gravity modes{traveling at speed *v*_{2}
= 1/[1–(*c*_{1}+*c*_{3})],
which leads to very strong bounds on the coefficients from the absence of
vacuum Cerenkov radiation}, two spin-1 modes and one spin-0 mode {each of
which has to travel at or above the speed of light, or possibly just a
little bit below, without this leading to causality violations};
Gravitational waves can have a longitudinal component.

@ __Cosmology in general__: Tartaglia & Radicella PRD(07);
Li et al PRD(08)-a0709
[primordial perturbations];
Zuntz et al PRL(08)-a0808;
Carruthers & Jacobson PRD(11)-a1011
[deviations from isotropy and alignment];
Meng & Du PLB(12)
[as an alternative to dark energy];
Barrow PRD(12)-a1201
[accelerating-universe solutions]; Saga et al PRD(13)-a1302
[generation of magnetic fields]; > s.a. cmb
polarization.

@ __Cosmological solutions__: Latta et al JCAP(16)-a1606 [perfect-fluid Kantowski-Sachs].

@ __Spherical solutions__: Eling & Jacobson CQG(06);
Coley et al JCAP(15)-a1508
[with a tilted perfect fluid source].

@ __Other solutions__: Bertolami & Páramos PRD(05)ht
[vacuum solutions]; Garfinkle et al PRD(07)gq
[gravitational collapse]; Eling et al PRD(07)-a0705
[neutron stars]; Foster PRD(07)-a0706
[binaries, strong field effects]; > s.a. black
holes; gödel solutions; White Hole [collapse].

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2016