Einstein-Æther Theories| Einstein-Æther 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] = (16πG)−1 ∫ d4x (−g)1/2 [R + c1 (∇a ub) (∇a ub) + c2 (∇a ua)2 + c3 (∇a ub) (∇b ua) + c4 (ua ∇a ub)2] ,
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 ci.
@ General References:
Jacobson & Mattingly PRD(01)gq/00,
PRD(01)gq/00,
gq/01-conf [in general relativity],
PRD(04)gq;
Eling et al gq/04-proc;
Foster PRD(05);
Foster & Jacobson PRD(06) [PN parameters];
Eling & Jacobson PRD(06)gq [2D theory];
Jacobson proc(08)-a0711,
PoS-a0801 [rev];
Withers CQG(09)-a0905 [quantum effective field theory];
Donnelly & Jacobson PRD(10)-a1008 [stability];
Garfinkle et al PRE(12)-a1207 [constraint equations and the weak gravitational field limit];
Haghani et al a1404
[with ua = ∇aφ];
Sarbach et al CQG(19)-a1902 [Cauchy formulation];
> s.a. Ether.
@ Constraints:
Bonvin et al PRD(08) [solar system];
Yagi et al PRD(14)-a1311 [binary pulsars].
@ Variations: Pujolàs & Sibiryakov JHEP(12)-a1109 [supersymmetric extension, and emergent Lorentz symmetry];
Jacobson & Speranza a1405 [on the scalar version];
Balakin & Lemos AP(14)-a1407 [with a Maxwell field];
Balakin PRD(16)-a1606
[axionic extension, and cosmology].
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
GN = G/[1−(c1+c4)/2] .
* Propagating modes:
There are 5, two spin-2 gravity modes {traveling at speed
v2 = 1/[1
− (c1
+ c3)], 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];
Trinh et al PRD(19)-a1811 [and the cmb];
> s.a. cmb polarization.
@ Cosmological solutions: Latta et al JCAP(16)-a1606 [perfect-fluid Kantowski-Sachs];
Campista et al CJP-a1807;
van den Hoogen et al JCAP(18)-a1809 [scalar field Kantowski-Sachs];
Roumeliotis et al EPJC(20)-a1911 [Bianchi V];
Casalino et al PRD(20)-a2003 [non-singular FLRW].
@ Spherical solutions:
Eling & Jacobson CQG(06);
Coley et al JCAP(15)-a1508 [with a tilted perfect fluid source];
Coley & Leon GRG(19)-a1905;
Chan et al a2003 [vacuum static, general solution].
@ 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];
Oost et al GRG(18)-a1804 [plane-fronted gravitational waves];
Paliathanasis & Leon EPJC(20)-a2004 [Einstein-æther-scalar];
> s.a. black holes;
gödel solutions; White Hole [collapse].
@ And observations: Oost et al PRD(18)-a1802 [constraints, after GW170817];
Khodadi & Saridakis a2012 [EHT observations of M87*].
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