Minimal extension of Einstein's theory: The quartic gravity

We study structure of solutions of the recently constructed minimal extensions of Einstein's gravity in four dimensions at the quartic curvature level. The extended higher derivative theory, just like Einstein's gravity, has only a massless spin-two graviton about its unique maximally symmetric vacuum. The extended theory does not admit the Schwarzschild or Kerr metrics as exact solutions, hence there is no issue of Schwarzschild type singularity but, approximately, outside a source, spherically symmetric metric with the correct Newtonian limit is recovered. We also show that for all Einstein space-times, the square of the Riemann tensor (the Kretschmann scalar or the Gauss-Bonnet invariant) obeys a nonlinear scalar Klein-Gordon equation.


Minimal massive gravity: Conserved charges, excitations, and the chiral gravity limit
Tekin, Bayram (2014-10-15)
We find the excitations and construct the conserved charges (mass and angular momentum) of the recently found minimal massive gravity (MMG) in 2 + 1 dimensions in asymptotically anti-de Sitter spacetimes. The field equation of the theory does not come from an action and lacks the required Bianchi identity needed to define conserved charges. But the theory, which also provides a healthy extension of the topologically massive gravity in the bulk and boundary of spacetime, does admit conserved charges for the ...
Stationary Lifshitz black hole of New Massive Gravity
Sarıoğlu, Bahtiyar Özgür (IOP Publishing, 2019-01-10)
I present the stationary Lifshitz black hole solution of three-dimensional New Massive Gravity theory and study its elementary geometric and thermodynamical properties.
Critical points of D-dimensional extended gravities
Deser, S.; Liu, Haishan; Lue, H.; Pope, C. N.; Sisman, Tahsin Cagri; Tekin, Bayram (2011-03-17)
We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D < 4 there are in general two distinct (anti)-de Sitter vacua. We show that, for an appropriate choice of the parameters, there exists a critical point for one of the vacua, with only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have formally vanishing energy (as do black hole solutions). A further restriction of the paramet...
Anti-de Sitter-Wave Solutions of Higher Derivative Theories
GÜRSES, METİN; Hervik, Sigbjorn; Sisman, Tahsin Cagri; Tekin, Bayram (American Physical Society (APS), 2013-09-05)
We show that the recently found anti-de Sitter (AdS)-plane and AdS-spherical wave solutions of quadratic curvature gravity also solve the most general higher derivative theory in D dimensions. More generally, we show that the field equations of such theories reduce to an equation linear in the Ricci tensor for Kerr-Schild spacetimes having type-N Weyl and type-N traceless Ricci tensors.
All bulk and boundary unitary cubic curvature theories in three dimensions
Gullu, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram (American Physical Society (APS), 2011-01-26)
We construct all the bulk and boundary unitary cubic curvature parity invariant gravity theories in three dimensions in (anti)-de Sitter spaces. For bulk unitarity, our construction is based on the principle that the free theory of the cubic curvature theory reduces to one of the three known unitary theories which are the cosmological Einstein-Hilbert theory, the quadratic theory of the scalar curvature, or the new massive gravity (NMG). Bulk and boundary unitarity in NMG is in conflict; therefore, cubic th...
Citation Formats
A. Karasu and B. Tekin, “Minimal extension of Einstein’s theory: The quartic gravity,” PHYSICAL REVIEW D, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: