Related papers: Brief Note on Thurston Geometries in 3D Quadratic …
We show that the three-dimensional Thurston geometries are vacuum solutions to the 3D new massive gravity equations of motion. We analyze their Lorentzian counterparts as well.
It has been established that the famous three-dimensional Thurston geometries have four intrinsically Lorentzian analogs. We explore these spacetimes in three-dimensional general relativity nonminimally coupled to a scalar field together…
The quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In $n>4$ dimensions, pure quadratic curvature lagrangian having second order trace constructed…
We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first order constrained variational principle. We find…
In this paper, we consider a family of $n$-dimensional, higher-curvature theories of gravity whose action is given by a series of dimensionally extended conformal invariants. The latter correspond to higher-order generalizations of the…
In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted…
We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form f(Ricci) that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher…
We study Kundt solutions of topologically massive gravity (TMG) and the new theory of massive gravity (NMG), proposed recently in arXiv:0901.1766. For topologically massive gravity, only the CSI Kundt solutions (i.e., solutions with…
In a recent reformulation of three-dimensional new massive gravity (NMG), the field equations of the theory consist of a massive (tensorial) Klein-Gordon type equation with a curvature-squared source term and a constraint equation. Using…
It has been suggested that new massive gravity with higher order terms in the curvature may be renormalizable and thus a candidate for renormalizable quantum gravity. We show that three-dimensional gravity that contains quadratic scalar…
Of the Thurston geometries, those with constant curvature geometries (Euclidean $\EUC$, hyperbolic $\HYP$, spherical $\SPH$) have been extensively studied, but the other five geometries, $\HXR$, $\SXR$, $\NIL$, $\SLR$, $\SOL$ have been…
We find the most general algebraic type N solution with non-vanishing scalar curvature, which comprises all type N solutions of new massive gravity in three dimensions. We also give the special forms of this solution, which correspond to…
We discuss locally Weyl (scale) covariant generalisation of quadratic curvature gravity theory in three dimensions using Riemann-Cartan-Weyl space-times. We show that this procedure of Weyl gauging yields a consistent generalisation for a…
In this expository paper, we present a survey about the history of the geometrization conjecture and the background material on the classification of Thurston's eight geometries. We also discuss recent techniques for immersive visualization…
We consider gravity in three dimensions with an arbitrary number of curvature corrections. We show that such corrections are always functions of only three independent curvature invariants. Demanding the existence of a holographic c-theorem…
New Massive Gravity is an alternative theory to General Relativity that is used to describe the gravitational field in a (2+1)-dimensional spacetime. Black hole solutions have been found in this theory, in particular an asymptotically…
We study gravitational waves with torsion as exact vacuum solutions of three-dimensional gravity with propagating torsion. The new solutions are a natural generalization of the plane-fronted gravitational waves in general relativity with a…
A review of recent investigations of black holes in higher curvature theories of gravity.
We present a three-dimensional gravitational Born-Infeld theory which reduces to the recently found New Massive Gravity (NMG) at the quadratic level in the small curvature expansion and at the cubic order reproduces the deformation of NMG…
We find exact solutions of topologically massive gravity (TMG) and new massive gravity (NMG) in ${2+1}$ dimensions (3D) with an arbitrary cosmological constant, pure radiation, and gyratons, i.e., with possibly non-zero $T_{uu}$ and…