Tahsin Çağrı Şişman

Critical Points of D-Dimensional Extended Gravities

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 parameters gives a one-parameter cosmological Einstein plus Weyl^2 model with a unique vacuum, whose Λ is determined.

Born?Infeld extension of new massive 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 obtained from AdS/CFT. Our action provides a remarkable extension of NMG to all orders in the curvature and might define a consistent quantum gravity.

All unitary cubic curvature gravities in D dimensions

We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D -dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the general cubic curvature theory and imposing ghost and tachyon freedom, which greatly simplifies the highly complicated problem of finding the propagator of cubic curvature theories in constant curvature backgrounds. To carry out the procedure we have also classified all the unitary quadratic models. We use our general results to study the recently found cubic curvature theories using different techniques and the string generated cubic curvature gravity model. We also study the scattering in critical gravity and give its cubic curvature extensions.

Energy and Angular Momentum in Generic F(Riemann) Theories

(Dated: September 12, 2012)We construct the conserved charge of generic gravity theories built on arbitrary contrac-tions of the Riemann tensor (but not on its derivatives) for asymptotically (anti)-de Sitterspacetimes. Our construction is a generalization of the ADT charges of linear and quadraticgravity theories in cosmological backgrounds. As an explicit example we find the energy andangular momentum of the BTZ black hole in the 2+1 dimensional Born-Infeld gravity.

Anti-de Sitter-wave solutions of higher derivative theories.

There is a vast literature on the exact solutions of fourdimensional Einstein’s gravity. But, as more powers of curvature are added, or computed in a microscopic theory such as string theory, to get a better UV behaved theory, the field equations become highly nontrivial and so solutions are not easy to find. In fact, only a few classes of solutions are known: For example, see [1–4] for solutions in low energy string theory. AdS5 × S, which played a major role in AdS/CFT, is also expected to be an exact solution of string theory [5]. In this work, we present new asymptotically AdS solutions, which are AdS-plane and AdS-spherical waves, to D-dimensional generic gravity theories based on the Riemann tensor and its arbitrary number of covariant derivatives which are in some sense natural geometric extensions of Einstein’s gravity. Certain low energy string theory actions constitute a subclass of this theory once all the non-gravitational fields are turned off [6]. Asymptotically AdS solutions in higher derivative theories are relevant in the context of generic gravity/gauge theory dualities and holography. Here, we shall provide such solutions.

Some exact solutions of all

We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form

f(R_{/mu/nu}

f({R}_{\ensuremath{\mu}\ensuremath{\nu}})

theories in three dimensions

that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher derivative theories inherit some of the previously studied solutions of the cosmological topologically massive gravity and the new massive gravity field equations, once the parameters of the theories are adjusted. Besides the generic higher curvature theory, we have considered in some detail the examples of the quadratic curvature theory, the cubic curvature theory, and the Born-Infeld extension of the new massive gravity.

Spectra, vacua and the unitarity of Lovelock gravity in D-dimensional AdS spacetimes

We explicitly confirm the expectation that generic Lovelock gravity in D dimensions has a unitary massless spin-2 excitation around any one of its constant curvature vacua just like the cosmological Einstein gravity. The propagator of the theory reduces to that of Einstein’s gravity, but scattering amplitudes must be computed with an effective Newton’s constant which we provide. Tree-level unitarity imposes a single constraint on the parameters of the theory yielding a wide range of unitary region. As an example, we explicitly work out the details of the cubic Lovelock theory.

Born-Infeld-Hořava gravity

We define various Born-Infeld gravity theories in 3+1 dimensions which reduce to Horavas model at the quadratic level in small curvature expansion. In their exact forms, our actions provide z{yields}{infinity} extensions of Horavas gravity, but when small curvature expansion is used, they reproduce finite z models, including some half-integer ones.