Linearization in stability in gravity theories

Altaş Kiracı, Emel
In a nonlinear theory, such as gravity, physically relevant solutions are usually hard to find. Therefore, starting from a background exact solution with symmetries, one uses the perturbation theory, which albeit approximately, provides a lot of information regarding a physical solution. But even this approximate information comes with a price: the basic premise of a perturbative solution is that it should be improvable. Namely, by going to higher order perturbation theory, one should be able to improve and better approximate the physical problem or the solution. While this is often the case in many theories and many background solutions, there are important cases where the linear perturbation theory simply fails for various reasons. This issue is well known in the context of general relativity through the works that started in the early 1970s, but it has only been recently studied in modified gravity theories. This thesis is devoted to the study of linearization instability in generic gravity theories where there are spurious solutions to the linearized equations which do not come from the linearization of possible exact solutions. For this purpose we discuss the Taub charges, the ADT charges and the quadratic constraints on the linearized solutions. We give the three dimensional chiral gravity and the D dimensional critical gravity as explicit examples and give a detailed ADM analysis of the topologically massive gravity with a cosmological constant.


Massive higher derivative gravity theories
Güllü, İbrahim; Tekin, Bayram; Department of Physics (2011)
In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in D dimensional (Anti)-de Sitter and flat spacetimes for the most general quadratic curvature theory augmented with the Pauli-Fierz mass term. From the amplitude expression, the Newtonian potential energies are calculated for various cases. Also, from this amplitude and the propagator structu...
Particle content of quadratic and f (R-mu nu sigma rho) theories in (A)dS
Tekin, Bayram (2016-05-17)
We perform a complete decoupling of the degrees of freedom of quadratic gravity and the generic f(R-mu nu sigma rho) theory about any one of their possible vacua, i.e. maximally symmetric solutions, and find the masses of the spin-2 and spin-0 modes in explicit forms.
Linearization instability for generic gravity in AdS spacetime
Altas, Emel; Tekin, Bayram (American Physical Society (APS), 2018-1-24)
In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure o...
Higher dimensional metrics of colliding gravitational plane waves
Gurses, M; Kahya, EO; Karasu, Atalay (2002-07-15)
We give a higher even dimensional extension of vacuum colliding gravitational plane waves with the combinations of collinear and noncollinear polarized four-dimensional metrics. The singularity structure of space-time depends on the parameters of the solution.
Covariant symplectic structure and conserved charges of new massive gravity
Alkaç, Gökhan; Sarıoğlu, Bahtiyar Özgür; Department of Physics (2012)
We show that the symplectic current obtained from the boundary term, which arises in the first variation of a local diffeomorphism invariant action, is covariantly conserved for any gravity theory described by that action.Therefore, a Poincaré invariant two-form can be constructed on the phase space, which is shown to be closed without reference to a specific theory.Finally, we show that one can obtain a charge expression for gravity theories in various dimensions, which plays the role of the Abbott-Deser-T...
Citation Formats
E. Altaş Kiracı, “Linearization in stability in gravity theories,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.