Bachian gravity in three dimensions

Tek, Mustafa
Modified theories in 3-dimensions such as the topologically massive gravity (TMG), new massive gravity (NMG) or Born-Infeld extension of NMG arise from the vari-ations of diffeomorphism invariant actions; hence the resulting field equations aredivergence free. Namely, the rank two tensor defining the field equations satisfy aBianchi identity for all smooth metrics. However there are some recently constructedtheories that do not identically satisfy Bianchi identities for all metrics, but only forthe solutions of the theory. These are called on-shell consistent theories of whichexamples are the minimal massive gravity (MMG) and the exotic massive gravity(EMG). We work out the generic on-shell consistent model in 3-dimensions as amodified Einstein gravity theory which is based on the analog of the Bach tensor,hence we name it as the Bachian gravity. Conserved charges are found by using thelinearization about maximally symmetric backgrounds for the Bañados-Teitelboim-Zanelli (BTZ)-black hole metric. It is complicated to solve the field equations of thegravity theory and hence very few solutions with only maximal symmetry are known. We use the projection formalism to obtain a reduction of the some relevant 2-tensorsdefining the field equations with the help of the Geroch’s reduction method.


Weyl-invariant higher curvature gravity theories
Dengiz, Suat; Tekin, Bayram; Department of Physics (2014)
In this thesis, Weyl-invariant extensions of three-dimensional New Massive Gravity, generic n-dimensional Higher Curvature Gravity theories and three-dimensional Born-Infeld gravity theory are analyzed in details. As required by Weyl-invariance, the actions of these gauge theories do not contain any dimensionful parameter, hence the local symmetry is spontaneously broken in (Anti) de Sitter vacua in analogy with the Standard Model Higgs mechanism. In flat vacuum, symmetry breaking mechanism is more complica...
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...
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.
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.
Bachian gravity in three dimensions
Alkaç, Gökhan; Tek, Mustafa; Tekin, Bayram (American Physical Society (APS), 2018-11-16)
In three dimensions, there exist modifications of Einstein's gravity akin to the topologically massive gravity that describe massive gravitons about maximally symmetric backgrounds. These theories are built on the three-dimensional version of the Bach tensor (a curl of the Cotton-York tensor) and its higher derivative generalizations; and they are on-shell consistent without a Lagrangian description based on the metric tensor alone. We give a generic construction of these models, find the spectra and comput...
Citation Formats
M. Tek, “Bachian gravity in three dimensions,” Thesis (Ph.D.) -- Graduate School of Natural and Applied Sciences. Physics., Middle East Technical University, 2019.