Exact solutions and the consistency of 3D minimal massive gravity

Altas, Emel
Tekin, Bayram
We show that all algebraic type-O, type-N and type-D and some Kundt-type solutions of topologically massive gravity are inherited by its holographically well-defined deformation, that is, the recently found minimal massive gravity. This construction provides a large class of constant scalar curvature solutions to the theory. We also study the consistency of the field equations both in the source-free and matter-coupled cases. Since the field equations of MMG do not come from a Lagrangian that depends on the metric and its derivatives only, it lacks the Bianchi identity valid for all nonsingular metrics. But it turns out that for the solutions of the equations, the Bianchi identity is satisfied. This is a necessary condition for the consistency of the classical field equations but not a sufficient one, since the rank-two tensor equations are susceptible to double divergence. We show that for the source-free case the double divergence of the field equations vanishes for the solutions. In the matter-coupled case, we show that the double divergences on the left-hand side and the right-hand side are equal to each other for the solutions of the theory. This construction completes the proof of the consistency of the field equations.


Öcal, Sultan Eylül; Tekin, Bayram; Kılıçarslan, Ercan; Department of Physics (2021-8)
Infinite Derivative Gravity (IDG) is a modified gravity theory which can avoid the singularities and Ultraviolet problem of gravity. This thesis examines the effects of IDG on these problems. First, the propagators and Newtonian potential will be examined as well as the conditions necessary for avoidance of singularities for perturbations around Minkowski background are found. Second, we study the exact pp-wave and AdS-plane wave solutions of quadratic and Infinite derivative gravity theories. We construct ...
Kundt solutions of minimal massive 3D gravity
Deger, Nihat Sadik; Sarıoğlu, Bahtiyar Özgür (AMER PHYSICAL SOC, ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA, 2015-11-04)
We construct Kundt solutions of minimal massive gravity theory and show that, similar to topologically massive gravity (TMG), most of them are constant scalar invariant (CSI) spacetimes that correspond to deformations of round and warped (A) dS. We also find an explicit non-CSI Kundt solution at the merger point. Finally, we give their algebraic classification with respect to the traceless Ricci tensor (Segre classification) and show that their Segre types match with the types of their counterparts in TMG.
Modeling of landfill settlement: Theory
Durmusoglu, E.; Corapcioglu, M.y.; Tuncay, Kağan (null; 2005-12-01)
Theory of a one-dimensional multiphase mathematical model developed to simulate the settlement involving liquid and gas flows in a compressible landfill is presented. Landfill domain is assumed comprised of a deformable solid matrix, a liquid phase, and a gas phase with transient gas generation. After a two-phase model, i.e., liquid and gas phase, was developed, a solid phase was incorporated into the model. A gas generation term was employed as source and sink for solid and gas phases. After governing equa...
Hermitian and gauge-covariant Hamiltonians for a particle in a magnetic field on cylindrical and spherical surfaces
Shikakhwa, M. S.; Chair, N. (IOP Publishing, 2017-01-01)
We construct the Hermitian Schrodinger Hamiltonian of spin-less particles and the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field, which are confined to cylindrical and spherical surfaces. The approach does not require the use of involved differential-geometrical methods and is intuitive and physical, relying on the general requirements of Hermicity and gauge-covariance. The surfaces are embedded in the full three-dimensional space and confinement to the surfaces is achieved...
Circularly symmetric solutions of minimal massive gravity at its merger point
Sarıoğlu, Bahtiyar Özgür (IOP Publishing, 2019-07-25)
I find all the static circularly symmetric solutions of minimal massive 3D gravity at its merger point, construct stationary versions of these and discuss some of their geometric and physical properties. It turns out that apart from a static hairy black hole, there is also a static gravitational soliton, that has been overlooked in the literature.
Citation Formats
E. Altas and B. Tekin, “Exact solutions and the consistency of 3D minimal massive gravity,” PHYSICAL REVIEW D, pp. 0–0, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46382.