Linearization instability for generic gravity in AdS spacetime

Download

10.1103:PhysRevD.97.024028.pdf

Date

2018-1-24

Author

Altas, Emel
Tekin, Bayram

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

34
views

49
downloads

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 of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

Subject Keywords

POSITIVE ENERGY, STABILITY, SYMMETRIES, PROOF, MASS

URI

https://hdl.handle.net/11511/52084

Journal

Physical Review D

DOI

https://doi.org/10.1103/physrevd.97.024028

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

Linearization in stability in gravity theories Altaş Kiracı, Emel; Tekin, Bayram; Department of Physics (2018) 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 ...
Equivariant Reduction of Gauge Theories over Fuzzy Extra Dimensions Kürkcüoğlu, Seçkin (IOP Publishing, 2012-2-8) In SU(N) Yang-Mills theories on a manifold M, which are suitably coupled to a set of scalars, fuzzy spheres may be generated as extra dimensions by spontaneous symmetry breaking. This process results in gauge theories over the product space of the manifold M and the fuzzy spheres with smaller gauge groups. Here we present the SU(2)- and SU(2) x SU(2)-equivariant parametrization of U(2) and U(4) gauge fields on S-F(2), and S-F(2), x S-F(2), respectively and outline the dimensional reduction of these theories...
Finite mass gravitating Yang monopoles CEBECİ, HAKAN; Sarıoğlu, Bahtiyar Özgür; Tekin, Bayram (American Physical Society (APS), 2008-12-01) We show that gravity cures the infrared divergence of the Yang monopole when a proper definition of conserved quantities in curved backgrounds is used, i.e. the gravitating Yang monopole in cosmological Einstein theory has a finite mass in generic even dimensions (including time). In addition, we find exact Yang-monopole type solutions in the cosmological Einstein-Gauss-Bonnet-Yang-Mills theory and briefly discuss their properties.
On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions Kaya Merdan, Songül; Rebholz, Leo G. (2014-11-01) We consider a Crank-Nicolson-Adams-Bashforth temporal discretization, together with a finite element spatial discretization, for efficiently computing solutions to approximate deconvolution models of incompressible flow in two dimensions. We prove a restriction on the timestep that will guarantee stability, and provide several numerical experiments that show the proposed method is very effective at finding accurate coarse mesh approximations for benchmark flow problems.
Parallel-MLFMA solution of CFIE discretized with tens of millions of unknowns Ergül, Özgür Salih (2007-11-16) We consider the solution of large scattering problems in electromagnetics involving three-dimensional arbitrary geometries with closed surfaces. The problems are formulated accurately with the combined-field integral equation and the resulting dense matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). With an efficient parallelization of MLFMA on relatively inexpensive computing platforms using distributed-memory architectures, we easily solve large-scale pro...

Citation Formats

E. Altas and B. Tekin, “Linearization instability for generic gravity in AdS spacetime,” Physical Review D, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52084.