arXiv subjects

Dhanya S. Menon

Publications and source records attributed to Dhanya S. Menon.

3 recordsLinked to original sources

arXiv2020

Nonlinear perturbations of higher dimensional anti-de Sitter spacetime

We study nonlinear gravitational perturbations of vacuum Einstein equations, with $Λ<0$ in $(n+2)$ dimensions, with $n>2$, generalizing previous studies for $n=2$. We follow the formalism by Ishibashi, Kodama and Seto to decompose the metric perturbations into tensor, vector and scalar sectors, and simplify the Einstein equations. The tensor perturbations are the new feature of higher dimensions. We render the metric perturbations asymptotically anti-de Sitter by employing a suitable gauge choice for each of the sectors. Finally, we analyze the resonant structure of the perturbed equations at second order for the five dimensional case, by a partial study of single mode tensor-type perturbations at the linear level. For the cases we studied, resonant terms vanish at second order.

gr-qc↗

arXiv2019

Gravitational Perturbations in a cavity: Nonlinearities

Motivated by recent studies of nonlinear perturbations of asymptotically anti-de Sitter spacetimes, we study gravitational perturbations of $(n+2)$ dimensional Minkowski spacetime with a spherical Dirichlet wall. By considering the tensor, vector and scalar perturbations on the $n$ sphere, we present simplified nonhomogeneous equations at arbitrary order in weakly nonlinear perturbation theory for each sector. A suitable choice of perturbative variables is required at higher orders to simplify the expression for the boundary conditions and to expand the variables in terms of linear order eigenfunctions. Finally we comment on the nonlinear stability of the system. Some of the tools used can easily be generalized to study nonlinear perturbations of anti-de Sitter spacetime.

gr-qc↗

arXiv2015

Necessary conditions for an AdS-type instability

In this work, we analyze the necessary conditions for a nonlinear AdS-type instability in the gravity-scalar field system. In particular, we discuss the necessary conditions for a cascade of energy to higher modes by applying results in KAM theory. Our analytical framework explains numerical observations of instability of spacetimes even when the spectrum is only asymptotically resonant, and the fact that a minimum field amplitude is needed to trigger it. Our framework can be applied for similar stability analyses of fields in (locally) asymptotically AdS spacetimes. We illustrate this with the example of the AdS soliton. Further, we conjecture on the possible reasons for quasi-periodic behaviour observed in perturbations of AdS spacetime. Certain properties of the eigenfunctions of the linear system dictate whether there will be localization in space leading to black hole formation. These properties are examined using the asymptotics of Jacobi polynomials. Finally we discuss recent results on the AdS instability in Einstein-Gauss-Bonnet gravity in light of our work.

gr-qc↗