Related papers: First and Second Order Perturbations of Hypersurfa…
The disformal transformation of metric $g_{\mu \nu} \to \Omega^2 (\phi)g_{\mu \nu}+\Gamma(\phi,X) \partial_{\mu}\phi \partial_{\nu}\phi$, where $\phi$ is a scalar field with the kinetic energy $X= \partial_{\mu}\phi \partial^{\mu}\phi/2$,…
An outline of a proof of the decomposition of the linear metric perturbation into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is discussed through an exlicit construction of gauge-invariant and gauge-variant…
It is now widely believed that if the gravitational field is (perturbatively) quantum, it would entangle two massive objects (in spatial superpositions) which were otherwise unentangled to begin with. Recently, actual table-top experiments…
We study second-order electromagnetic perturbations in the Schwarzschild background and derive the effective source terms for Regge-Wheeler equation which are quadratic in first-order gravitational and electromagnetic perturbations. In…
There is currently no rigorous definition of gravitational wave strain at second order in cosmological perturbation theory. The usual association of gravitational waves with transverse and traceless fluctuations of the metric on spatial…
We consider the evolution of perturbed cosmological spacetime with multiple fluids and fields in Einstein gravity. Equations are presented in gauge-ready forms, and are presented in various forms using the curvature (\Phi or \phi_\chi) and…
Perturbation theory in geometric theories of gravitation is a gauge theory of symmetric tensors defined on a Lorentzian manifold (the background spacetime). The gauge freedom makes uniqueness problems in perturbation theory particularly…
In this paper, we investigate the first and second order cosmological perturbations in the light mass Galileon (LMG) scenario. LMG action includes cubic Galileon term along with the standard kinetic term and a potential which is added…
Gravitational self-force theory is the primary way of modelling extreme-mass-ratio inspirals (EMRIs). One difficulty that appears in second-order self-force calculations is the strong divergence at the worldline of the small object, which…
The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…
We discuss the issue of observables in general-relativistic perturbation theory, adopting the view that any observable in general relativity is represented by a scalar field on spacetime. In the context of perturbation theory, an observable…
In this work, the effects of a nonminimally coupled model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. Based…
A review is given of recent work on topology changing solutions to the first order form of general relativity. These solutions have metrics which are smooth everywhere, invertible almost everywhere, and have bounded curvature. The…
We study the perturbations up to the 2nd-order for a power-law inflation driven by a scalar field in synchronous coordinates. We present the 1st-order solutions, and analytically solve the 2nd-order perturbed Einstein equation and scalar…
An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime which admits ADM decomposition is briefly discussed. We explicitly construct the…
We give an explicit relation, up to second-order terms, between scalar-field fluctuations defined on spatially-flat slices and the curvature perturbation on uniform-density slices. This expression is a necessary ingredient for calculating…
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
We study nonlinear gravitational perturbations of vacuum Einstein equations, with $\Lambda<0$ 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…
We consider metrics related to each other by functionals of a scalar field $\varphi(x)$ and it's gradient $\nabla \varphi(x)$, and give transformations of some key geometric quantities associated with such metrics. Our analysis provides…