Related papers: Gauge and motion in perturbation theory
That preferred-frame theory accounts for special relativity and reduces to it if the gravitation field cancels. Starting from an interpretation of gravity as a pressure force, it is based on just one scalar field. This scalar gives the…
Black hole perturbation theory beyond second order is not well understood because typically one defines the meaning of gauge invariance order by order which is ambiguous. In this series of works we therefore developed a new approach which…
The field-theoretical approach is reviewed. Perturbations in general relativity as well as in an arbitrary $D$-dimensional metric theory are studied on a background, which is a solution (arbitrary) of the theory. Lagrangian for…
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we re-derive the second-order Einstein equations on…
We derive the effects of a non-zero cosmological constant $\Lambda$ on gravitational wave propagation in the linearized approximation of general relativity. In this approximation we consider the situation where the metric can be written as…
Perturbative techniques are important for modified theories of gravity since they allow to calculate deviations from General Relativity without recurring to exact solutions, which can be difficult to find. When applied to models such as…
Hartle's model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in General Relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no…
This article is the second of a trilogy that addresses the perturbative response of general quantum systems, with possibly nontrivial ground state geometry, beyond linear order. Here, we establish concise, general formulae for second order…
We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example we give the gauge-invariant definition of the second-order curvature perturbation on uniform density…
We develop a second-order cosmological perturbation theory on a background geometry expressed in terms of light-cone coordinates, extending the first-order analyses available in the literature. In particular, we investigate the gauge…
In this paper we present a new formulation of the change of gauge formulas in second order cosmological perturbation theory which unifies and simplifies known results. Our approach is based on defining new second order scalar perturbation…
A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and shift whose centerpiece is a wave equation for curvature. In…
Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
Time-independent gauge transformations are implemented in the canonical formalism by the Gauss law which is not covariant. The covariant form of Gauss law is conceptually important for studying asymptotic properties of the gauge fields. For…
In this paper we find the first and second order perturbations of the induced metric and the extrinsic curvature of a non-degenerate hypersurface $\Sigma$ in a spacetime $(M,g)$, when the metric $g$ is perturbed arbitrarily to second order…
We extend the general framework of perturbative quantum field theory developped for the pure Yang-Mills model to gravity. First we present a variant of the elimination procedure of the anomalies in the second order of perturbation theory.…
We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear…
The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory.…
This paper defines the spacetime geometry attached with observor as vacuum geometry (it defines the idea physical measurement geometry) and the spacetime geometry attached with matter as spacetime geometry. The initial spacetime geometry…