Dirac procedure and the Hamiltonian formalism for cosmological perturbations in a Bianchi I universe

We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Bianchi I universe. We discuss and employ basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions, reduced phase space, physical Hamiltonian, canonical isomorphism between different gauge-fixing surfaces and spacetime reconstruction. We relate this approach to the gauge-fixing procedure for non-perturbative canonical relativity. We discuss the issue of propagating a basis for the scalar-vector-tensor decomposition as, in an anisotropic universe, the wavefronts of plane waves undergo a non-trivial evolution. We show that the definition of a gravitational wave as a traceless-transverse mode of the metric perturbation needs to be revised. Moreover there exist coordinate systems in which a polarization mode of the gravitational wave is given entirely in terms of a scalar metric perturbation. We first develop the formalism for the universe with a single minimally coupled scalar field and then extend it to the multi-field case. The obtained fully canonical formalism will serve as a starting point for a complete quantization of the cosmological perturbations and the cosmological background.

New metric reconstruction scheme for gravitational self-force calculations

Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a “no-string” radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of “gauge completion” as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological field equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-field reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the “gauge completion”. We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a sufficiently regular gauge, it should provide a first step toward second-order self-force calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.

Slow stationary sources

The linearized theory is applied to sources such as ordinary stars whose speed is small compared to the speed of light. This yields the “gravitoelectromagnetic” theory. The gravitoelectromagnetic field equations are obtained, along with their general solution via scalar and vector potentials. It is shown how to calculate the metric perturbation, and hence the field, due to a rotating ring or a ball, and thus how to calculate orbits, timing, and the Lense-Thirring precession.

Modified gravity over the linearized metric perturbation for two body dynamics

In this paper Modified gravity is studied over the weak field linearized metric perturbation in post-Minkowskian theory. This is a different aspect for studying the two body dynamics or binary system. Here despite of usual self force originated from the radiative backscattering of gravitational waves we are considering new paradigm of perturbation that is multiplicative approach. The new perturbed metric is determined over the multiplication of isolated background metric of curved space-time for two different massive sources in post-Newtonian theory. To verify the model and the theoretical result the binary system of Milky Way central super massive black hole to Sun is considered. The computation shows remarkable result without MOND for galactic flat rotation curve and solar rotational speed 249km/sec, obviously very good agreement with recent observed data.

Linear stability of Einstein and de Sitter universes in the quadratic theory of modified gravity

We consider the Einstein static and the de Sitter universe solutions and examine their instabilities in a subclass of quadratic modified theories for gravity. This modification proposed by Nash is an attempt to generalize general relativity. Interestingly, we discover that the Einstein static universe is unstable in the context of the modified gravity. In contrast to Einstein static universe, the de Sitter universe remains stable under metric perturbation up to the second order.

Perturbative correction terms to electromagnetic self-force due to metric perturbation: astrophysical and cosmological implications

We consider the equation of motion of a charged particle or a charged compact object in curved space-time, under the reaction of electromagnetic radiation and also consider a physical situation such that the charged particle or compact object emits gravitational radiation, thereby gravitational radiation reaction also acts on it. We investigate the effect of this metric perturbation i.e. the gravitational radiation on the electromagnetic self-force. We show that, besides the interaction terms derived by Zimmerman and Poisson (Phys Rev D 90:084030, 2014), additional perturbative terms are generated, which are linear in metric perturbation and are generated due to perturbation of the electromagnetic self-force by the metric perturbation. We discuss the conditions of significance of these perturbative terms and also the interaction terms with respect to the gravitational self-force in various astrophysical and cosmological cases; such as the motion of charged particles around black holes, some extreme mass-ratio inspirals (EMRIs) involving sufficiently accelerated motion of charged stars (specially neutron stars) or charged stellar mass black holes around supermassive black holes, and motion of charged particles around charged primordial black holes formed in the early Universe etc. We find that in some astrophysical and cosmological cases these perturbative terms can have significant effect in comparison with the gravitational radiation-reaction term.

The first-order symmetry operator on gravitational perturbations in the 5D Myers–Perry spacetime with equal angular momenta

It has been revealed that the first-order symmetry operator for the linearized Einstein equation on a vacuum spacetime can be constructed from a Killing–Yano 3-form. This might be used to construct all or part of the solutions to the field equation. In this paper, we perform a mode decomposition of a metric perturbation on the Schwarzschild spacetime and the Myers–Perry spacetime with equal angular momenta in 5 dimensions, and investigate the action of the symmetry operator on specific modes concretely. We show that, on such spacetimes, there is no transition between the modes of a metric perturbation by the action of the symmetry operator, and it ends up being the linear combination of the infinitesimal transformations of isometry.

Gravitational waves in modified Gauss–Bonnet gravity

We study the gravitational waves (GWs) in modified Gauss–Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the GWs. To find phenomena beyond the general relativity, the scalar mode mass is calculated as a function of the background curvature in some typical models.

Black holes in Gauss–Bonnet and Chern–Simons-scalar theory

We carry out the stability analysis of the Schwarzschild black hole in Gauss–Bonnet and Chern–Simons-scalar theory. Here, we introduce two quadratic scalar couplings ([Formula: see text]) to Gauss–Bonnet and Chern–Simons terms, where the former term is parity-even, while the latter one is parity-odd. The perturbation equation for the scalar [Formula: see text] is the Klein–Gordon equation with an effective mass, while the perturbation equation for [Formula: see text] is coupled to the parity-odd metric perturbation, providing a system of two coupled equations. It turns out that the Schwarzschild black hole is unstable against [Formula: see text] perturbation, leading to scalarized black holes, while the black hole is stable against [Formula: see text] and metric perturbations, implying no scalarized black holes.