Related papers: The second order spin-2 system in flat space near …
The ``close limit,'' a method based on perturbations of Schwarzschild spacetime, has proved to be a very useful tool for finding approximate solutions to models of black hole collisions. Calculations carried out with second order…
We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The…
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D…
We present a class of conformally flat solutions of the Einstein's field equations for spherical systems undergoing gravitational collapse accompanied with radial heat flux. The interior space-time of the collapsing matter is chosen to be…
We consider three-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We…
A system of equations that serves as a model for the Einstein field equation in generalised harmonic gauge called the good-bad-ugly system is studied in the region close to null and spatial infinity in Minkowski spacetime. This analysis is…
Gravitational waves are propagating undulations in the spacetime fabric, which interact very weakly with their environment. In cosmology, gravitational-wave distortions are produced by most of the inflationary scenarios and their…
We study the relationship between asymptotic characteristic initial data for the wave equation at past null infinity and the regularity of the solution at future null infinity on the Minkowski spacetime. By constructing estimates on a…
We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($d\geqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the…
We consider rotating wave solutions of the nonlinear wave equation \[ \left\{ \begin{aligned} \partial_{t}^2 v - \Delta v + m v & = |v|^{p-2} v \quad && \text{in $\mathbb{R} \times \textbf{B}$} \\ v & = 0 && \text{on $\mathbb{R} \times…
Here we study the wave propagation and stability of general relativistic non-resistive dissipative second-order magnetohydrodynamic equations in curved space-time. We solve the Boltzmann equation for a system of particles and antiparticles…
We present a simple, systematic and practical method to construct conformally invariant equations in arbitrary Riemann spaces. This method that we call "Weyl-to-Riemann" is based on two features of Weyl geometry. i) A Weyl space is defined…
A linear second order wave equation is presented based on cosmological general relativity, which is a space-velocity theory of the expanding Universe. The wave equation is shown to be exactly solvable, based on the Gaussian hypergeometric…
We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon…
Higher-order theories of gravity have received much attention from several areas including quantum gravity, string theory and cosmology. This paper proposes a higher-order gravity whose action includes all curvature scalar terms up to the…
We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding…
Complete expressions of time-domain gravitational waveforms for spinning binary inspirals via the post-Newtonian (PN) approximation would require determination of the phase, amplitude, inclination angle, precession phase and spin vectors as…
In this study, we formulate a set of differential equations for a binary system to describe the secular-tidal evolution of orbital elements, rotational dynamics, and deformation (flattening), under the assumption that one body remains…
We deal with a class of second order in time nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in the theory ofnonlinear plates. Our first result states well-posedness in a…
Local nonlinear approximations to the growth of cosmic perturbations are developed, resulting in relations, at a given epoch, between the peculiar velocity and gravity fields and their gradients. Only the equation of motion is approximated,…