Related papers: On a certain type of nonlinear hyperbolic equation…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring…
We explore a theory of large-scale gravitational quantization, using the general relativistic Hamilton-Jacobi equation to create quantization conditions via a new scalar wave equation dependent upon the total mass and the total vector…
We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schr\"odinger equation with Hartree non-linearity, where the linear part is…
We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor…
We study gravitational collapse with anisotropic pressures, whose end stage can mimic space-times that are seeded by galactic dark matter. To this end, we identify a class of space-times (with conical defects) that can arise out of such a…
We study static spherically symmetric solutions to Einstein's equations with a repulsive singularity at the centre. We show that geodesics are extendible across the singularity, so the singularity does not lead to pathological causality…
For the physically important case in which the viscosity coefficients depend on the density $\rho$ through a power law (i.e., $\rho^\delta$ with some exponent $\delta \in (\frac{1}{2},1)$), we establish the global well-posedness of regular…
Numerical investigation of the static spherically symmetric vacuum solution of the Logunov equations confirms the analytical results and demonstrates a strong repulsion at sub-Planckian distance from the Schwarzschild-like singularity,…
In this paper, analytical solutions describing static and spherically symmetric sources in the decoupling limit of massive gravity are derived. We analyze the model parameter range and specify when a Vainshtein mechanism is possible.…
We study a set of static solutions of the Einstein equations in presence of a massless scalar field and establish their connection to the Kantowski-Sachs cosmological solutions based on some kind of duality transformations. The physical…
This work obtains a fixed-point equation for the solution of linear parabolic partial differential problems based on solutions to heat problems. This is a pointwise equality, so we have required non-standard techniques that involve the…
We derive the master equations governing axial and polar gravitational perturbations of a generic static and spherically symmetric black hole spacetime within the framework of the revised Deser--Woodard nonlocal gravity theory. We then…
In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the…
We prove the existence of small amplitude time quasi-periodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…
We consider spherically symmetric spacetimes sourced by a fluid with pressure anisotropy in the radial direction. We use gauge-invariant perturbation theory to study the stability of this class of spacetimes under axial perturbations. We…
The averaged resonant equations of motion for the planar circular restricted three-body problem are solved on the linearization basis taking into account also non-gravitational effects. The averaged resonant equations are derived from…
Within the framework of the theory of strongly-interacting quantum Bose liquids, we consider a general relativistic model of self-interacting complex scalar fields with logarithmic nonlinearity taken from dense superfluid models. We…
We find spherically symmetric solutions in the modified Ho\v{r}ava-Lifshitz gravity proposed recently by Blas, Pujolas and Sibiryakov. The non-linear equations of the two derivative action turn out to be similar to those stemming from the…