Related papers: On weak solutions in Einstein theory and beyond
Quantum-mechanical model of self-gravitating dust shell is considered. To clarify the relation between classical and quantum spacetime which the shell collapse form, we consider various time slicing on which quantum mechanics is developed.…
Caustics-envelopes formed by the trajectories of fluid particles-arise in proposed dynamical extensions for shell-crossing singularities occurring in the Einstein-dust system. In this study, a local existence result is established,…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
The Weak Gravity Conjecture (WGC) demands the existence of superextremal particles in any consistent quantum theory of gravity. The standard lore is that these particles are introduced to ensure that extremal black holes are either unstable…
We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that…
Besides the singularity problem, the famous Oppenheimer and Snyder solution is discovered to be of deficiency in two aspects: the internal Friedmann space-time does not have the inherent symmetry and cannot connect to the external…
Alcubierre proposed in 1994 that the well known special relativistic limitation that particles cannot travel with velocities bigger than the light speed can be bypassed when such trips are considered globally within specific general…
Within a semiclassical framework, we investigate spherically symmetric solutions of the Einstein equations that (i) develop a trapped region within a finite time as measured by distant observers, and (ii) remain sufficiently regular at the…
We consider degenerate porous medium equations with a divergence type of drift terms. We establish the existence of $L^{q}$-weak solutions (satisfying energy estimates or even further with moment and speed estimates in Wasserstein spaces),…
In this paper we investigate the evolution of the viscous dark energy (DE) interacting with the dark matter (DM) in the Einstein cosmology model. Using the linearizing theory of the dynamical system, we find, in our model, there exists a…
The final state of the gravitational collapse of a marginally bound dust cloud is formulated in terms of an existence problem for the non-linear differential equation governing radial null geodesics near the singular point. Rigorous results…
We study the backreaction of quantum fields induced through the vacuum polarization and the conformal anomaly on the collapse of a thin shell of dust. It is shown that the final fate of the collapse process depends on the physical…
Singular solutions of the harmonic Einstein evolution equation are constructed which are related to spatially global and time-local solutions for a certain class of quasilinear hyperbolic systems of second order. The constructed…
In the presence of a minimal length physical objects cannot collapse to an infinite density, singular, matter point. In this note we consider the possible final stage of the gravitational collapse of "thick" matter layers. The energy…
To clarify observational consequence of bubble nucleations in inflationary era, we analyse dynamics of a spherical domain wall in an expanding universe. We consider a spherical shell of the domain wall with tension $\sigma$ collapsing in a…
Post-Newtonian theory is considered a reliable effective expansion of General Relativity in the weak-field and slow-motion limit. We argue that such a belief is misplaced. In generic many-body relativistic dynamics, the absence of globally…
The gravitational strength of the central singularity in spherically symmetric space-times is investigated. Necessary conditions for the singularity to be gravitationally weak are derived and it is shown that these are violated in a wide…
We investigate linear parabolic equations in divergence form with singular coefficients and non-smooth boundary data. When the diffusion, drift, or potential terms, as well as the initial or boundary conditions, are distributions rather…
Cosmological perturbation equations derived from low-energy effective actions are shown to be invariant under a duality transformation reminiscent of electric-magnetic, strong-weak coupling, S-duality. A manifestly duality-invariant…
Dark matter substructure has the potential to discriminate between broad classes of dark matter models. With this in mind, we construct novel solutions to the equations of motion governing condensate dark matter candidates, namely axion…