Related papers: Translation invariant time-dependent solutions to …
We point out that for a large class of parametrized theories, there is a constant in the constrained Hamiltonian which drops out of the classical equations of motion in configuration space. Examples include the mass of a relativistic…
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions…
Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a…
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
We study the long-time behavior of scale-invariant solutions of the 2d Euler equation satisfying a discrete symmetry. We show that all scale-invariant solutions with bounded variation on $\mathbb{S}^1$ relax to states that are piece-wise…
We present the exact time-dependent solutions on inhomogeneous spherically symmetric space-time in the conformal invariant Weyl gravity. For this purpose, the subclass of the Lemaitre-Tolman metric which is supported by an anisotropic fluid…
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local…
We prove a global well-posedness result for defocusing nonlinear Schrodinger equations with time dependent potential. We then focus on time dependent harmonic potentials. This aspect is motivated by Physics (Bose--Einstein condensation),…
We study a theory of gravity of the form $f(\mathcal{G})$ where $\mathcal{G}$ is the Gauss-Bonnet topological invariant without considering the standard Einstein-Hilbert term as common in the literature, in arbitrary $(d+1)$ dimensions. The…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between…
We construct gravitating superconducting string solutions of the U(1)_{local} x U(1)_{global} model solving the coupled system of Einstein and matter field equations numerically. We study the properties of these solutions in dependence on…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
We derive and discus the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the recently proposed by A. Saa model of gravity with covariantly constant volume with respect to the transposed…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the…
At the present paper, it is studied cosmological solutions and its stability in the frame of F(R) Horava-Lifshitz gravity. The perturbations around general spatially flat FRW solutions are analyzed and it is showed that the stability of…
The semiclassical gravity describes gravitational back-reactions of the classical spacetime interacting with quantum matter fields but the quantum effects on the background is formally defined as higher derivative curvatures. These induce…
We formulate JT quantum gravity on a finite Lorentzian strip. Due to the spatial boundaries of the strip, it is possible to define left and right proper times. With respect to these times we compute non-perturbatively the quantum gravity…
An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global $Z_2$ symmetry of 1+1D…
A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…