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A general formal definition of a theory of space and time compatible with the inertia principle is given. The formal definition of reference frame and inertial equivalence between reference frames are used to construct the class of inertial…
The dynamics of classical field theories is usually governed by field equations, but when fields are constrained to bounded domains it is also dependent on its boundary conditions. Usually boundary conditions are constrained by the…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
We describe a nonsmooth notion of globally hyperbolic, regular length metric spacetimes $(\mathrm{M},l)$. It is based on ideas of Kunzinger-S\"amann, but does not require Lipschitz continuity of causal curves. We study geodesics on…
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
In the context of inflationary models with a pre-inflationary stage, in which the Einstein equations are obeyed, the weak energy condition is satisfied, and spacetime topology is trivial, we argue that homogeneity on super-Hubble scales…
We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter…
The well-known energy problem is discussed in f(R) theory of gravity. We use the generalized Landau-Lifshitz energy-momentum complex in the framework of metric f(R) gravity to evaluate the energy density of plane symmetric solutions for…
We revisit the classical thermodynamic stability of the standard black hole solutions by implementing the intrinsic necessary and sufficient conditions for stable global and local thermodynamic equilibrium. The criteria for such equilibria…
We consider the Euler equations governing relativistic compressible fluids evolving in the Minkowski spacetime with several spatial variables. We propose a new symmetrization which makes sense for solutions containing vacuum states and, for…
In order to shed some light on the current discussion about f(R)-gravity theories we derive and discuss the bounds imposed by the energy conditions on a general f(R) functional form. The null and strong energy conditions in this framework…
Smooth solutions of the forced incompressible Euler equations satisfy an energy balance, where the rate-of-change in time of the kinetic energy equals the work done by the force per unit time. Interesting phenomena such as turbulence are…
There ought to exist a reformulation of quantum theory, even at energy scales much lower than Planck scale, which does not depend on classical time. Such a formulation is required also for the standard model of particle physics, at the low…
Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction…
We develop the formalism for determining the quasinormal modes of general relativistic multi-fluid compact stars in such a way that the impact of superfluid gap data can be assessed. Our results represent the first attempt to study true…
The energy conditions and the Dolgov-Kawasaki criterion in generalized $f(R)$ gravity with arbitrary coupling between matter and geometry are derived in this paper, which are quite general and can degenerate to the well-known energy…
In this sequel paper we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a…
This note summarizes a model-independent analysis of the age of the universe problem that trades off precision in favour of robustness: The energy conditions of Einstein gravity are designed to extract as much information as possible from…
Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum…