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The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular…
Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of…
We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate…
We investigate the energy of a theory with a unit vector field (the "aether") coupled to gravity. Both the Weinberg and Einstein type energy-momentum pseudotensors are employed. In the linearized theory we find expressions for the energy…
In the framework of standard static space times, we state a family of sufficient or necessary conditions for a set of physically reasonable energy and convergence conditions in relativity and related theories. We concentrate our study on…
In this short paper, Penrose's famous singularity theorem is applied to the Kerr space-time. In the case of the maximally extended space-time, the assumptions of Penrose's singularity theorem are not satisfied as the space-time is not…
Based on the conformal energy theorem we prove the uniqueness theorem for static higher dimensional electrically and magnetically charged black holes being the solution of Einstein (n-2)-gauge forms equations of motion. Black hole spacetime…
Tensor-scalar theories of gravitation are commonly employed as extensions of General Relativity that allow to describe a much wider phenomenology. They are also naturally generated as low energy limit of higher-dimensional or unified…
The positive energy theorem precludes the possibility of Minkowski flat space decaying by any mechanism. In certain circumstances, however, large quantum fluctuations of the gravitational field could arise---not only at the Planck scale,…
We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides,…
Starting from non-minimal supergravity theory with unified gauge symmetry, we obtain the low-energy effective theory by taking the flat limit and integrating out the superheavy fields in a model-independent manner. The scalar potential has…
Quantum weak energy inequalities have recently been extensively discussed as a condition on the dynamical stability of quantum field states, particularly on curved spacetimes. We formulate the notion of a quantum weak energy inequality for…
We study the properties of a class of quantum field theories endowed with an equal number of anti commuting and commuting field variables, the most common example being the supersymmetric models. Based on the scaling properties of the…
The Einstein equation in a semi-classical approximation is applied to a spherical region of the universe, with the stress-energy tensor consisting of the mass density and pressure of the LambdaCDM cosmological model plus an additional…
We discuss the set of constraints for Einstein-aether theories, comparing the flat background case with what is expected when the gravitational fields are dynamic. We note potential pathologies occurring in the weak gravitational field…
We consider the nonlinear energy conditions and their quantum extensions. These new energy conditions behave much better than the usual pointwise energy conditions in the presence of semiclassical quantum effects. Analogous quantum…
In this paper we investigate the energy distribution of states of a linear scalar quantum field with arbitrary curvature coupling on a curved spacetime which fulfill some local thermality condition. We find that this condition implies a…
We consider versions of the Penrose singularity theorem and the Hawking horizon topology theorem in weighted spacetimes that contain weighted versions of trapped surfaces, for arbitrary spacetime dimension and synthetic dimension. We find…
It was recently shown by Whinnett & Torres \cite{WT} that the phenomenon of spontaneous scalarization (SC) in compact objects (polytropes) was accompanied also by a {\it spontaneous violation of the weak energy condition} (WEC). Notably, by…
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables…