Related papers: General existence proof for rest frame systems in …
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
A quantum theory of asymptotically flat space-times is presented using the solutions of the Null Surface Formulation (NSF) field equations in a perturbative scheme. Free-field commutation relations are given for the null free data of NSF at…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used.…
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…
Popular wisdom amongst theoretical physicists says that the continuum structure of spacetime is probably not elementary, but rather emergent. While many arguments to support that view arise from speculative ideas, the argument can also be…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
There is proved an existence theorem, in the Newtonian theory, for static, self-gravitating bodies composed of elastic material. The theorem covers the case where these bodies are small, but allows them to have arbitrary shape.
In this paper we argue that classical, asymptotically AdS spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each…
In this paper, we establish global existence of smooth solutions for the Cauchy problem of the critical nonlinear wave equation with time dependent variable coefficients in three space dimensions…
The study of stable minimal surfaces in Riemannian $3$-manifolds $(M, g)$ with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when $(M, g)$ is asymptotically flat and has horizon…
We prove the uniqueness theorem for asymptotically flat static vacuum black hole solutions in higher dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same spacetime…
It is shown that in spite of a generally accepted concept, there exist nondiffeomorphic solutions to the Cauchy problem in nonempty spacetime, which implies the necessity for canonical complementary conditions. It is nonlocal quantum jumps…
We study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of…
In this paper, we introduce a nonresident computer virus model and prove the existence of at least one positive periodic solution. The proposed model is based on a biological approach and is obtained by considering that all rates (rates…
We investigate the Einstein vacuum equations as well as the Einstein-null fluid equations describing neutrino radiation. We find new structures in gravitational waves and memory for asymptotically-flat spacetimes of slow decay. These…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
We consider a globally hyperbolic, stationary spacetime containing a black hole but no white hole. We assume, further, that the event horizon, $\tn$, of the black hole is a Killing horizon with compact cross-sections. We prove that if…
The rigidity of the positive mass theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We prove a corresponding stability theorem for spaces that can be…
We find a class of exact solutions of differentially rotating dust in the framework of General Relativity. There exist asymptotically flat space-times of the flow with positive mass function that for radii sufficiently large is monotonic…