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The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
It has often been suggested that retrocausality offers a solution to some of the puzzles of quantum mechanics: e.g., that it allows a Lorentz-invariant explanation of Bell correlations, and other manifestations of quantum nonlocality,…
The well-known Bielinski-Khalatnikov-Lifshitz (BKL) scenario for the universe near the cosmological singularity is supplemented with a few exact results following from the BKL asymptotic of the Einstein equations: (1) The cosmological…
We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a…
By including appropriate Riemman cubic invariants, we find that the dynamics of classical time crystals can be straightforwardly realized in Einstein gravity on the FLRW metric. The time reflection symmetry is spontaneously broken in the…
One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of…
The problem of time is a deep paradox in our physical description of the world. According to Aristotle's relational theory, time is a measure of change and does not exist on its own. In contrast, quantum mechanics, just like Newtonian…
We show that Einstein's equations in a non-standard gauge have vacuum solutions with an asymptotically flat rotation curve as it is observed in the dark halos of galaxies. Introducing a material disk into this model we find a matter density…
A class of exact solutions of Einstein's equations is analysed which describes uniformly accelerating charged black holes in an asymptotically de Sitter universe. This is a generalisation of the C-metric which includes a cosmological…
The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could…
We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that solutions…
An exact solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects. The physical part of this solution has the topology of a torus,…
The metric of a spacetime can be greatly simplified if the spacetime is circular. We prove that in generic effective theories of gravity, the spacetime of a stationary, axisymmetric and asymptotically flat solution must be circular if the…
We consider the solvability of the direct scattering problem of an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. We prove the existence and uniqueness…
The Kasner metrics are among the simplest solutions of the vacuum Einstein equations, and we use them here to examine the conformal method of finding solutions of the Einstein constraint equations. After describing the conformal method's…
An electric monopole solution to the equations of Maxwell and Einstein's general relativity is displayed. It differs from the usual one in that all components of the metric vanish at large spatial distances from the charge rather than…
A simple yet systematic new algorithm to investigate the global structure of Kerr-Newman spacetime is suggested. Namely, the global structure of \theta=const. timelike submanifolds of Kerr-Newman metric are studied by introducing a new time…
The classical Avez-Seifert theorem is generalized to the case of the Lorentz force equation for charged test particles with fixed charge-to-mass ratio. Given two events x_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, and a…
In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that…