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The absence of unique time evolution in Einstein's spacetime description of gravity leads to the hitherto unresolved `problem of time' in quantum gravity. Shape Dynamics is an objectively equivalent representation of gravity that trades…
To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…
There are various types of global and local spacetime invariant in general relativity. Here I focus on the local invariants obtainable from the curvature tensor and its derivatives. The number of such invariants at each order of…
This paper presents the extension from flat spacetime into curved spacetime of the area of theoretical investigation that has been known as topological gauge field theory. The extension here presented is based upon a new derivation of the…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…
Based on the concept of curved spacetime in Einsteinian General Relativity, the field theories and their quantum theories in the curved octonion spaces etc are discussed. The research results discover the close relationships of the curved…
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…
Flat space cosmology spacetimes are exact time-dependent solutions of 3-dimensional gravity theories, such as Einstein gravity or topologically massive gravity. We exhibit a novel kind of phase transition between these cosmological…
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with…
As an alternative way of describing the cosmological velocity field, we discuss the evolution of rotational invariants constructed from the velocity gradient tensor. Compared with the traditional divergence-vorticity decomposition, these…
We investigate the thermodynamical properties of quantum fields in curved spacetime. Our approach is to consider quantum fields in curved spacetime as a quantum system undergoing an out-of-equilibrium transformation. The non-equilibrium…
Einstein's special theory of relativity revolutionized physics by teaching us that space and time are not separate entities, but join as ``spacetime''. His general theory of relativity further taught us that spacetime is not just a stage on…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
This letter presents a new approach using the cosmic peculiar velocity field to characterize the morphology and size of large scale structures in the local Universe. The algorithm developed uses the three-dimensional peculiar velocity field…
We present a comprehensive Eulerian (Hamiltonian) framework for relativistic fluid dynamics in curved spacetimes, with emphasis on Schwarzschild geometry. The key innovation lies in the consistent use of density and three-velocity fields,…
The idea that the Universe is a program in a giant quantum computer is both fascinating and suffers from various problems. Nonetheless, it can provide a unified picture of physics and this can be very useful for the problem of Quantum…
A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the…
Scalar features in time-dependent fluid flow are traditionally visualized using 3D representation, and their topology changes over time are often conveyed with abstract graphs. Using such techniques, however, the structural details of…