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General Relativity can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type $f(F\wedge F)$, where $F$ is the curvature 2-form of the spin connection. A theory from this class with a…
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from…
A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…
This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics…
Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring…
We develop a purely quantum theory based on the novel principle of relativity, termed the quantum principle of relativity, instead of directly applying the diffeomorphism invariance. We demonstrate that the essence of the principle can be…
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of…
Gravitational and electroweak interactions can be unified in analogy with the unification in the Weinberg-Salam theory. The Yang-Mills framework is generalized to include space-time translational group T(4), whose generators $T_{\mu}(=\p/\p…
The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the…
The Carrollian limit ($c \to 0$) of General Relativity provides the geometric language for describing null hypersurfaces, such as black hole event horizons and null infinity. Motivated by the well-established electric and magnetic limits of…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
The problem of observables in classical and quantum gravity is a long-standing one. It is sometimes argued that observable quantities should be diffeomorphsm invariant, following the philosophy of Dirac. We argue that diffeomorphism…
We give precise details to support that observations of gravitational lensing at scales of individual, groups and clusters of galaxies can be understood in terms of non-Newtonian gravitational interactions with a relativistic structure…
Taking a hint from Dirac's large number hypothesis, we note the existence of cosmic combined conservation laws that work to cosmologically long time. We thus modify or generalize Einstein's theory of general relativity with fixed…
General relativity describes the dynamics of gravitational waves, which can feature nonlinear interactions, such as those underlying turbulent processes. Theoretical and numerical explorations have demonstrated the existence of…
Soon after the Yang-Mills work, the gauge invariance became one of the basic principles in the elementary particles theory. The gauge invariance idea is that Lagrangian has to be invariant not only with respect to the coordinates…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
We explore the hypothesis that the set of symmetries enjoyed by the theory that describes gravity is not the full group of diffeomorphisms Diff(M), as in General Relativity, but a maximal subgroup of it, TransverseDiff(M), with its elements…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…