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Disformal transformation is a generalisation of the well-known conformal transformation commonly elaborated in mainstream graduate texts in gravity (relativity) and modern cosmology. This transformation is one of the most important…
A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the…
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a)…
The main obstacle in attempts to construct a consistent quantum gravity is the absence of independent flat time. This can in principle be cured by going out to higher dimensions. The modern paradigm assumes that the fundamental theory of…
We consider a model involving a self-interacting complex scalar field minimally coupled to gravity and emphasize the cylindrically symmetric classical solutions. A general ansatz is performed which transforms the field equations into a…
General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general…
We investigate the cosmological dynamics of scalar fields governed by higher-order gravity, with particular emphasis on models inspired by the Pais-Uhlenbeck oscillator--a prototypical fourth-order system known for its connection to…
The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This…
Cylindrical gravitational waves of Einstein gravity are described by an integrable system (Ernst system) whose quantization is a long standing problem. We propose to bootstrap the quantum theory along the following lines: The quantum theory…
Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of…
Picture yourself in the wave zone of a gravitational scattering event of two massive, spinning compact bodies (black holes, neutron stars or stars). We show that this system of genuine astrophysical interest enjoys a hidden $\mathcal{N}=2$…
If gravity is fundamentally quantum, any two quantum particles must get entangled with each other due to their mutual interaction through gravity. This phenomenon, dubbed gravity-mediated entanglement, has led to recent efforts of detecting…
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…
In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer's frame has an important role. The equations of…
The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce…
In asymptotically flat space a rotating black hole cannot be in thermodynamic equilibrium because the thermal radiation would have to be co-rotating faster than light far from the black hole. However in asymptotically anti-de Sitter space…
The main features of an alternative model of redshifts are described here. The model is based on conjectures about an existence of the graviton background with the Planckian spectrum and a super-strong character of quantum gravitational…
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly…
We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like…