Related papers: Generating new gravitational solutions by matrix m…
We illustrate and examine diverse approaches to the quantum matter-gravity system which refer to the Born-Oppenheimer (BO) method. In particular we first examine a quantum geometrodynamical approach introduced by other authors in a manner…
A class of solutions to the WDVV equations is provided by period matrices of hyperelliptic Riemann surfaces, with or without punctures. The equations themselves reflect associativity of explicitly described multiplicative algebra of…
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann…
We describe a simple technique for generating solutions to the classical field equations for an arbitrary nonlinear sigma-model minimally coupled to gravity. The technique promotes an arbitrary solution to the coupled Einstein/Klein-Gordon…
This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…
We present a new algorithm to decompose generic spinor polynomials into linear factors. Spinor polynomials are certain polynomials with coefficients in the geometric algebra of dimension three that parametrize rational conformal motions.…
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…
Due to higher-order Kaup-Newell (KN) system has more complex and diverse solutions than classical second-order flow KN system, the research on it has attracted more and more attention. In this paper, we consider a higher-order KN equation…
Compact binary systems with total masses between tens and hundreds of solar masses will produce gravitational waves during their merger phase that are detectable by second-generation ground-based gravitational-wave detectors. In order to…
Waveforms are classical observables associated with any radiative physical process. Using scattering amplitudes, these are usually computed in a weak-field regime to some finite order in the post-Newtonian or post-Minkowskian approximation.…
Extending the single-angular-momentum case analyzed in our previous work, we investigate the solution-generating technique based on the Breitenlohner-Maison (BM) linear system for asymptotically flat, stationary, bi-axisymmetric black hole…
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as…
We explore possible manifestations of an odd number of extra dimensions in gravitational radiation, which are associated with violation of Huygens' principle in flat odd-dimensional spacetime. Our setup can be regarded as the limit of an…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked points, we consider the moduli of generalized complex structures…
We present the second-order gravitational dynamics for a spacetime inhabited by matter fields which feature vacuum birefringence. The derivation follows a perturbative variant of the covariant constructive gravity program, ensuring…
We describe a unification of several apparently unrelated factorizations arisen from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differential equations. The unification is given by a Birkhoff type…
We propose a nonstandard approach to solving the apparent incompatibility between the coalgebra structure of some inhomogeneous quantum groups and their natural complex conjugation. In this work we sketch the general idea and develop the…
We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy which is used in the original methods, and…