Related papers: Gravitational Actions in Two Dimensions and the Ma…
We prove that Riemannian metrics in General Relativity in the \emph{`normal-coordinates'} gauge are in one-to-one correspondence with curvature 2-forms. We discuss how this can be used as a change of variables in the operator formalism to…
In this note we show the existence of the hyperbolical geometric quantum phase that is different from the ordinary trigonometric geometric quantum phase. Gravitomagnetic charge (dual mass) is the gravitational analogue of magnetic monopole…
The article deals with the role of gravitational radiation energy in the large-scale dynamics of the universe. Motivated by the observed accelerated expansion, we investigate whether gravitational energy, treated as a well-defined physical…
We obtain an analytic approximation for the effective action of a quantum scalar field in a general static two-dimensional spacetime. We apply this to the dilaton gravity model resulting from the spherical reduction of a massive,…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
Dynamics of the multi-component, multi-field quintessence and gravity is formulated as relativistic N-particle dynamics, embedded in a static viscus flat space and under the forces given by an interacting Lorentz scalar potential via…
We investigate the influence of the chimney topology $T\times T\times R$ of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One…
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. This is proved directly for the two body problem and for the three body problem by using the Garnier equations…
We study the effective action in 2D dilaton-Maxwell quantum gravity. Working with the one-loop renormalizable subset of such theories, we construct the improved effective Lagrangian which contains curvature under logarithm. This effective…
The ten dimensional heterotic string effective action with graviton, dilaton and antisymmetric tensor fields is dimensionally reduced to two spacetime dimensions. The resulting theory, with some constraints on backgrounds, admits infinite…
We study quantum gravity signatures emerging from phenomenologically motivated multiscale models, spectral actions, and Causal Set Theory within the detector approach to the Unruh effect. We show that while the Unruh temperature is…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…
Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show…
Let (M,J) be an almost complex manifold. We show that the infinite-dimensional space Tau of totally real submanifolds in M carries a natural connection. This induces a canonical notion of geodesics in Tau and a corresponding definition of…
Riemannian geometry is a particular case of Hamiltonian mechanics: the orbits of the hamiltonian $H=\frac{1}{2}g^{ij}p_{i}p_{j}$ are the geodesics. Given a symplectic manifold (\Gamma,\omega), a hamiltonian $H:\Gamma\to\mathbb{R}$ and a…
Donaldson conjectured \cite{Dona96} that the space of K\"ahler metrics is geodesic convex by smooth geodesic and that it is a metric space. Following Donaldson's program, we verify the second part of Donaldson's conjecture completely and…
Recently, motivated by certain loop quantum gravity inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second derivative theories of gravity exist (as revealed by the presence of three…
We consider a theory of modified gravity possessing d extra spatial dimensions with a maximally symmetric metric and a scale factor, whose (4+d)-dimensional gravitational action contains terms proportional to quadratic curvature scalars.…
We propose and study a new action for three-dimensional massive gravity. This action takes a very simple form when written in terms of connection and triad variables, but the connection can also be integrated out to obtain a triad…