相关论文: Generalized Darmois-Israel junction conditions

Starting with the relativistic Boltzmann equation where the collision term is generalized to include nonlocal effects via gradients of the phase-space distribution function, and using Grad's 14-moment approximation for the distribution…

We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the…

We investigate the global dynamics of the field equations of (pure) quadratic theories of gravity which generalise Einstein's theory in spatially flat homogeneous and isotropic cosmological models with a perfect fluid. We introduce global…

When speaking of the unification of quantum mechanics and relativity, one normally refers to special relativity (SR) or to Einstein general relativity (GR). The Dirac and Klein-Gordon wave equations are an example of unification of quantum…

General Relativity is expected to break down in the high-curvature regime. Beyond an effective field theory treatment with higher-order operators, it is important to identify consistent theories with higher-curvature terms at the…

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a…

Using the principle of least action, the motion equations for a singular hypersurface of arbitrary type in quadratic gravity are derived. Equations containing the "external pressure" and the "external flow" components of the surface…

Higher derivative theory is one of the important models of quantum gravity, renormalizable and asymptotically free within the standard perturbative approach. We consider the $4-\epsilon$ renormalization group for this theory, an approach…

We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group…

Exact solutions of an $ f(R) $-theory (of gravity) in a static central (gravitational) field have been studied in the literature quite well, but, to find and study exact solutions in the case of a non-static central field are not easy at…

We work out the junction conditions for the Palatini $f(\mathcal{R},T)$ extension of General Relativity, where $f$ is an arbitrary function of the curvature scalar $\mathcal{R}$ of an independent connection, and of the trace $T$ of the…

Let $A$ be a sufficiently dense subset of a finite field $\mathbb F_q$ or a finite, cyclic ring $\mathbb Z/ N\mathbb Z$. Assuming that $q$ and $N$ have no small prime divisors, we show that generalised Fermat equations have the expected…

We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the…

The quantum cosmology of a higher-derivative derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler-DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature…

This thesis aims at improving our understanding of the strong-field regime of gravity, where deviations from General Relativity (GR) are expected to be found on theoretical grounds. In particular, we have been concerned with the formulation…

We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra ${\cal A}$. Such a derivation, introduced by Bresar in 1991, is given by a linear mapping $u: {\cal A} \rightarrow {\cal A}$…

Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field.…

An alternative derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson-Myers 'Hamiltonian' method and it does not require computations on…

We present a general formalism for describing singular hypersurfaces in the Einstein theory of gravitation with a Gauss--Bonnet term. The junction conditions are given in a form which is valid for the most general embedding and matter…

We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector. For existence of a well-defined Hamiltonian variational principle taking into…