In order to treat quantum cosmology in the framework of Weyl spacetimes we take the first step of extending the Arnowitt-Deser-Misner formalism to Weyl geometry. We then obtain an expression of the curvature tensor in terms of spatial quantities by splitting spacetime in (3+1)-dimensional form. We next write the Lagrangian of the gravitation field based in Weyl-type gravity theory. We extend the general relativistic formalism in such a way that it can be applied to investigate the quantum cosmology of models whose spacetimes are endowed with a Weyl geometrical structure.
We present a detailed methodology for extracting the full set of Newman-Penrose Weyl scalars from numerically generated spacetimes without requiring a tetrad that is completely orthonormal or perfectly aligned to the principal null directions. We also describe how to implement an extrapolation technique for computing the Weyl scalars' contribution at asymptotic null infinity in postprocessing. These methods have been used to produce $Ψ_4$ and $h$ waveforms for the Simulating eXtreme Spacetimes (SXS) waveform catalog and now have been expanded to produce the entire set of Weyl scalars. These ne…
We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known results can be naturally extended to the new geometric scenario, although new difficulties arise. In pursuit of solving the embedding problem we have obtained some no-go theorems. We also highlight some of the difficulties that appear in the embedding problem, which are typical of the Weylian character of the geometry. The establishing of these new results may…
We consider a cosmological model in a Friedmann--Lema\^ıtre--Robertson--Walker background space with an ideal gas defined in Weyl Integrable gravity. In the Einstein-Weyl theory a scalar field is introduced in a geometric way. Furthermore, the scalar field and the ideal gas interact in the gravitational Action Integral. Furthermore, we introduce a potential term for the scalar field potential and we show that the field equations admit a minisuperspace description. Noether's theorem is applied for the constraint of the potential function and the corresponding conservation laws are constructed. …
A construction principle for ADM-type theories in maximal slicing gauge
广义相对论和量子力学中时间概念的不同被广泛指责为我们在寻找完整的量子引力理论方面持续失败的罪魁祸首。在这里，我们解决这个问题，直接从第一原理构建ADM型理论\emph{in a particular time gauge}。的原则表示为相空间约束的条件：我们搜索两组空间协变的约束，产生对称性（是第一类）和规范固定对方留下两个传播的自由度。其中一个集合是Weyl生成元tr $(π)$，另一个集合是包含ADM标量约束$λR- β(π^{ab}π_{ab}+(\mbox{tr}(π))^2/2))$的单参数族。这两组约束可以被看作是用最大切片规范固定来定义ADM型理论。这项工作提供了一个独立的，第一性原理推导ADM重力。上述原理的动机是一个启发式的论点依赖于对称性加倍和量子引力的精确重整化参数之间的关系，除了与空间的超同态兼容。作为一个副产品，这些结果解决了形状动力学最流行的批评之一：它的建设开始从ADM哈密顿公式。目前的工作切断这种依赖：一组约束产生减少相空间理论，可以自然地表示由形状动力学或ADM。更确切地说，由此产生的理论可以自然地“不固定”，以包括空间外尔不变性（形状动力学的对称性）或refoliation对称性（ADM）。
We discuss an enhancement of the Brown-Henneaux boundary conditions in three-dimensional AdS General Relativity to encompass Weyl transformations of the boundary metric. The resulting asymptotic symmetry algebra, after a field-dependent redefinition of the generators, is a direct sum of two copies of the Witt algebra and the Weyl abelian sector. The charges associated to Weyl transformations are non-vanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional non-trivial central extension in the Weyl sector, related to th…
We study the variational principle over an Hilbert-Einstein like action for an extended geometry taking into account torsion and non-metricity. By extending the semi-Riemannian geometry, we obtain an effective energy-momentum tensor which can be interpreted as physical sources. As an application we develop a new manner to obtain the gravitational wave equations on a Weyl-integrable manifold taking into account the non-metricity and non-trivial boundary conditions on the minimization of the action, which can be identified as possible sources for the cosmological constant and provides two differ…
The nature of the scalar field responsible for the cosmological inflation, the \qo{inflaton}, is found to be rooted in the most fundamental concept of the Weyl's differential geometry: the parallel displacement of vectors in curved space-time. The Euler-Lagrange theory based on a scalar-tensor Weyl-Dirac Lagrangian leads straightforwardly to the Einstein equation admitting as a source the characteristic energy-momentum tensor of the inflaton field. Within the dynamics of the inflation, e.g. in the slow roll transition from a \qo{false} toward a \qo{true vacuum}, the inflaton's geometry implies…
