Related papers: A Note On Boundary Conditions In Euclidean Gravity
The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Dirichlet conditions on the boundary induced metric;…
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semiclassical properties of quantum field theories. Within this…
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter…
Recent work in Euclidean quantum gravity has studied boundary conditions which are completely invariant under infinitesimal diffeomorphisms on metric perturbations. On using the de Donder gauge-averaging functional, this scheme leads to…
Invariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is…
We initiate a systematic study of Einstein-Gauss-Bonnet gravity in the presence of boundaries subject to conformal boundary conditions, in which the conformal class of the boundary metric is kept fixed. In Einstein gravity, the trace of the…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
Recent work in the literature has studied a new set of local boundary conditions for the quantized gravitational field, where the spatial components of metric perturbations, and ghost modes, are subject to Robin boundary conditions, whereas…
This paper studies a new set of mixed boundary conditions in Euclidean quantum gravity. These involve, in particular, Robin boundary conditions on the perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on the whole…
Non-local boundary conditions for Euclidean quantum gravity are proposed, consisting of an integro-differential boundary operator acting on metric perturbations. In this case, the operator P on metric perturbations is of Laplace type,…
We formulate the most general gravitational models with constant negative curvature ("hyperbolic gravity") on an arbitrary orientable two-dimensional surface of genus $g$ with $b$ circle boundaries in terms of a $\text{PSL}(2,\mathbb…
Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that,…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
This article studies the Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with \textit{mean concave} boundary in the sense that the mean curvature of the boundary is…
In the one-loop approximation for Euclidean quantum gravity, the boundary conditions which are completely invariant under gauge transformations of metric perturbations involve both normal and tangential derivatives of the metric…
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the…
A finite action principle for three-dimensional gravity with negative cosmological constant, based on a boundary condition for the asymptotic extrinsic curvature, is considered. The bulk action appears naturally supplemented by a boundary…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
According to Witten [1], the conformal boundary condition of gravity, which specifies the conformal geometry of the boundary and the trace of the extrinsic curvature, is elliptic and leads to well-defined perturbation theory of gravity…
Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary…