We first consider the Lagrangian formulation of general relativity for perturbations with respect to a background spacetime. We show that by combining Nœther’s method with Belinfante’s “symmetrization” procedure we obtain conserved vectors that are independent of any divergence added to the perturbed Hilbert Lagrangian. We also show that the corresponding perturbed energy-momentum tensor is sym...

One of the most interesting questions in Riemannian geometry is that of deciding whether a manifold admits curvatures of certain kinds. More specifically, one might want to know whether some given manifold admits a canonical metric, i.e. one with constant curvature of some form (sectional curvature, scalar curvature, etc.). (This will in fact have many topological implications.). One such probl...

Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with emergent extra dimension, described by dual holographic Einstein-Klein-Gordon type action. Here, the dynamics of both order-parameter and metric tensor originate from density-density energy-momentum tensor-tensor interactions, respectively, in transformation, per...

We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple proof of Friedrich’s result on the future hyperboloidal stability of Minkowski spacetime, and extends its validity to even dimensions.

The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton–Jacobi method to calculate the boundary counterterms necessary to remove the divergences and allow the study of the thermodynamics of Einstein–Gauss–Bonnet black holes. PACS numbers: 04.20.Fy, 04.50.Gh, 04.70.Dy, 11.10.Kk

The massless conformally coupled scalar field is characterized by the so-called “new improved stress-energy tensor”, which is capable of classically violating the null energy condition. When coupled to Einstein gravity we find a three-parameter class of exact solutions. These exact solutions include the Schwarzschild geometry, assorted naked singularities, and a large class of traversable wormh...

We discuss the Kaluza–Klein reduction of spaces with (anti-)self-dual Weyl tensor and point out the emergence of the Einstein–Weyl equations for the reduction from four to three dimensions. As a byproduct we get a simple expression for the gravitational instanton density in terms of the Kaluza–Klein functions. © 2007 Elsevier B.V. All rights reserved.

We reconsider the consistency constraints on a free massless symmetric, rank 2, tensor field in a background and confirm that they uniquely require it to be the linear deviation about (cosmological) Einstein gravity. Neither adding non-minimal higher derivative terms nor changing the gauge transformations by allowing terms non-analytic in the cosmological constant alters this fact.

In this essay, I consider the ontological status of spacetime from the points of view of the standard tensor formalism and three alternatives: twistor theory, Einstein algebras, and geometric algebra. I briefly review how classical field theories can be formulated in each of these formalisms, and indicate how this suggests a structural realist interpretation of spacetime.