Related papers: The Geometrical Trinity of Gravity
According to General Relativity gravity is the result of the interaction between matter and space-time geometry. In this interaction space-time geometry itself is dynamical: it can store and transport energy and momentum in the form of…
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation…
We consider the problem of finding a dual formulation of gravity in the presence of non-trivial matter couplings. In the absence of matter a dual graviton can be introduced only for linearised gravitational interactions. We show that the…
The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special…
There exists some confusion, as evidenced in the literature, regarding the nature of the gravitational field in Einstein's General Theory of Relativity. It is argued here the this confusion is a result of a change in interpretation of the…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
In the gauge theoretic approach of gravity, General Relativity is described by gauging the symmetry of the tangent manifold in four dimensions. Usually the dimension of the tangent space is considered to be equal to the dimension of the…
The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity…
This thesis is devoted to the study of gravitational theories which can be seen as modifications or generalisations of General Relativity. The motivation for considering such theories, stemming from Cosmology, High Energy Physics and…
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…
The Palatini formalism is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, but we follow a completely covariant approach by…
One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it…
We consider the formulation of entropic gravity in two spacetime dimensions. The usual gravitational force law is derived even in the absence of area, as normally required by the holographic principle. A special feature of this perspective…
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…
Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We…
Although it's widely believed that gravity should have a quantum nature like every other force, the conceptual obstacles to constructing a quantum theory of gravity compel us to explore other perspectives. Gravity is not like any other…
We present a modification to General Relativity by making a redefinition of the coupling constant in front of the Ricci curvature scalar along with the Generalized Quasi-topological Gravity theories added to the action, that we named…
The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…