Related papers: Dependence Relations in General Relativity
We propose a definition for background (in)/dependence in dynamical theories of the evolution of configurations that have a continuous symmetry and test this definition on particle models and on gravity. Our definition draws from Barbour's…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than…
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…
We establish a correspondence between higher-derivative gravitational scalar-tensor theories of the form $\Psi(R,(\nabla R)^2,\Box R)$ and generalized hybrid metric-Palatini models $f(R,\mathcal{R})$. Restricting to the physically relevant…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime…
We present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences…
Understanding the observer-dependent nature of quantum entanglement has been a central question in relativistic quantum information. In this paper we will review key results on relativistic entanglement in flat and curved spacetime and…
Space and time are central concepts for understanding our World. They are important ingredients at the core of every scientific theory and subject of intense debate in philosophy. Albert Einstein's Special and General theories of Relativity…
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety…
We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit…
It is known that in f(R) theories of gravity with an independent connection which can be both non-metric and non symmetric, this connection can always be algebraically eliminated in favour of the metric and the matter fields, so long as it…
Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge…
The Plebanski formulation of complex general relativity is given in terms of variables valued in the complexification of the $so(3)$ Lie algebra. Therefore, it is genuinely a gauge theory that is also diffeomorphism-invariant. For this…
The formulation of General Relativity presented in math-ph/0506077 and the Hamiltonian formulation of Gauge theories described in math-ph/0507001 are made to interact. The resulting scheme allows to see General Relativity as a constrained…
We explore a background-independent theory of composite gravity. The vacuum expectation value of the composite metric satisfies Einstein's equations (with corrections) as a consistency condition, and selects the vacuum spacetime. A…
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local…
Spacetime geometry is described by two -- {\em a priori} independent -- geometric structures: the symmetric connection $\Gamma$ and the metric tensor $g$. Metricity condition of $\Gamma$ (i.e. $\nabla g = 0$) is implied by the Palatini…
Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective average action of Quantum Einstein…