Marco Ferraris

Università degli Studi di Torino, Dipartimento di Matematica G. Peano, Faculty Member

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Address: Torino, Piemonte, Italy

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Papers by Marco Ferraris

Emergent Gravity from an Augmented Variational Principle

arXiv: General Relativity and Quantum Cosmology, 2016

A direct and non-trivial link between Padmanabhan's entropy used in emergent gravity and stan... more A direct and non-trivial link between Padmanabhan's entropy used in emergent gravity and standard GR action is established. To do that, Augmented Variational Principles (AVP) will be used. We shall discuss how this link accounts for the details of the variation of Padmanabhan's action based on gravitational entropy. It will also clarify the role of the background metric and its non-dynamical role.

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Discrete relativistic positioning systems

General Relativity and Gravitation, 2020

We discuss the design for a discrete, immediate, simple relativistic positioning system (rPS) whi... more We discuss the design for a discrete, immediate, simple relativistic positioning system (rPS) which is potentially able of self-positioning (up to isometries) and operating without calibration or ground control assistance. The design is discussed in 1+1 spacetimes, in Minkowski and Schwarzschild solutions, as well as in 2+1 spacetimes in Minkowski. The system works without calibration, i.e. clock synchronizations, or prior knowledge about the motion of clocks, it is robust, i.e. it is able to test hypotheses break down (for example, if one or more clocks temporarily become not-freely falling, or the gravitational field changes), and then it is automatically back and operational when the assumed conditions are restored. In the Schwarzschild case, we also check that the system can best fit the gravitational mass of the source of the gravitational field. We stress that no weak field assumptions are made anywhere. In particular, the rPS we propose can work in a region close to the horizon since it does not use approximations or PPN expansions. More generally, the rPS can be adapted as detectors for the gravitational field and we shall briefly discuss their role in testing different theoretical settings for gravity. In fact, rPS is a natural candidate for a canonical method to extract observables out of a gravitational theory, an activity also known as designing experiments to test gravity.

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$Research paper thumbnail of Hubble drift in Palatini $f(\mathcal{R})$ f ( R ) theories$

Hubble drift in Palatini $f(\mathcal{R})$ f ( R ) theories

The European Physical Journal Plus, 2019

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The emergent gravity’s entropy Ansatz from an augmented variational principle

Journal of Physics: Conference Series, 2017

In the last decade, physical and geometrical investigations about the relationship between horizo... more In the last decade, physical and geometrical investigations about the relationship between horizon thermodynamics and gravitational dynamics suggest that gravity could be an emergent phenomenon. Among the others, Padmanabhan's theory of "emergent gravity" focus on the concept of spacetime as an effective macroscopic description of a more fundamental microscopic theory ("atoms of spacetime") at the Planck scales, thus aiming to reconcile the large scale description of gravity and the small one of quantum physics. However, some mathematical aspects of this approach are still not clear as, for example, the derivation of Einstein equations from a suitable entropy functional (and not from an action as in standard General Relativity). Thus in this work, a direct and non-trivial link between Padmanabhan's entropy used in emergent gravity and standard General Relativity action is established. To do that, Augmented Variational Principles and Kerr-Schild metrics will be used. We shall also discuss how this link accounts for the details of the variation of Padmanabhan's action based on gravitational entropy. It will also clarify the role of the background metric used in Padmanabhan's functional and its non-dynamical role.

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On the Globalization of Lagrangian and Hamiltonian Formalisms in Higher-Order Mechanics

The Energy of a Solution from Different Lagrangians

International Journal of Geometric Methods in Modern Physics, 2006

It is known that superpotentials of so-called higher-order theories of gravitation and Einstein t... more It is known that superpotentials of so-called higher-order theories of gravitation and Einstein theories with a cosmological constant are different in the "Palatini" formulation. However, these theories share a number of solutions, the energy of which should be defined out of superpotentials. We shall check that using augmented variational principles, recently introduced by us, the energy of a solution is defined regardless of the theory, and hence regardless of the superpotential used.

Intrinsic ADM formalism for generally covariant higher-order field theories

Conservation laws in general relativity

Classical and Quantum Gravity, 1992

The conservation laws are examined from the transformation properties of the Lagrangian. The ener... more The conservation laws are examined from the transformation properties of the Lagrangian. The energymomentum complex obtained has mixed indices, T", whereas a symmetric quantity V" is required for the definition of angular momentum. Such a symmetric quantity has been constructed by Landau and Lifshitz. In the course of examining the relationship between these quantities, two hierarchies of complexes T'(")""and g"(")t"" are constructed. Under linear coordinate transformations the former are tensor densities of weight (I+1) and the latter of weight (++2).For I=0 these reduce to the canonical T""and the Landau-Lifshitz K"', respectively. By requiring the energy-momentum complex to generate the coordinate transformations, and the total energy and momentum to form a free vector, one can identify the canonical complex T"' as the appropriate quantity to describe the energy and momentum of the field plus matter. Similarly, by requiring the total angular momentum to behave as a free antisymmetric tensor, one can construct, in the usual manner, an appropriate quantity from T& 1)"".The angular momentum complex so defined differs from that proposed by Landau and Lifshitz as well as from an independent construction by Bergmann and Thomson.

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ADM pseudotensors, conserved quantities and covariant conservation laws in general relativity

Annals of Physics, 2012

The ADM formalism is reviewed and techniques for decomposing generic components of metric, connec... more The ADM formalism is reviewed and techniques for decomposing generic components of metric, connection and curvature are obtained. These techniques will turn out to be enough to decompose not only Einstein equations but also covariant conservation laws. Then a number of independent sets of hypotheses that are sufficient (though non-necessary) to obtain standard ADM quantities (and Hamiltonian) from covariant conservation laws are considered. This determines explicitely the range in which standard techniques are equivalent to covariant conserved quantities. The Schwarzschild metric in different coordinates is then considered, showing how the standard ADM quantities fail dramatically in non-Cartesian coordinates or even worse when asymptotically flatness is not manifest; while, in view of their covariance, covariant conservation laws give the correct result in all cases. * This paper is published despite the effects of the Italian law 133/08 (http://groups.google.it/group/scienceaction). This law drastically reduces public funds to public Italian universities, which is particularly dangerous for free scientific research, and it will prevent young researchers from getting a position, either temporary or tenured, in Italy. The authors are protesting against this law to obtain its cancellation.

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Variational formulation of general relativity from 1915 to 1925 ?Palatini's method? discovered by Einstein in 1925

General Relativity and Gravitation, 1982

Among the three basic variational approaches to general relativity, the metric-affine variational... more Among the three basic variational approaches to general relativity, the metric-affine variational principle, according to which the metric and the affine connection are varied independently, is commonly known as the "Palatini method." In this paper we revisit the history of the "golden age" of general relativity, through a discussion of the papers involving a variational formulation of the field problem. In particular we find that the original Palatini paper of 1919 was rather far from what is usually meant by "Palatini's method," which was instead formulated, to our knowledge, by Einstein in 1925.

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Extended cosmology in Palatini f(ℛ)-theories

Journal of Cosmology and Astroparticle Physics

We consider the cosmological models based on Palatini f (R)-theory for the function f (R) = αR− β... more We consider the cosmological models based on Palatini f (R)-theory for the function f (R) = αR− β 2 R 2 − γ 3R , which, when only dust visible matter is considered, is called dune cosmology in view of the shape of the function f (R(a)) (being a the scale factor). We discuss the meaning of solving the model, and interpret it according to the Ehlers-Pirani-Schild framework as defining a Weyl geometry on spacetime. Accordingly, we extend the definitions of luminosity distance, proper distance, and redshift to Weyl geometries and fit the values of parameters to SNIa data. Since the theoretical prediction is model-dependent, we argue that the fit is affected by an extra choice, namely a model for atomic clocks, which, in principle, produces observable effects. To the best of our knowledge, these effects have not being considered in the literature before.

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Geometric Unification of Electromagnetism and Gravitation

Using four equations, a recently proposed classical field theory that geometrically couples elect... more Using four equations, a recently proposed classical field theory that geometrically couples electromagnetism to gravitation in a fundamentally new way is reviewed. Maxwell’s field equations are a consequence of the new theory as are Einstein’s field equations augmented by a term that can replicate both dark matter and dark energy. To emphasize the unification brought to electromagnetic and gravitational phenomena by the new theory specific solutions are investigated: a spherically-symmetric charged particle solution, a cosmological solution representing a homogeneous and isotropic universe, and solutions representing electromagnetic and gravitational waves. A unique feature of the new theory is that both charge and mass density are treated as dynamic fields, this as opposed to their treatment in the classical Maxwell and Einstein field equations where they are introduced as external entities. This feature suggests a procedure for quantizing the mass, charge and angular m...

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Gauge Formalism for General Relativity and Fermionic Matter

General Relativity and Gravitation

A new formalism for spinors on curved spaces is developed in the framework of variational calculu... more A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and spinors. An appropriate gauge structure is also given to General Relativity, replacing the metric field with spin frames. Finally, conserved quantities and superpotentials are calculated under a general covariant form.

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Mechanics, Analysis and Geometry: 200 Years After Lagrange

This volume consists of articles written on the occasion of the bicentennial of the publication b... more This volume consists of articles written on the occasion of the bicentennial of the publication by J.-Louis Lagrange of his treatise, Mechanique Analytique (1788). This book opened a floodgate of contributions to mechanics by analysis. The resulting volume provides insight and perspective on various research problems in modern topics of physics, astrophysics, mathematics and the history of science. Furthermore it

N�ther charges, Brown-York quasilocal energy, and related topics

A Model of Topological Affine Gravity in Two Dimensions

A model of two--dimensional gravity with an action depending only on a linear connection is consi... more A model of two--dimensional gravity with an action depending only on a linear connection is considered. This model is a topological one, in the sense that the classical action does not contain a metric or zweibein at all. A metric and an additional vector field are instead introduced in the process of solving equations of motion for the connection. They satisfy the constant curvature equation. It is shown that the general solution of these equations of motion can be described by using the space of orbits under the action of the Weyl group in the functional space containing all pairs formed by a metric and a vectorfield. It is shown also that this model admits an equivalent description by using a family of actions depending on the metric and the connection as independent variables.

Gravitational Energies and Generalized Geometric Entropy

AIP Conference Proceedings, 2005

ABSTRACT A geometrical covariant definition of the variation of conserved quantities is introduce... more ABSTRACT A geometrical covariant definition of the variation of conserved quantities is introduced for Lagrangian field theories, suitable for both metric and affine gravitational theories. When this formalism is applied to the Hilbert Lagrangian we obtain a covariant definition of the Hamiltonian (and consequently a definition of the variation of Energy) for a gravitational system. The definition of the variation of Energy depends on boundary conditions one imposes. Different boundary conditions are introduced to define different energies: the gravitational heat (corresponding to Neumann boundary conditions) and the Brown‐York quasilocal energy (corresponding to Dirichlet boundary conditions) for a gravitational system. An analogy between the behavior of a gravitational system and a macroscopical thermodynamical system naturally arises and relates control modes for the thermodynamical system with boundary conditions for the gravitational system. This geometrical and covariant framework enables one to define entropy of gravitational systems, which turns out to be a geometric quantity with well‐defined cohomological properties arising from the obstruction to foliate spacetimes into spacelike hypersurfaces. This definition of gravitational entropy is found to be very general: it can be generalized to causal horizons and multiple‐horizon spacetimes and applied to define entropy for more exotic singular solutions of the Einstein field equations. The same definition is also well‐suited in higher dimensions and in the case of alternative gravitational theories (e.g. Chern‐Simons theories, Lovelock Gravity). © 2005 American Institute of Physics

On-shell symmetries

We define on-shell symmetries and characterize them for Lagrangian systems. The terms appearing i... more We define on-shell symmetries and characterize them for Lagrangian systems. The terms appearing in the variation of the Poincaré-Cartan form, which vanish because of field equations, are found to be strongly constrained if the space of solutions has to be preserved. The behaviour with respect to solution dragging is also investigated in order to discuss relations with the theory of internal symmetries of a PDE.

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Extended Cosmologies

Symmetry, Integrability and Geometry: Methods and Applications, 2016

We shall discuss cosmological models in extended theories of gravitation. We shall define a surfa... more We shall discuss cosmological models in extended theories of gravitation. We shall define a surface, called the model surface, in the space of observable parameters which characterises families of theories. We also show how this surface can be used to compare with observations. The model surface can potentially be used to falsify whole families of models instead reasoning on a single model basis as it is usually done by best fit arguments with observations.

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BRST invariance and Poincar�-Cartan forms

Il Nuovo Cimento B, 1995

Marco Ferraris

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