617 research outputs found
Una lettera perduta di Giovanni Della Casa a Piero Vettori e la corrispondenza burlesca con Antonio Bernardi della Mirandola
No full textThe essay informs of the discovery of a lost letter by Giovanni Della Casa to Piero Vettori in the Livorno Library F. D. Guerrazzi : the missive was published in the Eighteenth-century edition of Della Casa’s Opere and the author provides a new transcription in the Appendix. The essay compares the missive with two other
contemporary letters, focusing on the controversy that arose in those months around the diffusion of the Commentarius by Antonio Bernardi della Mirandola, a philosopher protected by Cardinal Alessandro Farnese. The author eventually claims that also the comic tenzone between Della Casa and Antonio Bernardi should be connected to this controversy, which involved many Florentine friends close to Della Casa (in particular Ubaldino Bandinelli). Through the literary skirmish, Della Casa wanted to mitigate the controversy with Bernardi, with whom he maintained, in the following years, a relationship of friendship and convenience
Lorentz-breaking massive gravity in curved space
No full textA systematic study of the different phases of Lorentz-breaking massive gravity in a curved background is performed. For tensor and vector modes, the analysis is very close to that of Minkowski space. The most interesting results are in the scalar sector where, generically, there are two propagating degrees of freedom (DOF). While in maximally symmetric spaces ghostlike instabilities are inevitable, they can be avoided in a FRW background. The phases with less than two DOF in the scalar sector are also studied. Curvature allows an interesting interplay with the mass parameters; in particular, we have extended the Higuchi bound of de Sitter to Friedman-Robertson-Walker and Lorentz-breaking masses. As in dS, when the bound is saturated there is no propagating DOF in the scalar sector. In a number of phases the smallness of the kinetic terms gives rise to strongly coupled scalar modes at low energies. Finally, we have computed the gravitational potentials for pointlike sources. In the general case we recover the general relativity predictions at small distances, whereas the modifications appear at distances of the order of the characteristic mass scale. In contrast with Minkowski space, these corrections may not spoil the linear approximation at large distances.A systematic study of the different phases of Lorentz-breaking massive gravity in a curved background is performed. For tensor and vector modes, the analysis is very close to that of Minkowski space. The most interesting results are in the scalar sector where, generically, there are two propagating degrees of freedom (DOF). While in maximally symmetric spaces ghostlike instabilities are inevitable, they can be avoided in a FRW background. The phases with less than two DOF in the scalar sector are also studied. Curvature allows an interesting interplay with the mass parameters; in particular, we have extended the Higuchi bound of de Sitter to Friedman-Robertson-Walker and Lorentz-breaking masses. As in dS, when the bound is saturated there is no propagating DOF in the scalar sector. In a number of phases the smallness of the kinetic terms gives rise to strongly coupled scalar modes at low energies. Finally, we have computed the gravitational potentials for pointlike sources. In the general case we recover the general relativity predictions at small distances, whereas the modifications appear at distances of the order of the characteristic mass scale. In contrast with Minkowski space, these corrections may not spoil the linear approximation at large distances
Spherically symmetric solutions in ghost-free massive gravity
No full textRecently, a class of theories of massive gravity has been shown to be ghost-free. We study the spherically symmetric solutions in the bigravity formulation of such theories. In general, the solutions admit both a Lorentz-invariant and a Lorentz-breaking asymptotically flat behavior and also fall into two branches. In the first branch, all solutions can be found analytically and are Schwarzschild-like, with no modification as is found for other classes of theories. In the second branch, exact solutions are hard to find, and relying on perturbation theory, Yukawa-like modifications of the static potential are found. The general structure of the solutions suggests that the bigravity formulation of massive gravity is crucial and more than a tool
Stars and (furry) black holes in Lorentz breaking massive gravity
No full textWe study the exact spherically symmetric solutions in a class of Lorentz-breaking massive gravity theories, using the effective-theory approach where the graviton mass is generated by the interaction with a suitable set of Stu ̈ckelberg fields. We find explicitly the exact black-hole solutions which generalizes the familiar Schwarzschild one, which shows a nonanalytic hair in the form of a powerlike term r. For realistic self-gravitating bodies, we find interesting features, linked to the effective violation of the Gauss law: (i) the total gravitational mass appearing in the standard 1=r term gets a multiplicative renormal- ization proportional to the area of the body itself; (ii) the magnitude of the powerlike hairy correction is also linked to size of the body. The novel features can be ascribed to the presence of the Goldstones fluid turned on by matter inside the body; its equation of state approaching that of dark energy near the center. The Goldstones fluid also changes the matter equilibrium pressure, leading to an upper limit for the graviton mass, m & 1028@29 eV, derived from the largest stable gravitational bound states in the Universe.We study the exact spherically symmetric solutions in a class of Lorentz-breaking massive gravity theories, using the effective-theory approach where the graviton mass is generated by the interaction with a suitable set of Stuckelberg fields. We find explicitly the exact black-hole solutions which generalizes the familiar Schwarzschild one, which shows a nonanalytic hair in the form of a powerlike term r(gamma). For realistic self-gravitating bodies, we find interesting features, linked to the effective violation of the Gauss law: (i) the total gravitational mass appearing in the standard 1/r term gets a multiplicative renormalization proportional to the area of the body itself; (ii) the magnitude of the powerlike hairy correction is also linked to size of the body. The novel features can be ascribed to the presence of the Goldstones fluid turned on by matter inside the body; its equation of state approaching that of dark energy near the center. The Goldstones fluid also changes the matter equilibrium pressure, leading to an upper limit for the graviton mass, m <= 10(-28 divided by 29) eV, derived from the largest stable gravitational bound states in the Universe
Weak massive gravity
No full textWe find a new class of theories of massive gravity with five propagating degrees of freedom where only rotations are preserved. Our results are based on a nonperturbative and background-independent Hamiltonian analysis. In these theories the weak field approximation is well behaved and the static gravitational potential is typically screened a` la Yukawa at large distances, while at short distances no van Dam-Veltman-Zakharov discontinuity is found and there is no need to rely on nonlinear effects to pass the solar system tests. The effective field theory analysis shows that the ultraviolet cutoff is ðmMPlÞ1=2 ’ 1="m, the highest possible. Thus, these theories can be studied in the weak-field regime at all the phenomenologically interesting scales and are candidates for a calculable large-distance modified gravity
Finite energy for a gravitational potential falling slower than 1/r
No full textThe total energy of any acceptable self-gravitating physical system has to be finite. In GR, the static gravitational potential of a self-gravitating body goes as 1=r at large distances and any slower decrease leads to infinite energy. In this work we show that in modified gravity theories the situation can be much different. We show that there exist spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1=r and generically of the form r. This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counter- balancing the apparently infinite energy budget.The total energy of any acceptable self-gravitating physical system has to be finite. In GR, the static gravitational potential of a self-gravitating body goes as 1/r at large distances and any slower decrease leads to infinite energy. In this work we show that in modified gravity theories the situation can be much different. We show that there exist spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1/r and generically of the form r(gamma). This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counterbalancing the apparently infinite energy budget
FRW cosmological perturbations in massive bigravity
No full textCosmological perturbations of Friedmann-Robertson-Walker solutions in ghost free massive bigravity, including also a second matter sector, are studied in detail. At early time, we find that subhorizon exponential instabilities are unavoidable and they lead to a premature departure from the perturbative regime of cosmological perturbations
Un ampliamento della biblioteca di Giovanni Della Casa
No full textThis paper proposes a different reading of the inventory of Giovanni Della Casa’s library to the one carried out previously by Lorenzo Campana and Emanuela Scarpa. Starting from a general description of the document, included in the manuscript volume Vat. lat. 14826, the author assigns to Giovanni Della Casa titles which Campana and Scarpa had attributed to Ubaldino Baldinelli (whose library, or part of it, was included in Della Casa’s in 1551). The author also attempts to identify some of these editions and proposes to date the inventory to 1551, when Della Casa was about to take definitive leave of Rome to move to Venice
Massive gravity: A general analysis
No full textMassive gravity can be described by adding to the Einstein-Hilbert action a function V of metric components. By using the Hamiltonian canonical analysis, we find the most general form of V such that five degrees of freedom propagate non perturbatively. The construction is based on a set of differential equations for V , that remarkably can be solved in terms of two arbitrary functions. Besides recovering the known “Lorentz invariant” massive gravity theory, we find an entirely new class of solutions, with healthy features on the phenomenological side, in particular they are weakly coupled in the solar system and have a high ultraviolet cutoff Λ2 = (mMpl)1/2, where m is the graviton mass scale
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