arXiv subjects
Publications and source records attributed to Valerio Faraoni.
We report a new one-parameter family of spherically symmetric, inhomogeneous, and time-dependent solutions of the vacuum Brans-Dicke field equations which are conformal to the Roberts scalar field geometries of Einstein gravity. The new solution is spherical and time-dependent and contains a naked central singularity. We use it as a seed to generate another two-parameter family of solutions using a known symmetry of vacuum Brans-Dicke gravity.
The concept of turnaround surface in an accelerating universe is generalized to arbitrarily large deviations from spherical symmetry, to close the gap between the idealized theoretical literature and the real world observed by astronomers. As an analytical application, the characterization of turnaround surface is applied to small deviations from spherical symmetry, recovering a previous result while extending it to scalar-tensor gravity.
We point out an association between anomalies in the Hawking quasilocal mass (or, in spherical symmetry, in its better known version, the Misner-Sharp-Hernandez mass) and unphysical properties of the spacetime geometry. While anomalous behaviors show up in certain quantum-corrected black holes, they are not unique to this context and signal serious physical pathologies of isolated gravitating systems in general.
We construct models of Einstein and $f(R)$ gravity with two scalar fields, which admit analytical solutions describing time-varying dynamical black holes. Their thermodynamics is investigated in the adiabatic approximation. In addition to the Misner-Sharp-Hernandez quasilocal mass, we provide time-dependent thermodynamical quantities, including the Hawking temperature, Helmholtz free energy, entropy, and thermodynamical energy. The latter does not always coincide with the Misner-Sharp-Hernandez mass at the horizon, although they coincide in the static limit. For Schwarzschild-type (i.e., $g_{tt}g_{rr}=-1$) black holes in Einstein gravity, one of the two scalars is always a ghost with negative kinetic energy. We show that this ghost can be avoided in $f(R)$ gravity.
Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing spatially homogeneous and isotropic cosmology in general relativity. These analogies are presented, together with their Lagrangian and Hamiltonian formulations and with an invariant of the Fibonacci sequence.
Emmy, a child prodigy, writes a letter to Santa Claus asking for a Vaidya solution sourced by a massless scalar field with null gradient for Christmas. Santa writes back explaining why such a toy cannot be built and offers an exact plane wave sourced by a scalar field with lightlike gradient as a replacement.
A four-force parallel to the trajectory of a massive particle can always be eliminated by going to an affine parametrization, but the affine parameter is different from the proper time. The main application is to cosmology, in which elements of the cosmic fluid are subject to a pressure gradient parallel to their four-velocities. Natural implementations of parallel four-forces occur when the particle mass changes and in scalar-tensor cosmology.
Using a suitable rescaling of the independent variable, a Lagrangian is found for the nonlinear Vialov equation ruling the longitudinal profiles of glaciers and ice caps in the shallow ice approximation. This leads to a formal analogy between the (rescaled) Vialov equation and the Friedmann equation of relativistic cosmology, which is explored. This context provides a new symmetry of the (rescaled) Vialov equation and gives, at least formally, all its solutions using a generating function, which is the Nye profile for the degenerate case of perfectly plastic ice.
A simplified climate model based on maximum entropy production, described by a variational principle, is revisited and an analytical solution to its Euler-Lagrange equation is found. Mindful of controversy about maximum or minimum entropy production in open thermodynamical systems, we show that the solution extremizing the action integral corresponds to a maximum.
We report a new symmetry of the Einstein-Friedmann equations for spatially flat Friedmann- Lemaître-Robertson-Walker universes. We discuss its application to barotropic perfect fluids and its use as a solution-generating technique for scalar field universes.
Painlevé-Gullstrand coordinates, a very useful tool in spherical horizon thermodynamics, fail in anti-de Sitter space and in the inner region of Reissner-Nordström. We predict this breakdown to occur in any region containing negative Misner-Sharp-Hernandez quasilocal mass because of repulsive gravity stopping the motion of PG observers in radial free fall with zero initial velocity. PG coordinates break down also in the static Einstein universe for completely different reasons. The more general Martel-Poisson family of charts, which normally has PG coordinates as a limit, is reported for static cosmologies (de Sitter, anti-de Sitter and the static Einstein universe).
Following an existing procedure in general relativity, the turnaround radius of a spherical structure is studied in scalar-tensor gravity using a new prescription for the analog of the Hawking-Hayward quasilocal mass in this class of theories.
A recent generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is adapted to general spherically symmetric geometries. It is then applied to several black hole and other spherical solutions of scalar-tensor and $f({\cal R}) $ gravity. The relations of this quasilocal energy with the Abreu-Nielsen-Visser gauge and the Kodama vector are discussed.
A formal analogy between the Friedmann equation of relativistic cosmology and models of convective-radiative cooling/heating of a body (including Newton's, Dulong-Petit's, Newton-Stefan's laws, and a generalization) is discussed. The analogy highlights Lagrangians, symmetries, and mathematical properties of the solutions of these cooling laws.
We study a quantum-corrected Schwarzschild black hole proposed recently in Loop Quantum Gravity. Prompted by the fact that corrections to the innermost stable circular orbit of Schwarzschild diverge, we investigate timelike and null radial geodesics. Massive particles moving radially outwards are confined, while photons make it to infinity with infinite redshift. This unsettling physics, which deviates radically from both Schwarzschild (near the horizon) and Minkowski (at infinity) is due to repulsion by the negative quantum energy density that makes the quasilocal mass vanish as one approaches spatial infinity.
A Newtonian uniform ball expanding in empty space constitutes a common heuristic analogy for FLRW cosmology. We discuss possible implementations of the corresponding general-relativistic problem and a variety of new cosmological analogies arising from them. We highlight essential ingredients of the Newtonian analogy, including that the quasilocal energy is always `Newtonian' in the sense that the magnetic part of the Weyl tensor does not contribute to it. A symmetry of the Einstein-Friedmann equations produces another one in the original Newtonian system.
Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities.
A recent model predicting Omori's law giving the number of aftershocks per unit time following an earthquake involves a differential equation analogous to the Friedmann equation of cosmology. The before-shock phase is analogous to an accelerating universe approaching a Big Rip, the main shock to the Big Rip singularity, and the aftershock to a contracting universe. The analogy provides some physical intuition and Lagrangian and Hamiltonian formulations for Omori's law and its generalizations.