arXiv subjects
Publications and source records attributed to Valerio Faraoni.
Existing literature implements the Dominant Energy Condition for dissipative fluids in general relativity. It is pointed out that this condition fails to forbid superluminal flows, which is what it is ultimately supposed to do. Tilted perfect fluids, which formally have the stress-energy tensor of imperfect fluids, are discussed for comparison.
With insight from examples and physical arguments, the Tolman-Ehrenfest criterion of thermal equilibrium for test fluids in static spacetimes is extended to local thermal equilibrium in conformally static geometries. The temperature of the conformally rescaled fluid scales with the inverse of the conformal factor, reproducing the evolution of the cosmic microwave background in Friedmann universes, the Hawking temperature of the Sultana-Dyer cosmological black hole, and a heuristic argument by Dicke.
The Bekenstein-Hawking entropy of a black hole is proportional to its horizon area, hence in $D=2$ spacetime dimensions it is constant because the horizon degenerates into two points. This fact is consistent with Einstein's gravity becoming topological in two dimensions. In $F(R)$ gravity, which is non-trivial even in $D=2$, we find that the entropy is constant, as for Bekenstein-Hawking. As shown in EPL 139 (2022) no.6, 69001 (arXiv:2208.10146), two-dimensional $F(R)$ gravity is equivalent to Jackiw-Teitelboim gravity, in turn equivalent to the Sachdev-Ye-Kitaev model where the entropy becomes constant in the large $N$ limit. Several recently proposed entropies are functions of the Bekenstein-Hawking entropy and become constant in $D=2$, but in two-dimensional dilaton gravity entropies are not always constant. We study general dilaton gravity and obtain arbitrary static black hole solutions for which the non-constant entropies depend on the mass, horizon radius, or Hawking temperature, and constitute new proposals for a generalized entropy.
Stealth solutions of scalar-tensor gravity and less-known de Sitter spaces that generalize them are analyzed regarding their possible role as thermal equilibria at non-zero temperature in the new first-order thermodynamics of scalar-tensor gravity. No stable equilibria are found, further validating the special role of general relativity as an equilibrium state in the landscape of gravity theories, seen through the lens of first-order thermodynamics.
Observations have found black holes spanning ten orders of magnitude in mass across most of cosmic history. The Kerr black hole solution is however provisional as its behavior at infinity is incompatible with an expanding universe. Black hole models with realistic behavior at infinity predict that the gravitating mass of a black hole can increase with the expansion of the universe independently of accretion or mergers, in a manner that depends on the black hole's interior solution. We test this prediction by considering the growth of supermassive black holes in elliptical galaxies over $0<z\lesssim2.5$. We find evidence for cosmologically coupled mass growth among these black holes, with zero cosmological coupling excluded at 99.98% confidence. The redshift dependence of the mass growth implies that, at $z\lesssim7$, black holes contribute an effectively constant cosmological energy density to Friedmann's equations. The continuity equation then requires that black holes contribute cosmologically as vacuum energy. We further show that black hole production from the cosmic star formation history gives the value of $Ω_Λ$ measured by Planck while being consistent with constraints from massive compact halo objects. We thus propose that stellar remnant black holes are the astrophysical origin of dark energy, explaining the onset of accelerating expansion at $z \sim 0.7$.
Formal analogies between the ordinary differential equations describing geophysical flows and Friedmann cosmology are developed. As a result, one obtains Lagrangian and Hamiltonian formulations of these equations, while laboratory experiments aimed at testing geophysical flows are shown to constitute analogue gravity systems for cosmology.
Two issues in the first-order thermodynamics of scalar-tensor (including ``viable'' Horndeski) gravity are elucidated. The application of this new formalism to FLRW cosmology is shown to be fully legitimate and then extended to all Bianchi universes. It is shown that the formalism holds thanks to the almost miraculous fact that the constitutive relations of Eckart's thermodynamics are satisfied, while writing the field equations as effective Einstein equations with an effective dissipative fluid does not contain new physics.
We apply to tensor-multi-scalar gravity the effective fluid analysis based on the representation of the gravitational scalar field as a dissipative effective fluid. This generalization poses new challenges as the effective fluid is now a complicated mixture of individual fluids mutually coupled to each other and many reference frames are possible for its description. They are all legitimate, although not all convenient for specific problems, and they give rise to different physical interpretations. Two of these frames are highlighted.
We refine and slightly enlarge the recently proposed first-order thermodynamics of scalar-tensor gravity to include gravitational scalar fields with timelike and past-directed gradients. The implications and subtleties arising in this situation are discussed and an exact cosmological solution of scalar-tensor theory in first-order thermodynamics is revisited in light of these results.
The Bekenstein-Hawking entropy is a cornerstone of horizon thermodynamics but quantum effects correct it, while inequivalent entropies arise also in non-extensive thermodynamics. Reviewing our previous work, we advocate for a new entropy construct that comprises recent and older proposals and satisfies four minimal key properties. The new proposal is then applied to black holes and to holographic dark energy and shown to have the potential to cause early universe inflation or to alleviate the current Hubble tension. We then analyze black hole temperatures and masses consistent with alternative entropies.
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.
While the Bekenstein-Hawking entropy is the unique notion of entropy that makes classical black hole thermodynamics consistent, alternative entropy notions (Rényi, Tsallis, and generalized constructs) abound in the literature. We explore conditions under which they are part of a consistent horizon thermodynamics for certain classes of modified gravity black holes. We provide examples in which black hole masses and temperatures going hand-in-hand with these alternative entropies coincide with their usual counterparts associated with the Bekenstein-Hawking entropy.
We generate new spherical and time-dependent solutions of viable Horndeski gravity by disforming a solution of the Einstein equations with scalar field source and positive cosmological constant. They describe dynamical objects embedded in asymptotically FLRW spacetimes and contain apparent horizons and a finite radius singularity that evolve in time in peculiar ways apparently not encountered before in Einstein and "old" scalar-tensor gravity.
Analytical solutions of nonminimally coupled scalar field cosmology corresponding to critical scalar field values constitute a potential challenge to the recent first-order thermodynamics of scalar-tensor gravity (a formalism picturing general relativity as the zero-temperature equilibrium state for modified gravity). The critical solutions are unstable with respect to homogeneous perturbations, hence unphysical.
Heuristic arguments and order of magnitude estimates for partial differential equations highlight essential features of the physics they describe. We present order of magnitude estimates, and their limitations, for the three classic second order PDEs of mathematical physics (wave, heat, and Laplace equations), for first order transport equations, and for two non-linear wave equations. It is beneficial to expose the beginning student to these considerations before jumping into more rigorous mathematics. Yet these simple arguments are missing from physics textbooks.
In the context of the recently proposed first-order thermodynamics of scalar-tensor gravity, we discuss the possibility of zero-temperature states of equilibrium other than Einstein gravity, including pathological Brans-Dicke theory, Palatini $f(R)$ gravity, and cuscuton gravity, all with non-dynamical scalar fields. The formalism is extended to Nordström gravity, which contains only a scalar degree of freedom and has negative temperature relative to general relativity.
We discuss the physical features of two recent classes of analytical solutions of the Einstein equations sourced by an exotic perfect fluid with equation of state $ P=-ρ/5$. These geometries depend on up to four parameters and are static and spherically symmetric. They describe compact spaces with naked central singularities.
We investigate a puzzle in the recent thermodynamics of scalar-tensor gravity, in which general relativity is a zero-temperature state of equilibrium and scalar-tensor gravity is the non-equilibrium configuration of an effective dissipative fluid. A stealth solution of Brans-Dicke gravity with constant positive temperature is shown to be analogous to a metastable state for the effective fluid and to suffer from an instability. The stability analysis employs a version of the Bardeen-Ellis-Bruni-Hwang gauge-invariant formalism for cosmological perturbations adapted to modified gravity. The metastable state is destroyed by tensor perturbations.