arXiv subjects

Roberto A Sussman

Publications and source records attributed to Roberto A Sussman.

17 recordsLinked to original sources

arXiv2024

Schouten-Codazzi Gravity

We propose a new phenomenological second order gravity theory to be denoted as ''Schouten-Codazzi' Gravity'' (SCG), as it is based on Schouten and Codazzi tensors. The theory is related, but is clearly distinct from Cotton Gravity. By assuming as source the energy momentum of General Relativity, we form a second order system with its geometric sector given by the sum of the Schouten tensor and a generic second order symmetric tensor complying with the following properties: (i) it must satisfy the Codazzi differential condition and (ii) it must be concomitant with the invariant characterization based on the algebraic structure of curvature tensors for specific spacetimes or classes of spacetimes. We derive and briefly discuss the properties of SCG solutions for static spherical symmetry (vacuum and perfect fluid), FLRW models and spherical dust fluids. While we do recognize that SCG is ``work in progress'' in an incipient stage that still requires significant theoretical development, we believe that the theory provides valuable guidelines in the search for alternatives to General Relativity

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arXiv2024

Exact solutions of Cotton Gravity in its Codazzi formulation

The "Codazzi formulation", based on a Codazzi tensor, provides a more robust and straightforward theoretical framework for "Cotton Gravity" (CG) than its original formulation in terms of the Cotton tensor. Using this formulation we provide a self-consistent procedure to generate non-trivial exact solutions in CG that generalize well known General Relativity (GR) solutions. We re-derive a known CG solution that generalizes the Schwarzschild solution of GR, showing that it is the unique vacuum solution of static spherical symmetry in CG, extending this result to a CG generalization of the Reissner-Nordstrom solution of GR, all of which places a strong case supporting the fulfillment of Birkhoff's theorem. When applied to Friedman-Lema\^ıtre-Robertson-Walker (FLRW) models CG naturally identifies the $Λ$CDM model as the unique FLRW dust model with constant negative spatial curvature. We also obtain CG generalizations of the Lema\^ıtre-Tolman-Bondi (LTB) and Szekeres dust solutions of GR, allowing for time and space dependent changes from decelerated to accelerated evolution, without necessarily assuming a dark energy source. The CG generalization of static perfect fluid spheres allows in the weak field regime to model the flattening of rotation velocities in spherical galactic systems without assuming dark matter. We also generalize non-static spherically symmetric perfect fluid solutions with a shear-free 4 velocity. Our results suggest the need for further research using the Codazzi formulation to explore the potential for applications of CG to current open problems in gravitational systems.

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arXiv2024

Response to a critique of "Cotton Gravity"

We address in this article the criticism in a recently submitted article by Clement and Noiucer (arXiv:2312.17662 [gr-qc]) on "Cotton Gravity" (CG), a gravity theory alternative to General Relativity. These authors claim that CG is "not predictive" for producing "too many" spherically symmetric vacuum solutions, while taking the Bianchi I vacuum as test case they argue that geometric constraint on the Cotton tensor lead to an undetermined problem, concluding in the end that CG "is not a physical theory". We provide arguments showing that this critique is incorrect and misrepresents the theory.

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arXiv2023

Cotton Gravity: the cosmological constant as spatial curvature

We derive Friedman-Lemaitre-Robertson-Walker (FLRW) models as non-trivial solutions of "Cotton Gravity" (CG), a recently proposed gravity theory alternative to General Relativity (GR) based on the Cotton tensor. Using an equivalent formulation, we show that CG leads to FLRW models with a modified expression for spatial curvature in terms of the Ricci scalar of hypersurfaces orthonormal to the 4-velocity. Considering models compatible with a well posed initial value formulation leads to operationally the same FLRW models in GR, but endowed with a precise covariant characterization of the positive/negative cosmological constant as the case with constant negative/positive spatial curvature. Under CG, the $Λ$CDM model becomes the unique FLRW dust model with constant negative spatial curvature.

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arXiv2017

Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis

We examine the evolution of an inhomogeneous mixture of non-relativistic pressureless cold dark matter (CDM), coupled to dark energy (DE) characterised by the equation of state parameter $w<-1/3$, with the interaction term proportional to the DE density. This coupled mixture is the source of a spherically symmetric Lema\^\ itre-Tolman-Bondi (LTB) metric admitting an asymptotic Friedman-Lema\^\ itre-Robertson-Walker (FLRW) background. Einstein's equations reduce to a 5-dimensional autonomous dynamical system involving quasi--local variables related to suitable averages of covariant scalars and their fluctuations. The phase space evolution around the critical points (past/future attractors and five saddles) is examined in detail. For all parameter values and both directions of energy flow (CDM to DE and DE to CDM) the phase space trajectories are compatible with a physically plausible early cosmic times behaviour near the past attractor. This result compares favourably with mixtures with the interaction driven by the CDM density in which conditions for a physically plausible past evolution are more restrictive. Numerical examples are provided describing the evolution of an initial profile that can be associated with idealised structure formation scenarios

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arXiv2017

Lemaitre-Tolman-Bondi dust solutions in f(R) gravity

We derive a class of non-static inhomogeneous dust solutions in f(R) gravity described by the Lemaitre-Tolman-Bondi (LTB) metric. The field equations are fully integrated for all parameter subcases and compared with analogous subcases of LTB dust solutions of GR. Since the solutions do not admit regular symmetry centres, we have two possibilities: (i) a spherical dust cloud with angle deficit acting as the source of a vacuum Schwarzschild-like solution associated with a global monopole, or (ii) fully regular dust wormholes without angle deficit, whose rest frames are homeomorphic to the Schwarzschild-Kruskal manifold or to a 3d torus. The compatibility between the LTB metric and generic f(R) ansatzes furnishes an "inverse procedure" to generate LTB solutions whose sources are found from the f(R) geometry. While the resulting fluids may have an elusive physical interpretation, they can be used as exact non--perturbative toy models in theoretical and cosmological applications of f(R) theories.

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arXiv2014

Gravitational entropies in LTB dust models

We consider generic Lemaitre-Tolman-Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non--local domain dependent manner for the two HB proposals. By looking at the fulfillment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to an FLRW background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a "gravitational entropy" may be a theoretically robust concept applicable to more general spacetimes.

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arXiv2013

Invariant characterization of the growing and decaying density modes in LTB dust models

We obtain covariant expressions that generalize the growing and decaying density modes of linear perturbation theory of dust sources by means of the exact density perturbation from the formalism of quasi--local scalars associated to weighed proper volume averages in LTB dust models. The relation between these density modes and theoretical properties of generic LTB models is thoroughly studied by looking at the evolution of the models through a dynamical system whose phase space is parametrized by variables directly related to the modes themselves. The conditions for absence of shell crossings, as well as sign conditions on the modes, become interrelated fluid flow preserved constraints that define phase space invariant subspaces. In the general case (both density modes being nonzero) the evolution of phase space trajectories exhibits the expected dominance of the decaying/growing in the early/late evolution times defined by past/future attractors characterized by asymptotic density inhomogeneity. In particular, the growing mode is also dominant for collapsing layers that terminate in a future attractor associated with a "Big Crunch" singularity, which is qualitatively different from the past attractor marking the "Big Bang". Suppression of the decaying mode modifies the early time evolution, with phase space trajectories emerging from an Einstein--de Sitter past attractor associated with homogeneous conditions. Suppression of the growing mode modifies the late time evolution as phase space trajectories terminate in future attractors associated with homogeneous states. General results are obtained relating the signs of the density modes and the type of asymptotic density profile (clump or void). A critical review is given of previous attempts in the literature to define these density modes for LTB models.

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arXiv2011

Back-reaction and effective acceleration in generic LTB dust models

We provide a thorough examination of the conditions for the existence of back-reaction and an "effective" acceleration (in the context of Buchert's averaging formalism) in regular generic spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. By considering arbitrary spherical comoving domains, we verify rigorously the fulfillment of these conditions expressed in terms of suitable scalar variables that are evaluated at the boundary of every domain. Effective deceleration necessarily occurs in all domains in: (a) the asymptotic radial range of models converging to a FLRW background, (b) the asymptotic time range of non-vacuum hyperbolic models, (c) LTB self-similar solutions and (d) near a simultaneous big bang. Accelerating domains are proven to exist in the following scenarios: (i) central vacuum regions, (ii) central (non-vacuum) density voids, (iii) the intermediate radial range of models converging to a FLRW background, (iv) the asymptotic radial range of models converging to a Minkowski vacuum and (v) domains near and/or intersecting a non-simultaneous big bang. All these scenarios occur in hyperbolic models with negative averaged and local spatial curvature, though scenarios (iv) and (v) are also possible in low density regions of a class of elliptic models in which local spatial curvature is negative but its average is positive. Rough numerical estimates between -0.003 and -0.5 were found for the effective deceleration parameter. While the existence of accelerating domains cannot be ruled out in models converging to an Einstein de Sitter background and in domains undergoing gravitational collapse, the conditions for this are very restrictive. The results obtained may provide important theoretical clues on the effects of back-reaction and averaging in more general non-spherical models.

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arXiv2010

Radial asymptotics of Lemaitre-Tolman-Bondi dust models

We examine the radial asymptotic behavior of spherically symmetric Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length $\ell$, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular "open" LTB models whose space slices allow for a diverging $\ell$, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as $\ell\to\infty$. The "asymptotic state" is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By looking at different sets of initial conditions, we examine and classify the asymptotic states of parabolic, hyperbolic and open elliptic models admitting a symmetry center. We show that in the radial direction the models can be asymptotic to any one of the following spacetimes: FLRW dust cosmologies with zero or negative spatial curvature, sections of Minkowski flat space (including Milne's space), sections of the Schwarzschild--Kruskal manifold or self--similar dust solutions.

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arXiv2010

A new approach for doing theoretical and numeric work with Lemaitre-Tolman-Bondi dust models

We introduce quasi-local integral scalar variables for the study of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. Besides providing a covariant, and theoretically appealing, interpretation for the parameters of these models, these variables allow us to study their dynamics (in their full generality) by means of fluid flow evolution equations that can be handled with simple numerical techniques and has a significant potential for astrophysical and cosmological applications. These evolution equations can also be understood in the framework of a gauge invariant and covariant formalism of spherical non-linear perturbations on a FLRW background. The covariant time splitting associated with the new variables leads, in a natural way, to rephrase the known analytic solutions within an initial value framework in which covariant scalars are given by simple scaling laws. By using this re-parametrization of the analytic solutions, we re-examine and provide an alternative outlook to various theoretical issues already treated in the literature: regularity conditions, an Omega parameter, as well as the fitting of a given LTB model to radial profiles of density or velocity at different cosmic times. Other theoretical issues and numeric applications will be examined in separate articles.

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arXiv2008

Shear viscosity, relaxation and collision times in spherically symmetric spacetimes

We interpret as shear viscosity the anisotropic pressure that emerges in inhomogeneous spherically symmetric spacetimes described by the Lemaitre-Tolman-Bondi (LTB) metric in a comoving frame. By assuming that local isotropic pressure and energy density satisfy a generic ideal gas equation of state, we reduce the field equations to a set of evolution equations based on auxiliary quasi-local variables. We examine the transport equation of shear viscosity from Extended Irreversible Thermodynamics and use a numerical solution of the evolution equations to obtain the relaxation times for the full and "truncated" versions. Considering a gas of cold dark matter WIMPS after its decoupling from the cosmic fluid, we show that the relaxation times for the general equation are qualitatively analogous to collision times, while the truncated version is inadequate to describe transient phenomena of transition to equilibrium.

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arXiv2008

Quasi-local variables, non-linear perturbations and back-reaction in spherically symmetric spacetimes

We introduce a quasi-local integral functional and scalar quasi-local variables to examine a wide class of spherically symmetric inhomogeneous spacetimes that generalize the Lemaitre-Tolman-Bondi (LTB) dust solutions ("LTB" spacetimes). By using these variables, we can transform the fluid flow evolution equations into evolution equations for non-linear, covariant, gauge--invariant perturbations of Friedman-Lemaitre-Robertson-Walker (FLRW) cosmologies. In the linear limit, we obtain spherical perturbations in the synchronous gauge under the long wavelength approximation. The formalism has a significant potential for cosmological applications, as it allows one to examine a wide variety of sources with different "equations of state", generalizing known FLRW solutions to idealized but non-trivial and non-linear inhomogeneous conditions. The quasi-local functional can be reformulated as a weighed proper volume average distribution, with the weight factor given by a scalar invariant related to the quasi-local mass-energy function. The back-reaction terms, emerging in Buchert's proper averaging formalism, can be expressed as differences between fluctuations of averaged and quasi-local energy densities. By comparing this average with the weighed quasi-local one, we can define a binding energy functional related to spatial gradients of the averaged and quasi-local variables that appear in the back-reaction terms.

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arXiv2005

Stellar polytropes and Navarro--Frenk--White dark matter halos: a connection to Tsallis entropy

We present an alternative for the description of galactic halos based on Tsallis' non--extensive entropy formalism; on this scheme, halos are stellar polytropes characterized by three parameters, the central density, $ρ_c$, the central velocity dispersion, $σ_c$ and the polytropic index, $n$. To evaluate these parameters we take the Navarro-Frenk-White paradigm as a comparative model and make the following assumptions: both halo models must have the same virial mass, the same total energy and the same maximal velocity. These three conditions fix all the parameters for a given stellar polytrope allowing us to compare both halo models. The halos studied have virial masses on the range $10^{12}-10^{15} M_\odot$, and it was found after the analysis that they are described, at all scales, by almost the same polytropic index, $n\approx 4.8$, implying an empirical estimation of Tsallis non--extensive parameter for this type of dynamical systems: $q\approx 1.3$.

astro-ph↗

arXiv2005

Inhomogeneous models of interacting dark matter and dark energy

We derive and analyze a class of spherically symmetric cosmological models whose source is an interactive mixture of inhomogeneous cold dark matter (DM) and a generic homogeneous dark energy (DE) fluid. If the DE fluid corresponds to a quintessense scalar field, the interaction term can be associated with a well motivated non--minimal coupling to the DM component. By constructing a suitable volume average of the DM component we obtain a Friedman evolution equation relating this average density with an average Hubble scalar, with the DE component playing the role of a repulsive and time-dependent $Λ$ term. Once we select an ``equation of state'' linking the energy density ($μ$) and pressure ($p$) of the DE fluid, as well as a free function governing the radial dependence, the models become fully determinate and can be applied to known specific DE sources, such as quintessense scalar fields or tachyonic fluids. Considering the simple equation of state $p= (γ-1) μ$ with $0\leqγ<2/3$, we show that the free parameters and boundary conditions can be selected for an adequate description of a local DM overdensity evolving in a suitable cosmic background that accurately fits current observational data. While a DE dominated scenario emerges in the asymptotic future, with total $Ω$ and $q$ tending respectively to 1 and -1/2 for all cosmic observers, the effects of inhomogeneity and anisotropy yield different local behavior and evolution rates for these parameters in the local overdense region. We suggest that the models presented can be directly applied to explore the effects of various DE formalisms on local DM cosmological inhomogeneities.

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arXiv2004

A general relativistic approach to the Navarro-Frenk-White (NFW) galactic halos

In order to study their interplay with large scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, we construct a post-Newtonian fluid framework for the "Navarro-Frenk-White'' (NFW) models of galactic halos that follow from N-body numerical simulations. Since these simulations are unable to resolve regions very near the halo center, the extrapolation of the fitting formula leads to a spherically averaged "universal'' density profile that diverges at the origin. We remove this inconvenient feature by replacing a small central region of the NFW halo with an interior Schwarzschild solution with constant density, continuously matched to the remaining NFW spacetime. A model of a single halo, as an isolated object with finite mass, follows by smoothly matching the NFW spacetime to a Schwarzschild vacuum exterior along the virial radius, the physical "cut-off'' customarily imposed, as the mass associated with NFW profiles diverges asymptotically. Numerical simulations assume weakly interacting collisionless particles, hence we suggest that NFW halos approximately satisfy an "ideal gas'' type of equation of state, where mass-density is the dominant rest--mass contribution to matter--energy, with the internal energy contribution associated with an anisotropic kinetic pressure. We show that, outside the central core, this pressure and the mass density roughly satisfy a polytropic relation. Since stellar polytropes are the equilibrium configurations in Tsallis' non-extensive formalism of Statistical Mechanics, we argue that NFW halos might provide a rough empirical estimate of the free parameter $q$ of Tsallis' formalism.

astro-ph↗

arXiv2004

Scalar field "mini--MACHOs": a new explanation for galactic dark matter

We examine the possibility that galactic halos are collisionless ensembles of scalar field ``massive compact halo objects'' (MACHOs). Using mass constraints from MACHO microlensing and from theoretical arguments on halos made up of massive black holes, as well as demanding also that scalar MACHO ensambles of all scales do not exhibit gravothermal instability (as required by consistency with observations of LSB galaxies), we obtain the range: $m\alt 10^{-7} M_\odot$ or $30 M_\odot\alt m\alt 100 M_\odot$. The rather narrow mass range of large MACHOs seems to indicate that the ensambles we are suggesting should be probably made up of scalar MACHOs in the low mass range (``mini--MACHOs''). The proposed model allows one to consider a non--baryonic and non--thermal fundamental nature of dark matter, while at the same time keeping the same phenomenology of the CDM paradigm.

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