arXiv subjects

Roberto A. Sussman

Publications and source records attributed to Roberto A. Sussman.

At least 55 records · Page 3Linked to original sources

arXiv2009

On spatial volume averaging in Lema\^ıtre--Tolman--Bondi dust models. Part I: back reaction, spacial curvature and binding energy

We provide a comprehensive analytic study (rigorous and qualitative) of the conditions for the existence of a a positive kinematic back reaction term $\QQ>0$, in the context of Buchert's scalar averaging formalism applied to spherically symmetric Lemaître-Tolman-Bondi (LTB) dust solutions in which averaging domains are given as spherical comoving regions containing a symmetry center. We introduce proper volume and quasi-local average functionals and functions in order to examine the conditions for $\QQ\geq 0$, and in the process we also explore the relation between back reaction, spatial curvature and binding energy for a wide variety of LTB configurations. The back reaction term is positive for all "hyperbolic" regular domains with negative spatial curvature, either in the full radial range or in the radial asymptotic range. This result is also valid if these domains contain an inner "elliptic" region with positive curvature undergoing local collapse. For some cases in which positive spatial curvature decreases asymptotically, the conditions for a positive back reaction can still be met but seem to be more restrictive. Since $\QQ>0$ is a necessary condition for a positive "effective" acceleration that would mimic the effect of dark energy (in the context of Buchert's formalism), we examine this issue in LTB models in a follow up paper (part II).

gr-qc↗

arXiv2009

Quasi-local variables and scalar averaging in LTB dust models

We introduce quasi--local (QL) scalar variables in spherically symmetric LTB models. If the QL scalars are defined as functionals, they become weighed averages that generalize the standard proper volume averages on space slices orthogonal to the 4-velocity. We examine the connection between QL functions and functionals and the "back-reaction" term $Q$ in the context of Buchert's scalar averaging formalism. With the help of the QL scalars we provide rigorous proof that back--reaction is positive for (i) all LTB models with negative and asymptotically negative spatial curvature, and (ii) models with positive curvature decaying to zero asymptotically in the radial direction. We show by means of qualitative, but robust, arguments that generic LTB models exist, either with clump or void profiles, for which an "effective" acceleration associated with Buchert's formalism can mimic the effects of dark energy.

gr-qc↗

arXiv2008

Quasi-local variables in spherical symmetry: numerical applications to dark matter and dark energy sources

A numerical approach is considered for spherically symmetric spacetimes that generalize Lemaitre-Tolman-Bondi dust solutions to nonzero pressure ("LTB spacetimes"). We introduce quasi-local (QL) variables that are covariant LTB objects satisfying evolution equations of Friedman-Lemaitre-Robertson-Walker (FLRW) cosmologies. We prove rigorously that relative deviations of the local covariant scalars from the QL scalars are non-linear, gauge invariant and covariant perturbations on a FLRW formal "background" given by the QL scalars. The dynamics of LTB spacetimes is completely determined by the QL scalars and these exact perturbations. Since LTB spacetimes are compatible with a wide variety of "equations of state", either single fluids or mixtures, a large number of known solutions with dark matter and dark energy sources in a FLRW framework (or with linear perturbations) can be readily examined under idealized but non-trivial inhomogeneous conditions. Coordinate choices and initial conditions are derived for a numerical treatment of the perturbation equations, allowing us to study non-linear effects in a variety of phenomena, such as gravitational collapse, non-local effects, void formation, dark matter and dark energy couplings and particle creation. In particular, the embedding of inhomogeneous regions can be performed by a smooth matching with a suitable FLRW solution, thus generalizing the Newtonian "top hat" models that are widely used in astrophysical literature. As examples of the application of the formalism, we examine numerically the formation of a black hole in an expanding Chaplygin gas FLRW universe, as well as the evolution of density clumps and voids in an interactive mixture of cold dark matter and dark energy.

gr-qc↗

arXiv2008

Quasi-local variables and inhomogeneous cosmological sources with spherical symmetry

We examine a large class of inhomogeneous spherically symmetric spacetimes that generalize the Lemaitre-Tolman-Bondi dust solutions to nonzero pressure ("LTB spacetimes"). Local covariant LTB objects can be expressed as perturbations of covariant quasi-local (QL) scalars that satisfy evolution equations of equivalent Friedman-Lemaitre-Robertson-Walker (FLRW) scalars. Thus, the dynamics of these spacetimes can be rigorously described as non-linear, gauge invariant and covariant perturbations on a formal FLRW background given by the QL scalars. Since LTB spacetimes are compatible with a wide variety of "equations of state" and theoretical assumptions, they provide an ideal framework for numerical models of cosmological sources under idealized but fully non-linear conditions. As an illustrative example, we briefly examine the formation of a black hole in an expanding Chaplygin gas universe.

gr-qc↗

arXiv2008

Constraining the mSUGRA parameter space using the entropy of dark matter halos

We derive an expression for the entropy of a dark matter halo described by a Navarro-Frenk-White model with a core. The comparison of this entropy with the one of dark matter at the freeze-out era allows us to constraint the parameter space in mSUGRA models. Moreover, joining these constraints with the ones obtained from the usual abundance criteria and demanding both criteria to be consistent with the 2$σ$ bounds for the abundance of dark matter: $0.112\leqΩ_{DM}h^2\leq0.122$, we are able to clearly discriminate validity regions among the values of $\tan β$, one of the parameters of the mSUGRA model. We found that for the explored regions of the parameter space, small values of tan$β$ are not favored; only for tan$β\simeq50$ are both criteria significantly consistent. In the region where both criteria are consistent we also found a lower bound for the neutralino mass, $m_χ\geq 141$ GeV.

astro-ph↗

arXiv2008

Dynamics of a self--gravitating magnetized source

We consider a magnetized degenerate gas of fermions as the matter source of a homogeneous but anisotropic Bianchi I spacetime with a Kasner--like metric. We examine the dynamics of this system by means of a qualitative and numerical study of Einstein-Maxwell field equations which reduce to a non--linear autonomous system. For all initial conditions and combinations of free parameters the gas evolves from an initial anisotropic singularity into an asymptotic state that is completely determined by a stable attractor. Depending on the initial conditions the anisotropic singularity is of the ``cigar'' or ``plate'' types.

gr-qc↗

arXiv2007

Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4-dimensional phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3-dimensional sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H_{0} is negative. If H_{0} is positive, and depending on initial conditions, the trajectories end up in a curvature singularity that could be isotropic(singular "point") or anisotropic (singular "line"). In particular, for a sufficiently large initial value of the magnetic field it is always possible to obtain an anisotropic type of singularity in which the "line" points in the same direction of the field.

gr-qc↗

arXiv2007

A dynamical system approach to inhomogeneous dust solutions

We examine numerically and qualitatively the Lema\^ıtre--Tolman--Bondi (LTB) inhomogeneous dust solutions as a 3--dimensional dynamical system characterized by six critical points. One of the coordinates of the phase space is an average density parameter, $<Ω>$, which behaves as the ordinary $Ω$ in Friedman-Lema\^ıtre--Robertson--Walker (FLRW) dust spacetimes. The other two coordinates, a shear parameter and a density contrast function, convey the effects of inhomogeneity. As long as shell crossing singularities are absent, this phase space is bounded or it can be trivially compactified. This space contains several invariant subspaces which define relevant particular cases, such as: ``parabolic'' evolution, FLRW dust and the Schwarzschild--Kruskal vacuum limit. We examine in detail the phase space evolution of several dust configurations: a low density void formation scenario, high density re--collapsing universes with open, closed and wormhole topologies, a structure formation scenario with a black hole surrounded by an expanding background, and the Schwarzschild--Kruskal vacuum case. Solution curves start expanding from a past attractor (source) in the plane $<Ω>=1$, associated with self similar regime at an initial singularity. Depending on the initial conditions and specific configurations, the curves approach several saddle points as they evolve between this past attractor and other two possible future attractors: perpetually expanding curves terminate at a line of sinks at $<Ω>=0$, while collapsing curves reach maximal expansion as $<Ω>$ diverges and end up in sink that coincides with the past attractor and is also associated with self similar behavior.

gr-qc↗

arXiv2006

Stellar polytropes and Navarro-Frenk-White halo models: comparison with observations

Motivated by the possible conflict between the Navarro-Frenk-White(NFW) model predictions for the dark matter contents of galactic systems and its correlation with baryonic surface density, we will explore an alternative paradigm for the description of dark matter halos. Such an alternative emerges from Tsallis' non-extensive thermodynamics applied to self-gravitating systems and leads to the so-called ``stellar polytrope'' (SP) model. We consider that this could be a better approach to real structures rather than the isothermal model, given the fact that the first one takes into account the non-extensivity of energy and entropy present in these type of systems characterized by long-range interactions. We compare a halo based on the Navarro-Frenk-White (NFW) and one which follows the SP description. Analyzing the dark matter contents estimated by means of global physical parameters of galactic disks, obtained from a sample of actual galaxies, with the ones of the unobserved dark matter halos, we conclude that the SP model is favored over the NFW model in such a comparison.

astro-ph↗

arXiv2006

Empirical testing of Tsallis' Thermodynamics as a model for dark matter halos

We study a dark matter halo model from two points of view: the ``stellar polytrope'' (SP) model coming from Tsallis' thermodynamics, and the one coming from the Navarro-Frenk-White (NFW) paradigm. We make an appropriate comparison between both halo models and analyzing the relations between the global physical parameters of observed galactic disks, coming from a sample of actual galaxies, with the ones of the unobserved dark matter halos, we conclude that the SP model is favored over the NFW model in such a comparison.

astro-ph↗

arXiv2006

Entropy considerations in constraining the mSUGRA parameter space

We explore the use of two criteria to constraint the allowed parameter space in mSUGRA models. Both criteria are based in the calculation of the present density of neutralinos as dark matter in the Universe. The first one is the usual ``abundance'' criterion which is used to calculate the relic density after the ``freeze-out'' era. To compute the relic density we used the numerical public code micrOMEGAs. The second criterion applies the microcanonical definition of entropy to a weakly interacting and self-gravitating gas evaluating then the change in the entropy per particle of this gas between the ``freeze-out'' era and present day virialized structures. An ``entropy-consistency'' criterion emerges by comparing theoretical and empirical estimates of this entropy. The main objective of our work is to determine for which regions of the parameter space in the mSUGRA model are both criteria consistent with the 2$σ$ bounds according to WMAP for the relic density: $0.0945<Ω_{CDM}h^2<0.1287$. As a first result, we found that for $A_0=0$, sgn$μ=+$, small values of tan$β$ are not favored; only for tan$β\simeq50$ are both criteria significantly consistent.

astro-ph↗

arXiv2004

The Maxwell--Boltzmann gas with non-standard self--interactions: a novel approach to galactic dark matter

Using relativistic kinetic theory, we study spherically symmetric, static equilibrium configurations of a collisionless Maxwell-Boltzmann gas with non-standard self-interactions, modelled by an effective one--particle force. The resulting set of equilibrium conditions represents a generalization of the classical Tolman-Oppenheimer-Volkov equations. We specify these conditions for two types of Lorentz--like forces: one coupled to the 4-acceleration and the 4--velocity and the other one coupled to the Riemann tensor. We investigate the weak field limits in each case and show that they lead to various Newtonian type configurations that are different from the usual isothermal sphere characterizing the conventional Newtonian Maxwell--Boltzmann gas. These configurations could provide a plausible phenomenological and theoretical description of galactic dark matter halo structures. We show how the self--interaction may act phenomenologically as an effective cosmological constant and discuss possible connections with Modified Newtonian Dynamics(MOND).

astro-ph↗

arXiv2004

Using Entropy to Discriminate Annihilation Channels in Neutralinos Making up Galactic Halos

Applying the microcanonical definition of entropy to a weakly interacting and self--gravitating neutralino gas, we evaluate the change in the local entropy per particle of this gas between the freeze out era and present day virialized halo structures. An ``entropy consistency'' criterion emerges by comparing theoretical and empirical estimates of this entropy. We apply this criterion to the cases when neutralinos are mostly B-inos and mostly Higgsinos, in conjunction with the usual ``abundance'' criterion requiring that present neutralino relic density complies with $0.2<Ω_{\tildeχ^1_0} < 0.4$ for $h\simeq 0.65$. The joint application of both criteria reveals that a much better fitting occurs for the B-ino than for the Higgsino channels, so that the former seems to be a favored channel along the mass range of $155 \hbox{GeV} < m_{\tildeχ^1_0} < 230 \hbox{GeV}$. These results are consistent with neutralino annihilation patterns that emerge from recent theoretical analysis on cosmic ray positron excess data reported by the HEAT collaboration. The suggested methodology can be applied to test other annihilation channels of the neutralino, as well as other particle candidates of thermal WIMP gas relics.

hep-ph↗

arXiv2004

The spacetime associated with galactic dark matter halos

We show how an adequate post--Newtonian generalization can be obtained for Newtonian dark matter halos associated with an empiric density profile. Applying this approach to halos that follow from the well known numerical simulations of Navarro, Frenk and White (NFW), we derive all dynamical variables and show that NFW halos approximatelly follow an ideal gas type of equation of state which fits very well to a polytropic relation in the region outside the core. This fact suggests that ``outer'' regions of NFW halos might be related to equilibrium states in the non--extensive Statistical Mechanics formalism proposed by Tsallis.

astro-ph↗

arXiv2003

On the newtonian limit and cut--off scales of isothermal dark matter halos with cosmological constant

We examine isothermal dark matter halos in hydrostatic equilibrium with a cosmological constant Lambda =Omega_Λrho_{crit}c^2, where Omega_Λ=0.7, and rho_{crit} is the present value of the critical density with h=0.65. The Newtonian limit of General Relativity yields equilibrium equations that are different from those arising by merely coupling an ``isothermal sphere'' to the Lambda-field within a Newtonian framework. The conditions for the existence and stability of circular geodesic orbits show the existence of (I) an ``isothermal region'' (0 r_1) dominated by the Lambda-field, where the Newtonian potential oscillates and circular orbits exist in disconnected patches of the domain of r; (III) a ``transition region'' (r_2 0.008 M_\odot {pc}^3, in agreement with rotation curve studies of dwarf galaxies. Since r_2 marks the largest radius of a stable circular orbit, it provides a ``cut off'' radius. For current estimates of rho_c and velocity dispersion of galactic structures, this is around five times larger than the virialization radius. The effects of the Lambda$--field can hence be ignored in structure formation models, but could be significant in the dynamics of superclusters in the linear regime or of gravitational clustering at large scales.

astro-ph↗

arXiv2003

A New Method to Infere Which Type of Neutralinos Make Up Galactic Halos

Applying the microcanonical definition of entropy to a weakly interacting and self--gravitating neutralino gas, we evaluate the change in the local entropy per particle of this gas between the freeze out era and present day virialized halo structures. An ``entropy consistency'' criterion emerges by comparing the obtained theoretical entropy per particle of the virialized halos with an empirical entropy per particle given in terms of dynamical halo variables of actual galactic structures. We apply this criterion to the cases when neutralinos are mostly B-inos and mostly Higgsinos, in conjunction with the usual ``abundance'' criterion requiring that present neutralino relic density complies with $0.2<Ω_{\tildeχ^1_0} < 0.4$ for $h\simeq 0.65$. The joint application of both criteria reveals that a much better fitting occurs for the B-ino than for the Higgsino channels, so that the former seems to be a favored channel along the mass range of $150 \hbox{GeV} < m_{\tildeχ^1_0} < 250 \hbox{GeV}$. These results are consistent with neutralino annihilation patterns that emerge from recent theoretical analysis on cosmic ray positron excess data reported by the HEAT collaboration. The suggested methodology can be applied to test other annihilation channels of the neutralino, as well as other particle candidates of thermal WIMP gas relics.

hep-ph↗

arXiv2003

On the thermal footsteps of Neutralino relic gases

Current literature suggests that neutralinos are the dominant cold dark matter particle species. Assuming the microcanonical definition of entropy, we examine the local entropy per particle produced between the ``freeze out'' era to the present. An ``entropy consistency'' criterion emerges by comparing this entropy with the entropy per particle of actual galactic structures given in terms of dynamical halo variables. We apply this criterion to the cases when neutralinos are mosly b-inos and mostly higgsinos, in conjunction with the usual ``abundance'' criterion requiring that present neutralino relic density complies with $0.1 < Ω_{\chic{\tildeχ^0_1}} < 0.3$ for $h\simeq 0.65$. The joint application of both criteria reveals that a better fitting occurs for the b-ino channels, hence the latter seem to be favoured over the higgsino channels. The suggested methodology can be applied to test other annihilation channels of the neutralino, as well as other particle candidates of thermal gases relics.

hep-ph↗

arXiv2002

A qualitative and numerical study or the matter-radiation interaction in Kantowski-Sachs cosmologies

We examine, from both a qualitative and a numerical point of view, the evolution of Kantowski--Sachs cosmological models whose source is a mixture of a gas of weakly interacting massive particles (WIMP's) and a radiative gas made up of a ``tightly coupled'' mixture of electrons, baryons and photons from the end of nucleosynthesis up to the duration of radiative interactions. In this cosmic era annihilation processes are negligible, while the WIMP's only interact gravitationally with the radiative gas and the latter behaves as a single dissipative fluid that can be studied within a hydrodynamical framework. Applying the full transport equations of Extended Irreversible Thermodynamics, coupled with the field and balance equations, we obtain a set of governing equations that becomes an autonomous system of ordinary differential equations once the shear viscosity relaxation time is specified; assuming the latter to be proportional to the Hubble time, the qualitative analysis indicates that models begin in the radiation dominated epoch close to an isotropic equilibrium point. We show how the relaxation time governs the relaxation of the models towards an equilibrium photon entropy, leading to ``near-Eckart'' and transient regimes associated with `abrupt' and `smooth' relaxation processes, respectively. Assuming the WIMP particle to be a super-symmetric neutralino of a 100$ GeV, the numerical analysis reveals that a physically plausible evolution, compatible with a stable equilibrium state and with observed bounds on CMB anisotropies and neutralino abundance, is only possible for models characterized by initial conditions associated with nearly zero spatial curvature and total initial energy density very close to unity.

astro-ph↗