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**Abstract**

In the last decade new observational and theoretical results have given a new impulse on the investigation of structural questions and phenomenological applications of general relativity. On one hand, cosmology is in a period where new data suggest new and challenging visions of the universe. In this context, new approaches are necessary to explain what is observed and also what is not directly observed. On the other hand, a hole new set of theoretical possibilities were open with the so-called anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. This correspondence suggests a deep relation between gravity and problems relating field theories and integrable models. This project proposes to investigate structural questions and possible applications in these great lines of research. Concerning cosmology, we focus on aspects related to the characteristics of dark matter and energy, especially in cases where it is possible to formulate dark energy settings distinct from the standard model, where the cosmological acceleration is generated by a cosmological constant. In the latter case, the dynamics being described by a standard field, there must be an interaction between the matter and energy sectors, possibilities which we have being treating and constraining in terms of observations. From the observational point of view, we are proposing to be members of the J-PAS project, that will get, among other results, an excellent catalogue of galaxies and quasars permitting a precise measurement of the matter power spectrum and the baryonic acoustic oscillations, leading to a measurement of the dark energy equation of state parameter with a precision better than 4%.Going from cosmological to astrophysical scales, we propose to investigate systems with cylindrical and axial symmetries in d-dimensional models. Of particular interest are black hole solutions. Such scenarios include black holes and ring holes in brane world models and in the Gauss-Bonnet gravity. The focus will be non-asymptotically flat solutions. Basic aspects to be treated are thermo dynamical and dynamical stability of the systems to be considered. Perturbing the known solutions of the gravity theories considered, both the Einstein gravity as well as its variations, we not only study their basic structures but also their implications with the use of the AdS/CFT relation, involving condensed matter theories of physical interests in the CFT side. In this case, models describing superconductors and superfluids have being emphasized in the pertinent literature and will be research topics in this project. The AdS/CFT correspondence gives us a link between gravity and field theories. Integrable models have well defined relations with gauge theories within this celebrated relation, being considered themselves a topic of study. In this context, we will treat a series of problems associated with the formulation of the quantum inverse scattering method applied to twisted and Temperley-Lieb algebras. (AU)

Scientific publications
(19)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ARBANIL, JOSE D. V.;
ZANCHIN, VILSON T.
Relativistic polytropic spheres with electric charge: Compact stars, compactness and mass bounds, and quasiblack hole configurations.
** Physical Review D**,
v. 97,
n. 10
MAY 25 2018.
Web of Science Citations: 0.

VIEIRA, R. S.;
BRENTAN, H. B.
Covariant theory of gravitation in the framework of special relativity.
** EUROPEAN PHYSICAL JOURNAL PLUS**,
v. 133,
n. 4
APR 27 2018.
Web of Science Citations: 0.

LIMA-SANTOS, ANTONIO;
NEPOMECHIE, RAFAEL I.;
PIMENTA, RODRIGO A.
A tale of two Bethe ansatze.
** JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT**,
APR 2018.
Web of Science Citations: 0.

BALLON-BAYONA, ALFONSO;
BOSCHI-FILHO, HENRIQUE;
MAMANI, LUIS A. H.;
MIRANDA, ALEX S.;
ZANCHIN, VILSON T.
Effective holographic models for QCD: Glueball spectrum and trace anomaly.
** Physical Review D**,
v. 97,
n. 4
FEB 1 2018.
Web of Science Citations: 6.

VIEIRA, R. S.;
LIMA SANTOS, A.
Reflection K-matrices for a nineteen vertex model with U-q[osp (2 vertical bar 2)((2))] symmetry.
** Physics Letters A**,
v. 381,
n. 36,
p. 3015-3020,
SEP 25 2017.
Web of Science Citations: 2.

VIEIRA, R. S.;
LIMA-SANTOS, A.
Reflection matrices with U-q [osp((2)) (2|2m)] symmetry.
** Journal of Physics A-Mathematical and Theoretical**,
v. 50,
n. 37
SEP 15 2017.
Web of Science Citations: 2.

VIEIRA, R. S.;
LIMA-SANTOS, A.
Boundary algebraic Bethe Ansatz for a nineteen vertex model with U-q [osp(2 vertical bar 2)((2))] symmetry.
** JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT**,
SEP 2017.
Web of Science Citations: 0.

LEMOS, JOSE P. S.;
ZANCHIN, VILSON T.
Plethora of relativistic charged spheres: The full spectrum of Guifoyle's static, electrically charged spherical solutions.
** Physical Review D**,
v. 95,
n. 10
MAY 30 2017.
Web of Science Citations: 2.

MELLO, MARINA M. C.;
MACIEL, ALAN;
ZANCHIN, VILSON T.
Evolving black holes from conformal transformations of static solutions.
** Physical Review D**,
v. 95,
n. 8
APR 19 2017.
Web of Science Citations: 5.

VIEIRA, R. S.
On the number of roots of self-inversive polynomials on the complex unit circle.
** RAMANUJAN JOURNAL**,
v. 42,
n. 2,
p. 363-369,
FEB 2017.
Web of Science Citations: 2.

LANDIM, RICARDO G.;
ABDALLA, ELCIO.
Metastable dark energy.
** Physics Letters B**,
v. 764,
p. 271-276,
JAN 10 2017.
Web of Science Citations: 11.

LIMA-SANTOS, A.
On the Temperley-Lieb Model.
** Journal of Statistical Physics**,
v. 165,
n. 5,
p. 953-969,
DEC 2016.
Web of Science Citations: 0.

MARCONDES, RAFAEL J. F.;
LANDIM, RICARDO C. G.;
COSTA, ANDRE A.;
WANG, BIN;
ABDALLA, ELCIO.
Analytic study of the effect of dark energy-dark matter interaction on the growth of structures.
** Journal of Cosmology and Astroparticle Physics**,
n. 12
DEC 2016.
Web of Science Citations: 15.

RODRIGUES, MANUEL E.;
JUNIOR, EDNALDO L. B.;
MARQUES, GLAUBER T.;
ZANCHIN, VILSON T.
Regular black holes in f (R) gravity coupled to nonlinear electrodynamics.
** Physical Review D**,
v. 94,
n. 2
JUL 29 2016.
Web of Science Citations: 13.

MIRANDA, ALEX S.;
MORGAN, JAQUELINE;
KANDUS, ALEJANDRA;
ZANCHIN, VILSON T.
Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings.
** Classical and Quantum Gravity**,
v. 32,
n. 23
DEC 2 2015.
Web of Science Citations: 1.

VIEIRA, R. S.;
LIMA-SANTOS, A.
Where are the roots of the Bethe Ansatz equations?.
** Physics Letters A**,
v. 379,
n. 37,
p. 2150-2153,
OCT 2 2015.
Web of Science Citations: 5.

PIMENTA, R. A.;
LIMA-SANTOS, A.
Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices.
** JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT**,
NOV 2014.
Web of Science Citations: 2.

PIMENTA, R. A.;
LIMA-SANTOS, A.
Algebraic Bethe ansatz for the six vertex model with upper triangular K-matrices.
** Journal of Physics A-Mathematical and Theoretical**,
v. 46,
n. 45
NOV 15 2013.
Web of Science Citations: 19.

LIMA-SANTOS, A.
Temperley-Lieb K-matrices.
** JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT**,
OCT 2013.
Web of Science Citations: 1.

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