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My research interests in General Relativity are Minimal Geometric Deformation, GR Polytropes, Geodesic motion, Geometric methods applied to General Relativity and Quantum Gravity.
Minimal Geometric Deformation (MGD)
Minimal Geometric Deformation (MGD)
One of my principal research interests in General Relativity is a novel method called Minimal Geometric Deformation (MGD) [1, 2, 3], which is a systematic and powerful method used to extend well-known solutions. In this regard, the method was widely used in the process of anisotropization of well-known solutions [1-23]. In this context, I am interested in applying this method, but I am also intrigued by the mathematical foundations of this method. My questions arise on why the method work and what could be the possible physical mechanism that involved the method. Moreover, not only the direct method has been studied but also the inverse method, where it takes a well-known solution, in general anisotropic, and the "sources" of that solutions are obtained [3,4,]. This process has exhibit a duality between the regularity of black hole solutions and the energy conditions. This problem was partially studied in 2+1 dimensions in my Bachelor's thesis; however, they're still open questions to solve.
General Relativity Anisotropic Polytropes
General Relativity Anisotropic Polytropes
One of my recent works is related to General Relativity anisotropic polytropes, where in order to saturate the systems of differential equations, we embed the space into a five-dimensional Euclidean space. In this regard, it appears a geometric constrain called the Karmakar condition for Class I interior solutions. This extra constrain allow us to solve the system and obtain a novel result that hasn't been studied before. The work has boot analytical and numerical results.
Geometrical Methods in General Relativity
Geometrical Methods in General Relativity
I strongly believe that geometry is the language of nature, and General Relativity is one of the most beautiful geometrical theories in physics. It is the only physical theory, where geometry has such an important role. In this regard, as an enthusiast of geometry, it is one of my favorite fields in physics. However, most of the mathematical building blocks of the theory are relatively old, and novel geometrical methods have appeared in the field of mathematics. Just to mention few: algebraic topology, category theory, tropical geometry and algebraic geometry. Them has marked a new era in the field of mathematics with several applications in diverse areas of science [24-29]. In this respect, I believe that General Relativity can be studied using some of these new methods in mathematics, which could allow us to reach new and more interesting results in the field. Furthermore, it can open new doors towards a quantum gravity theory. In my current state, I am not able to contribute to the field but I am in constant self-studying topics related to mathematics and in particular in geometry.
Publications and Ongoing Research:
Publications and Ongoing Research:
Abstract: In a recent paper Ovalle et al. (2021) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time-like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship with the rotation parameter of the Kerr black hole giving the same innermost stable circular orbit radius and give the numerical values for the supermassive black holes at Ark 564 and NGC 1365. The photon sphere and the impact parameter associated to null geodesics are also discussed.
Abstract: In a recent paper Ovalle et al. (2021) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time-like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship with the rotation parameter of the Kerr black hole giving the same innermost stable circular orbit radius and give the numerical values for the supermassive black holes at Ark 564 and NGC 1365. The photon sphere and the impact parameter associated to null geodesics are also discussed.
Abstract: In this work we study class I interior solutions supported by anisotropic polytropes. The generalized Lane-Emden equation compatible with the embedding condition is obtained and solved for a different set of parameters in both the isothermal and non-isothermal regimes. For completeness, the Tolman mass is computed and analysed to some extend. As a complementary study we consider the impact of the Karmarkar condition on the mass and the Tolman mass functions respectively. Comparison with other results in literature are discussed.
Abstract: In this work we study class I interior solutions supported by anisotropic polytropes. The generalized Lane-Emden equation compatible with the embedding condition is obtained and solved for a different set of parameters in both the isothermal and non-isothermal regimes. For completeness, the Tolman mass is computed and analysed to some extend. As a complementary study we consider the impact of the Karmarkar condition on the mass and the Tolman mass functions respectively. Comparison with other results in literature are discussed.
Undergraduate Thesis Project:
Undergraduate Thesis Project:
Abstract: Minimal Geometric Deformation(MGD) is a systematic and powerful method to extend well known isotropic solutions to anisotropic domains. Within this framework, the inverse MGD, namely the process to obtain the isotropic sector of an anisotropic solution, has been studied in 2+1 dimensions revealing a kind of duality between the topologies and/or sources from both sectors. To be more precise, it has been found that for a particular regular anisotropic black hole solution satisfying the weak energy condition, the isotropic sector obtained from the inverse problem leads to either a regular black hole that violates the weak energy condition, or a non-regular black hole that satisfies the weak energy condition. This graduation project aims to describe the duality observed on the application of the inverse MGD in a (2+1) dimensional spherically symmetric source. With a general anisotropic spherical symmetric initial solution, we analyze the behavior of the density and the regularity of the new solution obtained by inverse MGD. We obtained a set of constraints to satisfy the positivity of the density and a set of weak constraints to ensure the regularity of the solutions. Moreover, it was found that the BTZ black hole solution act as an upper boundfor the energy constraints. After examining a specific case of a duality behavior in (2+1) dimensions, presented in the literature, we show that our constraints explain why such a duality appears. Finally, we motivate a more deep study of the duality by studying the relation of the weak energy conditions and the cores of the solutions, as it is conjectured by Dymnikova.
Abstract: Minimal Geometric Deformation(MGD) is a systematic and powerful method to extend well known isotropic solutions to anisotropic domains. Within this framework, the inverse MGD, namely the process to obtain the isotropic sector of an anisotropic solution, has been studied in 2+1 dimensions revealing a kind of duality between the topologies and/or sources from both sectors. To be more precise, it has been found that for a particular regular anisotropic black hole solution satisfying the weak energy condition, the isotropic sector obtained from the inverse problem leads to either a regular black hole that violates the weak energy condition, or a non-regular black hole that satisfies the weak energy condition. This graduation project aims to describe the duality observed on the application of the inverse MGD in a (2+1) dimensional spherically symmetric source. With a general anisotropic spherical symmetric initial solution, we analyze the behavior of the density and the regularity of the new solution obtained by inverse MGD. We obtained a set of constraints to satisfy the positivity of the density and a set of weak constraints to ensure the regularity of the solutions. Moreover, it was found that the BTZ black hole solution act as an upper boundfor the energy constraints. After examining a specific case of a duality behavior in (2+1) dimensions, presented in the literature, we show that our constraints explain why such a duality appears. Finally, we motivate a more deep study of the duality by studying the relation of the weak energy conditions and the cores of the solutions, as it is conjectured by Dymnikova.
References:
References:
Casadio, R.; Ovalle, J.; da Rocha, R. The minimal geometric deformation approach extended.Classical and Quantum Gravity 2015,32, 215020.
Ovalle, J. Extending the geometric deformation: New black hole solutions.International Journal of Modern Physics: Conference Series 2016,41, 1660132.
Contreras, E. Minimal Geometric Deformation: the inverse problem. The European Physical Journal C2018,78, 678.
Contreras, E., & Bargueño, P. (2018). Minimal geometric deformation in asymptotically (A-) dS space-times and the isotropic sector for a polytropic black hole. The European Physical Journal C, 78(12), 1-5.
Arias, C., Tello-Ortiz, F., & Contreras, E. (2020). Extra packing of mass of anisotropic interiors induced by MGD. The European Physical Journal C, 80, 1-9.
Ovalle, J., Casadio, R., Contreras, E., & Sotomayor, A. (2021). Hairy black holes by gravitational decoupling. Physics of the Dark Universe, 31, 100744.
Contreras, E., Tello-Ortiz, F., & Maurya, S. K. (2020). Regular decoupling sector and exterior solutions in the context of MGD. Classical and Quantum Gravity, 37(15), 155002.
Ovalle, J., Casadio, R., da Rocha, R., & Sotomayor, A. (2018). Anisotropic solutions by gravitational decoupling. The European Physical Journal C, 78(2), 1-11.
Gabbanelli, L., Rincón, Á., & Rubio, C. (2018). Gravitational decoupled anisotropies in compact stars. The European Physical Journal C, 78(5), 370.
Estrada, M., & Tello-Ortiz, F. (2018). A new family of analytical anisotropic solutions by gravitational decoupling. The European Physical Journal Plus, 133(11), 1-15.
Las Heras, C., & León, P. (2018). Using MGD gravitational decoupling to extend the isotropic solutions of Einstein equations to the anisotropical domain. Fortschritte der Physik, 66(7), 1800036.
Sharif, M., & Sadiq, S. (2018). Gravitational decoupled charged anisotropic spherical solutions. The European Physical Journal C, 78(5), 1-10.
Contreras, E., Rincón, Á., & Bargueño, P. (2019). A general interior anisotropic solution for a BTZ vacuum in the context of the minimal geometric deformation decoupling approach. The European Physical Journal C, 79(3), 1-6.
Morales, E., & Tello-Ortiz, F. (2018). Charged anisotropic compact objects by gravitational decoupling. The European Physical Journal C, 78(8), 1-17.
Sharif, M., & Sadiq, S. (2018). Gravitational decoupled anisotropic solutions for cylindrical geometry. The European Physical Journal Plus, 133(6), 1-11.
Morales, E., & Tello-Ortiz, F. (2018). Compact anisotropic models in general relativity by gravitational decoupling. The European Physical Journal C, 78(10), 1-12.
Estrada, M., & Prado, R. (2019). The gravitational decoupling method: the higher-dimensional case to find new analytic solutions. The European Physical Journal Plus, 134(4), 168.
Sharif, M., & Saba, S. (2018). Gravitational decoupled anisotropic solutions in $$ f ({\mathcal {G}}) $$ f (G) gravity. The European Physical Journal C, 78(11), 1-12.
Sharif, M., & Waseem, A. (2019). Effects of charge on gravitational decoupled anisotropic solutions in f (R) gravity. Chinese Journal of Physics, 60, 426-439.
Sharif, M., & Waseem, A. (2019). Anisotropic spherical solutions by gravitational decoupling in f (R) gravity. Annals of Physics, 405, 14-28.
Sharif, M., & Saba, S. (2020). Gravitational decoupled Durgapal–Fuloria anisotropic solutions in modified Gauss–Bonnet gravity. Chinese Journal of Physics, 63, 348-364.
Contreras, E. (2019). Gravitational decoupling in 2+ 1 dimensional space-times with cosmological term. Classical and Quantum Gravity, 36(9), 095004.
Ovalle, J., Casadio, R., Da Rocha, R., Sotomayor, A., & Stuchlik, Z. (2018). Einstein-Klein-Gordon system by gravitational decoupling. EPL (Europhysics Letters), 124(2), 20004.
Schmidt, R. (2008). Arithmetic gravity and Yang-Mills theory: An approach to adelic physics via algebraic spaces. arXiv preprint arXiv:0809.3579.
Raptis, I. (2006). Finitary-algebraic ‘resolution’of the inner Schwarzschild singularity. International Journal of Theoretical Physics, 45(1), 79-128.
Coecke, B., & Paquette, E. O. (2010). Categories for the practising physicist. In New structures for physics (pp. 173-286). Springer, Berlin, Heidelberg.
Chamblin, A. (1994). Some applications of differential topology in general relativity. Journal of Geometry and Physics, 13(4), 357-377.
Heller, M., & Sasin, W. (1995). Sheaves of Einstein algebras. International Journal of Theoretical Physics, 34(3), 387-398.
Laubinger, M. (2008). Differential geometry in cartesian closed categories of smooth spaces.
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