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Casals, M., Fabbri, A., Martinez, C., & Zanelli, J. (2016). Quantum dress for a naked singularity. Phys. Lett. B, 760, 244–248.
Abstract: We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2 + 1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak) cosmic censorship.
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Belchior, F. M., Moreira, A. R. P., Maluf, R. V., & Almeida, C. A. S. (2023). 5D Elko spinor field non-minimally coupled to nonmetricity in f (Q) gravity. Phys. Lett. B, 843, 138029–8pp.
Abstract: This paper aims to investigate the localization of the five-dimensional spinor field known as Elko (dual-helicity eigenspinors of the charge conjugation operator) by employing a Yukawa-like geometrical coupling in which the Elko field is non-minimally coupled to nonmetricity scalar Q. We adopt the braneworld scenarios in which the first-order formalism with sine-Gordon and linear superpotentials is employed to obtain the warp factors. A linear function supports the zero-mode trapping within the geometric coupling, leading to the same effective potential as the scalar field. Moreover, an exotic term must be added to obtain real-valued massive modes. Such modes are investigated through the Schrodinger-like approach.
Keywords: Elko field; Dark matter; Thick brane; Symmetric teleparallel gravity
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Beltran Jimenez, J., Heisenberg, L., Olmo, G. J., & Rubiera-Garcia, D. (2018). Born-Infeld inspired modifications of gravity. Phys. Rep., 727, 1–129.
Abstract: General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important. This is related to the existence of spacetime singularities when the solutions of General Relativity are extrapolated to regimes where curvatures are large. In this sense, Born-Infeld inspired modifications of gravity have shown an extraordinary ability to regularise the gravitational dynamics, leading to non-singular cosmologies and regular black hole spacetimes in a very robust manner and without resorting to quantum gravity effects. This has boosted the interest in these theories in applications to stellar structure, compact objects, inflationary scenarios, cosmological singularities, and black hole and wormhole physics, among others. We review the motivations, various formulations, and main results achieved within these theories, including their observational viability, and provide an overview of current open problems and future research opportunities.
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Olmo, G. J., Rubiera-Garcia, D., & Wojnar, A. (2020). Stellar structure models in modified theories of gravity: Lessons and challenges. Phys. Rep., 876, 1–75.
Abstract: The understanding of stellar structure represents the crossroads of our theories of the nuclear force and the gravitational interaction under the most extreme conditions observably accessible. It provides a powerful probe of the strong field regime of General Relativity, and opens fruitful avenues for the exploration of new gravitational physics. The latter can be captured via modified theories of gravity, which modify the Einstein-Hilbert action of General Relativity and/or some of its principles. These theories typically change the Tolman-Oppenheimer-Volkoff equations of stellar's hydrostatic equilibrium, thus having a large impact on the astrophysical properties of the corresponding stars and opening a new window to constrain these theories with present and future observations of different types of stars. For relativistic stars, such as neutron stars, the uncertainty on the equation of state of matter at supranuclear densities intertwines with the new parameters coming from the modified gravity side, providing a whole new phenomenology for the typical predictions of stellar structure models, such as mass-radius relations, maximum masses, or moment of inertia. For non-relativistic stars, such as white, brown and red dwarfs, the weakening/strengthening of the gravitational force inside astrophysical bodies via the modified Newtonian (Poisson) equation may induce changes on the star's mass, radius, central density or luminosity, having an impact, for instance, in the Chandrasekhar's limit for white dwarfs, or in the minimum mass for stable hydrogen burning in high-mass brown dwarfs. This work aims to provide a broad overview of the main such results achieved in the recent literature for many such modified theories of gravity, by combining the results and constraints obtained from the analysis of relativistic and non-relativistic stars in different scenarios. Moreover, we will build a bridge between the efforts of the community working on different theories, formulations, types of stars, theoretical modelings, and observational aspects, highlighting some of the most promising opportunities in the field.
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Bazeia, D., Losano, L., Olmo, G. J., & Rubiera-Garcia, D. (2017). Geodesically complete BTZ-type solutions of 2+1 Born-Infeld gravity. Class. Quantum Gravity, 34(4), 045006–21pp.
Abstract: We study Born-Infeld gravity coupled to a static, non-rotating electric field in 2 + 1 dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of general relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on their innermost region. This seems to be a generic prediction of extensions of general relativity formulated in metric-affine (or Palatini) spaces, where metric and connection are regarded as independent degrees of freedom.
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