International Journal of Modern Physics D

A regular static, spherically symmetric electrically charged black hole solution of general relativity coupled to a new theory for nonlinear electrodynamics is presented. This theory has the interesting feature that, at far distances from the black hole, in the weak field limit, the theory reduces to Maxwell Lagrangian with Heisenberg–Euler correction term of quantum electrodynamics. The singular center of the black hole is replaced by flat, de Sitter, or anti de Sitter space, if the spacetime in which the black hole is embedded is asymptotically flat, de Sitter, or anti de Sitter, respectively. Requiring the correspondence to Heisenberg–Euler Lagrangian at large distances, in the weak field limit, we find that (i) a minimum mass is required for the formation of an event horizon for the regular static, spherically symmetric solution of the theory, and, (ii) the mass of the solution must be quantized. We also study the basic thermodynamic properties of the black hole solution and show that they are qualitatively similar to those of Reissner–Nordström black hole.

In this work, we investigate the anisotropic Bianchi type I cosmological model in the chiral set-up in a twofold manner. Firstly, we consider a quintessence plus a $k$-essence-like model, where two scalar fields but only one potential term is considered. Secondly, we look at a model where in addition to the two scalar fields the two potential terms are taken into account as well as the standard kinetic energy and the mixed term. Regarding this second model, it is shown that two possible cases can be studied: a quintom-like case and a quintessence-like case. In each of the models, we were able to find both classical and quantum analytical solutions.

We have studied constant-roll inflation using the q-de Sitter scale factor. Both the cold and warm inflation have been considered, and the scalar potential and inflaton field have been determined. Also tensor to scalar ratio and the spectral index are obtained. In the cold inflation case, the perturbations have been investigated using Mukhanov–Sasaki equation, and the results determined for the spectral index and tensor to scalar ration are consistent with observations. In the warm inflation two cases of constant damping ($\mathrm{\Gamma }={\mathrm{\Gamma }}_0$) and the field dependent damping ($\mathrm{\Gamma }={\mathrm{\Gamma }}_{1}V(\varphi )$) have been studied. In both cases the power spectrum and the tensor to scalar ratio are determined as a function of the inflaton field. It has been shown that in both cases the spectral index is independent of the inflaton field. In the case of constant damping the obtained value for the spectral index is inconsistent with observations but for the case of field dependent damping the parameter $q$ can be chosen such that the value obtained for all the physical quantities including the spectral index be consistent with present cosmological observations.

It is interesting to note that most black holes are born very slowly rotating. We investigate scalarization of slowly rotating black holes in the Einstein-scalar-Chern–Simons (EsCS) theory. In the slow rotation approximation, the CS term takes a linear form of rotation parameter $a$ which determines the tachyonic instability. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. It is shown that the slowly rotating black holes are unstable against a spherically symmetric scalar-mode perturbation for positive coupling $\alpha$, whereas these black holes are unstable for negative coupling without any $a$-bound.

We compute the cosmological constant of a spherical space in the limit of weak gravity. To this end, we use a duality developed by the present authors in a previous work. This duality allows one to treat the Newtonian cosmological fluid as the probability fluid of a single particle in nonrelativistic quantum mechanics. We apply this duality to the case when the spacetime manifold on which this quantum mechanics is defined is given by $ℝ\times {𝕊}^3$. Here, $ℝ$ stands for the time axis and ${𝕊}^3$ is a 3-dimensional sphere endowed with the standard round metric. A quantum operator $\mathrm{\Lambda }$ satisfying all the requirements of a cosmological constant is identified, and the matrix representing $\mathrm{\Lambda }$ within the Hilbert space $L^2({𝕊}^3)$ of quantum states is obtained. Numerical values for the expectation value of the operator $\mathrm{\Lambda }$ in certain quantum states are obtained, which are in good agreement with the experimentally measured cosmological constant.

We explore the aspects of the electromagnetism on the stability of gravastar in a particular modified theory, i.e. $f(R,T,Q)$ where $Q=R_{\mu \nu }{T}^{\mu \nu }$, $R$ is the Ricci scalar and $T$ is the trace of energy–momentum tensor. We assume a spherically symmetric static metric coupled comprising of perfect fluid in the presence of electric charge. The purpose of this paper is to extend the results of [S. Ghosh, F. Rahaman, B. K. Guha and S. Ray, Phys. Lett. B 767 (2017) 380.] to highlight the effects of $f(R,T,Q)$ gravity in the formation of charged gravastars. We demonstrated the mathematical formulation, utilizing different equations of state, for the three respective regions (i.e. inner, shell, exterior) of the gravastar. We have matched smoothly the interior de Sitter and the exterior Reissner–Nordström metric at the hypersurface. At the end we extracted few conclusions by working on the physical features of the charged gravastar, mathematically and graphically.

The existence or not of pathologies in the context of Lagrangian theory is studied with the aid of Machine Learning algorithms. Using an example in the framework of classical mechanics, we make a proof of concept, that the construction of new physical theories using machine learning is possible. Specifically, we utilize a fully-connected, feed-forward neural network architecture, aiming to discriminate between “healthy” and “nonhealthy” Lagrangians, without explicitly extracting the relevant equations of motion. The network, after training, is used as a fitness function in the concept of a genetic algorithm and new healthy Lagrangians are constructed. These new Lagrangians are different from the Lagrangians contained in the initial data set. Hence, searching for Lagrangians possessing a number of pre-defined properties is significantly simplified within our approach. The framework employed in this work can be used to explore more complex physical theories, such as generalizations of General Relativity in gravitational physics, or constructions in solid state physics, in which the standard procedure can be laborious.

Many recent researches have investigated the deviations from the Friedmannian cosmological model, as well as their consequences on unexplained cosmological phenomena, such as dark matter and the acceleration of the Universe. On one hand, a first-order perturbative study of matter inhomogeneity returned a partial explanation of dark matter and dark energy, as relativistic effects due to the retarded potentials of far objects. On the other hand, the fractal cosmology, now approximated by a Lemaitre–Tolman–Bondi (LTB) metric, results in distortions of the luminosity distances of SNe Ia, explaining the acceleration as apparent. In this work, we extend the LTB metric to ancient times. The origin of the fractal distribution of matter is explained as the matter remnant after the matter–antimatter recombination epoch. We show that the evolution of such a inhomogeneity necessarily requires a dynamical generalization of LTB, and we propose a particular solution.

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.