Dynamo seeds from Gravitational Torsional Anomalies and De Sitter Magnetized Metrics

Recently gravitational and Nieh-Yan chiral anomalies have been obtained in Riemann-Cartan spacetime Class and Quantum Gravity 38 (2021)], where electrodynamics is encoddded in the metric. In this paper we follow the path of obtaining a class of deformed de Sitter metrics in teleparallelism. The existence of the unmagnetized DSMM without axial anomalies is proved. Here we obtain unified theories a la Einstein and Eddington and Schroedinger, called modified de Sitter metric (MDSM) with the novel following features: (i) First we show that a pure de Sitter unmagnetized metric in T4 does not induce gravitational anomalies. Therefore this is a motivation to study modifications of De Sitter metric. What is done in the following items. (ii) Nieh-Yan torsion anomaly in (DSMM) in teleparallel T4 geometry is shown to vanish in all cases. Gravitational non-tivial anomalies are obtained from these metrics. But torsional anomaly much used in condensed matter physics, does not vanish. From these magnetized metrics, we show that with dynamo equation with torsion gradients sources is valid from class 3 of the metrics but is torsionless sourced in second class. (iii) We show that in the gravitational anomaly of new deformed de Sitter metric one may cancell the gravitational anomaly by a proper choice of the metric function. The axial anomaly is obtained for some metric deformation as well. Use original de Sitter nonconformal metric . A simple deformation leads to the existence of the NY form in the case of magnetized de Sitter metric. This would be class IV of DSMM.

Kottler spacetime in isotropic static coordinates

The Kottler spacetime in isotropic coordinates is known where the metric is time-dependent. In this paper, the Kottler spacetime is given in isotropic static coordinates (i.e., the metric components are time-independent). The metric is found in terms of the Jacobian elliptic functions through coordinate transformations from the Schwarzschild-(anti-)de Sitter metric. In canonical coordinates, it is known that the unparameterized spatially projected null geodesics of the Kottler and Schwarzschild spacetimes coincide. We show that in isotropic static coordinates, the refractive indices of Kottler and Schwarzschild are not proportional, yielding spatially projected null geodesics that are different.

Inhomogeneous compact extra dimensions and de Sitter cosmology

In the framework of multidimensional f(R) gravity, we study the possible metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even higher energy scales. It is shown that in the presence of a scalar field, it is possible to obtain a variety of inhomogeneous metrics in the extra factor space $${{\mathbb {M}}}_2$$ M 2 . Each of these metrics leads to a certain value of the 4D cosmological constant $$\varLambda _4$$ Λ 4 , and in particular, it is possible to obtain $$\varLambda _4 =0$$ Λ 4 = 0 , as is confirmed by numerically obtained solutions. A nontrivial scalar field distribution in the extra dimensions is an important feature of this family of metrics. The obtained solutions are shown to be stable under extra-dimensional perturbations.

Extension Rules of Newman–Janis Algorithm for Rotation Metrics in General Relativity

Aims: The aim of this study is to extend the formula of Newman–Janis algorithm (NJA) and introduce the rules of the complexifying seed metric. The extension of NJA can help determine more generalized axisymmetric solutions in general relativity.Methodology: We perform the extended NJA in two parts: the tensor structure and the seed metric function. Regarding the tensor structure, there are two prescriptions, the Newman–Penrose null tetrad and the Giampieri prescription. Both are mathematically equivalent; however, the latter is more concise. Regarding the seed metric function, we propose the extended rules of a complex transformation by r2/Σ and combine the mass, charge, and cosmologic constant into a polynomial function of r. Results: We obtain a family of axisymmetric exact solutions to Einstein’s field equations, including the Kerr metric, Kerr–Newman metric, rotating–de Sitter, rotating Hayward metric, Kerr–de Sitter metric and Kerr–Newman–de Sitter metric. All the above solutions are embedded in ellipsoid- symmetric spacetime, and the energy-momentum tensors of all the above metrics satisfy the energy conservation equations. Conclusion: The extension rules of the NJA in this research avoid ambiguity during complexifying the transformation and successfully generate a family of axisymmetric exact solutions to Einsteins field equations in general relativity, which deserves further study.

Localization of Energy and Momentum in an Asymptotically Reissner-Nordström Non-Singular Black Hole Space-Time Geometry

The space-time geometry exterior to a new four-dimensional, spherically symmetric and charged black hole solution that, through a coupling of general relativity with a non-linear electrodynamics, is non-singular everywhere, for small r it behaves as a de Sitter metric, and asymptotically it behaves as the Reissner-Nordström metric, is considered in order to study energy-momentum localization. For the calculation of the energy and momentum distributions, the Einstein, Landau-Lifshitz, Weinberg and Møller energy-momentum complexes were applied. The results obtained show that in all prescriptions the energy depends on the mass M of the black hole, the charge q, two parameters a ∈ Z + and γ ∈ R + , and on the radial coordinate r. The calculations performed in each prescription show that all the momenta vanish. Additionally, some limiting and particular cases for r and q are studied, and a possible connection with strong gravitational lensing and microlensing is attempted.

An Extension of Newman–Janis algorithm for Rotation Metrics in General Relativity

The Newman-Janis algorithm is widely known in the solution of rotating black holes in general relativity. By means of complex transformation, the solution of the rotating black hole can be obtained from the seed metric of a static black hole. This study shows that the extended Newman-Janis algorithm must treat the tensor structure and the seed metric function separately. In the tensor structure, there are two prescriptions, the Newman–Penrose null tetrad and the Giampieri prescription. Both are mathematically the same, while the latter is more concise. In the seed metric function, the extended rules of complex transformation are given in the power of r, and the formulaic solution is deduced. Some exact solutions are derived by the extended algorithm, including the Kerr metric, the Kerr–Newman metric, the rotating–de Sitter, the Kerr–de Sitter metric, and the Kerr–Newman–de Sitter metric.

Quantum thermodynamics in a static de Sitter space-time and initial state of the universe

Using Relativistic Quantum Geometry we study back-reaction effects of space-time inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of space-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around $$r=0$$r=0. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of space-time. We found that temperature and entropy are dependent on the number of sub-states on each energy’s level and the Bekenstein–Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy $$E_p=m_p\,c^2$$Ep=mpc2, and a B–H temperature: $$T_{BH}=\left( \frac{\hbar \,c}{2\pi \,l_p\,K_B}\right) $$TBH=ħc2πlpKB.

The influence of cosmological constant in temperature oscillations of a gas moving close to circular geodesic

The aim of this work is to analyze and to verify the effects of the charge and cosmological constant on the temperature oscillations that occur in a gas in a circular motion close to geodesic under the action of a Reissner–Nordström–de Sitter metric. The temperature oscillations are determined from Tolman’s law written in Fermi normal coordinates for a comoving observer. The temperature oscillations are calculated for a theoretical model obtained in the literature. Comparing the different configurations analyzed, it is possible to verify that the cosmological constant term causes a small displacement in the oscillation peaks. We also calculated the ratio between frequencies for some particular cases of the Reissner–Nordström–de Sitter metric and verified that the cases with null cosmological constant are closer of the 3/2 value found in QPOs. In another hand, the addition of the cosmological constant causes a direct increase of the ratio between frequencies.