We consider a Weyl-Lorentz-U (1)-invariant gravity model written in terms of a scalar field, elec... more We consider a Weyl-Lorentz-U (1)-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity without torsion and curvature, the socalled symmetric teleparallel geometry, in three dimensions. Firstly, we obtain variational field equations from a Lagrangian. Then, we find some classes of circularly symmetric rotating solutions by making only a metric ansatz. The coincident gauge of symmetric teleparallel spacetime allows us for doing so.
Rendiconti lincei. Scienze fisiche e naturali, Aug 18, 2018
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and math... more The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The non-analyticity of these orbitals at r = 0, however, requires analytical relations for multi-center integrals to be derived. This is nearly insurmountable. Previous papers by present authors eliminated this difficulty. Highly accurate results can be achieved by the procedure described in these papers, which place no restrictions on quantum numbers in all ranges of orbital parameters. The purpose of this work is to investigate computational aspects of the formulae given in the previous paper. It is to present a method which helps to increase computational efficiency. In terms of the processing time, evaluation of integrals over Slater-type orbitals with non-integer principal quantum numbers are competitive with those over Slater-type orbitals with integer principal quantum numbers. Keywords Slater-type orbitals • Multi-center integrals • Auxiliary functions 1 Introduction In the first paper [1] of aforementioned series, history and importance of usage the auxiliary function method was summarized. Applications in molecular calculations were briefly
We investigate anisotropic cosmological solutions of the theory with non-minimal couplings betwee... more We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in Y (R)F 2 form. After we derive the field equations by the variational principle, we look for spatially flat cosmological solutions with magnetic fields or electric fields. Then we give exact anisotropic solutions by assuming the hyperbolic expansion functions. We observe that the solutions approach to the isotropic case in late-times.
The Dirac lagrangian is minimally coupled to the most general R + T + T 2-type lagrangian in (1+2... more The Dirac lagrangian is minimally coupled to the most general R + T + T 2-type lagrangian in (1+2)-dimensions. The field equations are obtained from the total lagrangian by a variational principle. The space-time torsion is calculated algebraically in terms of the Dirac condensate plus coupling coefficients. A family of circularly symmetric rotating exact solutions which is asymptotically AdS 3 is obtained. Finally BTZ-like solutions are discussed.
We investigate anisotropic compact stars in the non-minimal Y (R)F 2 model of gravity which coupl... more We investigate anisotropic compact stars in the non-minimal Y (R)F 2 model of gravity which couples an arbitrary function of curvature scalar Y (R) to the electromagnetic field invariant F 2. After we obtain exact anisotropic solutions to the field equations of the model, we apply the continuity conditions to the solutions at the boundary of the star. Then we find the mass, electric charge, and surface gravitational redshift by the parameters of the model and radius of the star. I. INTRODUCTION Compact stars are the best sources to test a theory of gravity under the extreme cases with strong fields. Although they are generally considered as isotropic, there are important reasons to take into account anisotropic compact stars which have different radial and tangential pressures. First of all, the anisotropic spherically symmetric compact stars can be more stable than the isotropic ones [1]. The core region of the compact stars with very high nuclear matter density becomes more realistic in the presence of anisotropic pressures [2, 3]. Moreover the phase transitions [4], pion condensations [5] and the type 3A superfluids [6] in the cooling neutron matter core can lead to anisotropic pressure distribution. Furthermore, the mixture of two perfect fluid can generate anisotropic fluid [7]. Anisotropy can be also sourced by the rotation of the star [8-10]. Additionally, strong magnetic fields may lead to anisotropic pressure components in the compact stars[11]. Some analytic solutions of anisotropic matter distribution were studied in Einsteinian Gravity [8-17]. Recently it was shown that the "scalarization" can not arise without anisotropy and the anisotropy range can be determined by observations on binary pulsar in the Scalar-Tensor Gravity and General Relativity [10]. The anisotropic star solutions in R 2 gravity can shift the mass-radius curves to the region given by observations [18]. It is interesting to note that anisotropic compact stars were 1
We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigat... more We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigate cosmological solutions in three dimensions. We arrive at a family of solutions which exists even in the limit of vanishing cosmological constant.
Field equations of the Chern-Simons modified gravity in 4-dimensions are obtained by a truncation... more Field equations of the Chern-Simons modified gravity in 4-dimensions are obtained by a truncation of the field equations of the low energy effective string models with first order corrections in the string constant included.
We retreat the well-known Einstein-Cartan theory by slightly modifying the covariant derivative o... more We retreat the well-known Einstein-Cartan theory by slightly modifying the covariant derivative of spinor field by investigating double cover of the Lorentz group. We first write the Lagrangian consisting of the Einstein-Hilbert term, Dirac term and a scalar field term in a non-Riemannian spacetime with curvature and torsion. Then by solving the affine connection analytically we reformulate the theory in the Riemannian spacetime in a self-consistent way. Finally we discuss our results and give future perspectives on the subject.
We study (2+1)-dimensional holographic superconductors in the presence of non-minimally coupled e... more We study (2+1)-dimensional holographic superconductors in the presence of non-minimally coupled electromagnetic field to gravity by considering an arbitrary linear combination of RF 2-type invariants with three parameters. Our analytical analysis shows that the non-minimal couplings affect the condensate and the critical temperature.
A 2D symmetric teleparallel gravity model is given by a generic 4parameter action that is quadrat... more A 2D symmetric teleparallel gravity model is given by a generic 4parameter action that is quadratic in the non-metricity tensor. Variational field equations are derived. A class of conformally flat solutions are found. We also give static or cosmological solutions that need not be in this class.
The contribution of gravitational neutrino oscillations to the solar neutrino problem is studied ... more The contribution of gravitational neutrino oscillations to the solar neutrino problem is studied by constructing the Dirac Hamiltonian and calculating the corresponding dynamical phase in the vicinity of the Sun in a non-Riemann background Kerr space-time with torsion and non-metricity. We show that certain components of non-metricity and the axial as well as non-axial components of torsion may contribute to neutrino oscillations. We also note that the rotation of the Sun may cause a suppression of transitions among neutrinos. However, the observed solar neutrino deficit could not be explained by any of these effects because they are of the order of Planck scales.
We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigat... more We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigate cosmological solutions in three dimensions. We arrive at a family of solutions which exists even in the limit of vanishing cosmological constant.
After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure ... more After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple minimally a Dirac spinor field to our gravitational Lagrangian 2-form which is quadratic in the nonmetricity and both linear and quadratic in the curvature in two dimensions. Subsequently we obtain field equations by varying the total Lagrangian with respect to the independent variables. Finally we find some classes of solutions of the vacuum theory and then a solution of the Dirac equation in a specific background and analyse them.
Teleparallel gravity models, in which the curvature and the nonmetricity of spacetime are both se... more Teleparallel gravity models, in which the curvature and the nonmetricity of spacetime are both set zero, are widely studied in the literature. We work a different teleparallel theory, in which the curvature and the torsion of spacetime are both constrained to zero, but the nonmetricity is nonzero. After reformulating the general relativity in this spacetime we find a solution and investigate its singularity structure.
In this paper, we investigate the inflation and the late-time acceleration of the universe by usi... more In this paper, we investigate the inflation and the late-time acceleration of the universe by using the modified gravity approach which involves the non-minimal $Y(R) F^2$-type couplings of electromagnetic fields to gravity. After we derive field equations by a first order variational principle from the Lagrangian of the non-minimally coupled theory, we look for spatially flat cosmological solutions with the large-scale magnetic fields. At the end we estimate certain values according to observations for three parameters occurring in the solutions.
Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting... more Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting the connection from the tangent bundle to the spinor bundle over spacetime. Foldy-Wouthuysen transformation of the Dirac equation in a Schwarzschild background spacetime is considered and it is shown that both the torsion and non-metricity couples to the momentum and spin of a massive, spinning particle. However, the effects are small to be observationally significant.
Journal of Cosmology and Astroparticle Physics, Nov 16, 2017
We consider the non-minimal model of gravity in Y (R)F 2-form. We investigate a particular case o... more We consider the non-minimal model of gravity in Y (R)F 2-form. We investigate a particular case of the model, for which the higher order derivatives are eliminated but the scalar curvature R is kept to be dynamical via the constraint Y R F mn F mn = − 2 κ 2. The effective fluid obtained can be represented by interacting electromagnetic field and vacuum depending on Y (R), namely, the energy density of the vacuum tracks R while energy density of the conventional electromagnetic field is dynamically scaled with the factor Y (R) 2. We give exact solutions for anisotropic inflation by assuming the volume scale factor of the Universe exhibits a power-law expansion. The directional scale factors do not necessarily exhibit power-law expansion, which would give rise to a constant expansion anisotropy, but expand non-trivially and give rise to a non-monotonically evolving expansion anisotropy that eventually converges to a non-zero constant. Relying on this fact, we discuss the anisotropic e-fold during the inflation by considering observed scale invariance in CMB and demanding the Universe to undergo the same amount of e-folds in all directions. We calculate the residual expansion anisotropy at the end of inflation, though as a result of non-monotonic behaviour of expansion anisotropy all the axes of the Universe undergo the same of amount of e-folds by the end of inflation. We also discuss the generation of the modified electromagnetic field during the first few e-folds of the inflation and its persistence against to the vacuum till end of inflation.
We consider a Weyl-Lorentz-U (1)-invariant gravity model written in terms of a scalar field, elec... more We consider a Weyl-Lorentz-U (1)-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity without torsion and curvature, the socalled symmetric teleparallel geometry, in three dimensions. Firstly, we obtain variational field equations from a Lagrangian. Then, we find some classes of circularly symmetric rotating solutions by making only a metric ansatz. The coincident gauge of symmetric teleparallel spacetime allows us for doing so.
Rendiconti lincei. Scienze fisiche e naturali, Aug 18, 2018
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and math... more The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The non-analyticity of these orbitals at r = 0, however, requires analytical relations for multi-center integrals to be derived. This is nearly insurmountable. Previous papers by present authors eliminated this difficulty. Highly accurate results can be achieved by the procedure described in these papers, which place no restrictions on quantum numbers in all ranges of orbital parameters. The purpose of this work is to investigate computational aspects of the formulae given in the previous paper. It is to present a method which helps to increase computational efficiency. In terms of the processing time, evaluation of integrals over Slater-type orbitals with non-integer principal quantum numbers are competitive with those over Slater-type orbitals with integer principal quantum numbers. Keywords Slater-type orbitals • Multi-center integrals • Auxiliary functions 1 Introduction In the first paper [1] of aforementioned series, history and importance of usage the auxiliary function method was summarized. Applications in molecular calculations were briefly
We investigate anisotropic cosmological solutions of the theory with non-minimal couplings betwee... more We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in Y (R)F 2 form. After we derive the field equations by the variational principle, we look for spatially flat cosmological solutions with magnetic fields or electric fields. Then we give exact anisotropic solutions by assuming the hyperbolic expansion functions. We observe that the solutions approach to the isotropic case in late-times.
The Dirac lagrangian is minimally coupled to the most general R + T + T 2-type lagrangian in (1+2... more The Dirac lagrangian is minimally coupled to the most general R + T + T 2-type lagrangian in (1+2)-dimensions. The field equations are obtained from the total lagrangian by a variational principle. The space-time torsion is calculated algebraically in terms of the Dirac condensate plus coupling coefficients. A family of circularly symmetric rotating exact solutions which is asymptotically AdS 3 is obtained. Finally BTZ-like solutions are discussed.
We investigate anisotropic compact stars in the non-minimal Y (R)F 2 model of gravity which coupl... more We investigate anisotropic compact stars in the non-minimal Y (R)F 2 model of gravity which couples an arbitrary function of curvature scalar Y (R) to the electromagnetic field invariant F 2. After we obtain exact anisotropic solutions to the field equations of the model, we apply the continuity conditions to the solutions at the boundary of the star. Then we find the mass, electric charge, and surface gravitational redshift by the parameters of the model and radius of the star. I. INTRODUCTION Compact stars are the best sources to test a theory of gravity under the extreme cases with strong fields. Although they are generally considered as isotropic, there are important reasons to take into account anisotropic compact stars which have different radial and tangential pressures. First of all, the anisotropic spherically symmetric compact stars can be more stable than the isotropic ones [1]. The core region of the compact stars with very high nuclear matter density becomes more realistic in the presence of anisotropic pressures [2, 3]. Moreover the phase transitions [4], pion condensations [5] and the type 3A superfluids [6] in the cooling neutron matter core can lead to anisotropic pressure distribution. Furthermore, the mixture of two perfect fluid can generate anisotropic fluid [7]. Anisotropy can be also sourced by the rotation of the star [8-10]. Additionally, strong magnetic fields may lead to anisotropic pressure components in the compact stars[11]. Some analytic solutions of anisotropic matter distribution were studied in Einsteinian Gravity [8-17]. Recently it was shown that the "scalarization" can not arise without anisotropy and the anisotropy range can be determined by observations on binary pulsar in the Scalar-Tensor Gravity and General Relativity [10]. The anisotropic star solutions in R 2 gravity can shift the mass-radius curves to the region given by observations [18]. It is interesting to note that anisotropic compact stars were 1
We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigat... more We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigate cosmological solutions in three dimensions. We arrive at a family of solutions which exists even in the limit of vanishing cosmological constant.
Field equations of the Chern-Simons modified gravity in 4-dimensions are obtained by a truncation... more Field equations of the Chern-Simons modified gravity in 4-dimensions are obtained by a truncation of the field equations of the low energy effective string models with first order corrections in the string constant included.
We retreat the well-known Einstein-Cartan theory by slightly modifying the covariant derivative o... more We retreat the well-known Einstein-Cartan theory by slightly modifying the covariant derivative of spinor field by investigating double cover of the Lorentz group. We first write the Lagrangian consisting of the Einstein-Hilbert term, Dirac term and a scalar field term in a non-Riemannian spacetime with curvature and torsion. Then by solving the affine connection analytically we reformulate the theory in the Riemannian spacetime in a self-consistent way. Finally we discuss our results and give future perspectives on the subject.
We study (2+1)-dimensional holographic superconductors in the presence of non-minimally coupled e... more We study (2+1)-dimensional holographic superconductors in the presence of non-minimally coupled electromagnetic field to gravity by considering an arbitrary linear combination of RF 2-type invariants with three parameters. Our analytical analysis shows that the non-minimal couplings affect the condensate and the critical temperature.
A 2D symmetric teleparallel gravity model is given by a generic 4parameter action that is quadrat... more A 2D symmetric teleparallel gravity model is given by a generic 4parameter action that is quadratic in the non-metricity tensor. Variational field equations are derived. A class of conformally flat solutions are found. We also give static or cosmological solutions that need not be in this class.
The contribution of gravitational neutrino oscillations to the solar neutrino problem is studied ... more The contribution of gravitational neutrino oscillations to the solar neutrino problem is studied by constructing the Dirac Hamiltonian and calculating the corresponding dynamical phase in the vicinity of the Sun in a non-Riemann background Kerr space-time with torsion and non-metricity. We show that certain components of non-metricity and the axial as well as non-axial components of torsion may contribute to neutrino oscillations. We also note that the rotation of the Sun may cause a suppression of transitions among neutrinos. However, the observed solar neutrino deficit could not be explained by any of these effects because they are of the order of Planck scales.
We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigat... more We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigate cosmological solutions in three dimensions. We arrive at a family of solutions which exists even in the limit of vanishing cosmological constant.
After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure ... more After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple minimally a Dirac spinor field to our gravitational Lagrangian 2-form which is quadratic in the nonmetricity and both linear and quadratic in the curvature in two dimensions. Subsequently we obtain field equations by varying the total Lagrangian with respect to the independent variables. Finally we find some classes of solutions of the vacuum theory and then a solution of the Dirac equation in a specific background and analyse them.
Teleparallel gravity models, in which the curvature and the nonmetricity of spacetime are both se... more Teleparallel gravity models, in which the curvature and the nonmetricity of spacetime are both set zero, are widely studied in the literature. We work a different teleparallel theory, in which the curvature and the torsion of spacetime are both constrained to zero, but the nonmetricity is nonzero. After reformulating the general relativity in this spacetime we find a solution and investigate its singularity structure.
In this paper, we investigate the inflation and the late-time acceleration of the universe by usi... more In this paper, we investigate the inflation and the late-time acceleration of the universe by using the modified gravity approach which involves the non-minimal $Y(R) F^2$-type couplings of electromagnetic fields to gravity. After we derive field equations by a first order variational principle from the Lagrangian of the non-minimally coupled theory, we look for spatially flat cosmological solutions with the large-scale magnetic fields. At the end we estimate certain values according to observations for three parameters occurring in the solutions.
Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting... more Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting the connection from the tangent bundle to the spinor bundle over spacetime. Foldy-Wouthuysen transformation of the Dirac equation in a Schwarzschild background spacetime is considered and it is shown that both the torsion and non-metricity couples to the momentum and spin of a massive, spinning particle. However, the effects are small to be observationally significant.
Journal of Cosmology and Astroparticle Physics, Nov 16, 2017
We consider the non-minimal model of gravity in Y (R)F 2-form. We investigate a particular case o... more We consider the non-minimal model of gravity in Y (R)F 2-form. We investigate a particular case of the model, for which the higher order derivatives are eliminated but the scalar curvature R is kept to be dynamical via the constraint Y R F mn F mn = − 2 κ 2. The effective fluid obtained can be represented by interacting electromagnetic field and vacuum depending on Y (R), namely, the energy density of the vacuum tracks R while energy density of the conventional electromagnetic field is dynamically scaled with the factor Y (R) 2. We give exact solutions for anisotropic inflation by assuming the volume scale factor of the Universe exhibits a power-law expansion. The directional scale factors do not necessarily exhibit power-law expansion, which would give rise to a constant expansion anisotropy, but expand non-trivially and give rise to a non-monotonically evolving expansion anisotropy that eventually converges to a non-zero constant. Relying on this fact, we discuss the anisotropic e-fold during the inflation by considering observed scale invariance in CMB and demanding the Universe to undergo the same amount of e-folds in all directions. We calculate the residual expansion anisotropy at the end of inflation, though as a result of non-monotonic behaviour of expansion anisotropy all the axes of the Universe undergo the same of amount of e-folds by the end of inflation. We also discuss the generation of the modified electromagnetic field during the first few e-folds of the inflation and its persistence against to the vacuum till end of inflation.
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Papers by Muzaffer Adak