Gravity's Rainbow Research Articles

Effects of gravity rainbow on scalar bosonic and oscillator fields in Bonnor–Melvin space-time with a cosmological constant

In this paper, we explore the relativistic quantum motion of spin-zero scalar charge-free particles influenced by rainbow gravity’s (RG’s) in Bonnor–Melvin magnetic space-time, a four-dimensional solution featuring a positive cosmological constant. We solve the Klein–Gordon equation in this scenario by using two sets of rainbow function: (i) f(χ)=1(1-βχ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\chi )=\\frac{1}{(1-\\beta \\,\\chi )}$$\\end{document}, h(χ)=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h(\\chi )=1$$\\end{document} and (ii) f(χ)=1(1-βχ)=h(χ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\chi )=\\frac{1}{(1-\\beta \\,\\chi )}=h(\\chi )$$\\end{document}, where 0<χ=|E|Ep≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 < \\chi \\left( =\\frac{|E|}{E_p}\\right) \\le 1$$\\end{document} with Ep\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_p$$\\end{document} being the Planck’s energy, E is the particle’s energy, and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} is the rainbow parameter. Furthermore, we study the relativistic quantum oscillator through the Klein–Gordon oscillator equation in the same Bonnor–Melvin magnetic space-time under RG effects. Employing the first pair of rainbow function, we obtain an approximate eigenvalue solution of the quantum oscillator fields. Notably, we demonstrate that the relativistic energy profile of scalar and oscillator particles are influenced by the topology of the geometry and the cosmological constant which is related with the magnetic field strength lies along the symmetry axis. Additionally, we see the impact of rainbow parameter on these approximate relativistic energy profiles in both quantum systems.

Complexity factor for a static self-gravitating sphere in Rastall–Rainbow gravity

We generalized Herrera’s definition of complexity factor for static spherically symmetric fluid distributions to Rastall–Rainbow theory of gravity. For this purpose, an energy-dependent equation of motion is employed in accordance with the principle of gravity’s rainbow. It is found that the complexity factor appears in the orthogonal splitting of the Riemann curvature tensor, and measures the deviation of the value of the active gravitational mass from the simplest system under the combined corrections of Rastall and rainbow. In the low-energy limit, all the results we have obtained reduce to the counterparts of general relativity when the non-conserved parameter is taken to be one. We also demonstrate how to build an anisotropic or isotropic star model using complexity approach. In particular, the vanishing complexity factor condition in Rastall–Rainbow gravity is exactly the same as that derived in general relativity. This fact may imply a deeper geometric foundation for the complexity factor.

Maximal acceleration in Rainbow gravity

In this paper, we derive maximal acceleration of a massive particle in Rainbow gravity. Using eight-dimensional phase-space metric compatible with Rainbow gravity, we obtain the maximal acceleration, valid up to first order in the Rainbow gravity parameter η. Using the positivity condition on maximal acceleration, we find that the upper bound on the Rainbow gravity parameter is of the order of for positron and for a black hole. After obtaining the expression for maximal acceleration for different choices of Rainbow functions, we derive corresponding modifications to Unruh temperature. Comparing with the observational value of the Unruh temperature, we find the upper bound on η as for positron radiation. We then derive geodesic equations for different choices of Rainbow functions and also obtain the Newtonian limit of these geodesic equations. We find that the changes in the value of maximum acceleration, maximum temperature and Newtonian force equation are dependent on the choices of Rainbow functions.

Effect of rainbow gravity, PDM, and external magnetic field on optical properties and energy spectra of GaAs quantum dot

Effect of rainbow gravity, PDM, and external magnetic field on optical properties and energy spectra of GaAs quantum dot

Possible existence of Rastall–Rainbow wormholes in dark matter galactic halos

The Rastall–Rainbow gravity theory has recently been proposed as a combination of the Rastall and rainbow theories. This theory can be thought as a generalization of the Rastall gravity to an energy dependent Rastall theory, and leads to an additional degrees of freedom. In this paper, we construct models that admit the wormhole geometries within this theory. We analyze the properties of static wormholes based on the profiles of dark matter halos, which was demonstrated earlier in Rahaman et al. (Eur Phys J C 74:2750, 2014) that galactic halo possesses the necessary properties in favour of the existence of wormholes. The main properties are being analyzed by considering three different kinds of halo density profiles. Our results indicate that such wormholes could potentially exist but the NEC is violated in the vicinity of the wormhole throat. We have further examined the stability of the configuration through the adiabatic sound velocity.

The Klein-Gordon equation in the cosmic string and rainbow gravity spacetime under the influence of an external magnetic field and Coulomb potential for PDM particles

Abstract The Klein-Gordon equation in the cosmic string and rainbow gravity spacetime under the influence of an external magnetic field and Coulomb potential for PDM particles is investigated using the NU method. From solution of the Klein-Gordon system with PDM particles, the energy levels are obtained. The energy levels are numerically calculated as a function of rainbow gravity parameters, as a function of magnetic field parameters, as a function of position-dependent mass parameters. We apply some rainbow functions and the results show that the negative and positive energy levels for rainbow function 1 are symmetrical compared to rainbow function 2.

Unraveling the mysteries of wormhole formation in Rastall–Rainbow gravity: a comprehensive study using the embedding approach

The present work looks for the possible existence of static and spherically symmetric wormhole geometries in Rastall–Rainbow gravity. Since, the Rastall–Rainbow gravity model has been constructed with the combination of Rastall theory and the gravity’s rainbow formalism. Taking advantage of the Karmarkar condition for embedding class one metrics, we solve the modified field equations analytically that describe wormholes for specific choice of redshift function. For specific parameter ranges, the solution represents a traversable wormhole that exhibits the violation of null energy condition and consequently the weak energy condition also. Furthermore, we focus on the wormhole stability via adiabatic sound velocity analysis. This model establishes a strong connection between two model parameters, namely, the Rastall parameters and the Rainbow functions, and how it affects the wormhole solution.

Exploring the physical properties of strange star SAXJ1808.4–3658 in rainbow gravity

This study investigated the formation and evolution of a strange star known as SAX.J1808.4–3658 in the Krori–Barua Rainbow spacetime, resulting from the collapse of string fluid. The study examined the dynamical variables derived from the field equations, taking into consideration the influence of the particle’s energy on the mass density, pressure, and string tension. Additionally, various techniques were employed to analyze the physical properties, including gradients, energy conditions, anisotropy, stability, the Tolman–Oppenheimer–Volkoff equation, mass function, compactness, and red-shift. The study’s findings revealed that the strange star SAX.J1808.4–3658 satisfies all the conditions necessary for its evolution from an anisotropic string fluid. This discovery suggests that strange stars might have emerged during the string-oriented quark era of the Universe. The researchers presented all the physical quantities within the frameworks of both rainbow gravity and general relativity, while also utilizing graphical representations to aid in comprehending the study’s findings. The energy conditions and anisotropy were found to be fulfilled, indicating the stability of the strange star. Furthermore, the Tolman–Oppenheimer–Volkoff equation was employed to determine the maximum mass of the strange star, which was found to align with observational data.

KG-particles in a cosmic string rainbow gravity spacetime in mixed magnetic fields

We investigate and report the effects of rainbow gravity on the spectroscopic structure of KG-oscillators in a mixed magnetic field (in the sense that it has the usually described as a uniform and a non-uniform magnetic fields, each at a time) introduced by the 4-vector potential Aμ=(0,0,Aφ,0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_\\mu =(0,0,A_\\varphi ,0)$$\\end{document}, where Aφ=B1r2/2+B2r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_\\varphi =B_1 r^2/2+B_2 r$$\\end{document}, and B1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_1$$\\end{document} and B2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_2$$\\end{document} are magnetic field strengths. We also discuss and report the effects of such a mixed magnetic field on the spectra of KG-oscillators in cosmic string rainbow gravity. In so doing, we introduce a new and quite handy conditionally exact solution associated with the truncation of the biconfluent Heun functions into polynomials. Using a loop quantum gravity motivated rainbow functions, we observe interesting effects when the magnetic field strength B2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_2$$\\end{document} grows up from zero. Such effects include energy levels crossings which, in this case, turns the spectra of the KG-oscillators upside down. Moreover, Landau-like signature on the spectra are observed and discussed. Yet, interestingly, we also observe that rainbow gravity affects the magnetic field as well, in the sense that the magnetic field becomes probe particle energy-dependent one.

Study of scalar particles through the Klein–Gordon equation under rainbow gravity effects in Bonnor–Melvin-Lambda space-time

In our investigation, we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity, considering the Bonnor–Melvin-Lambda (BML) space-time background. The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constant Λ and the topological parameter α of the geometry. The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated, utilizing two sets of rainbow functions: (i) f(χ)=(eβχ−1)βχ , h(χ) = 1 and (ii) f(χ) = 1, h(χ)=1+βχ2 . Here 0<χ=∣E∣Ep≤1 with E representing the particle’s energy, E p is the Planck’s energy, and β is the rainbow parameter. We obtain the approximate analytical solutions for the scalar particles and conduct a thorough analysis of the obtained results. Afterwards, we study the quantum dynamics of quantum oscillator fields within this BML space-time, employing the Klein–Gordon oscillator. Here also, we choose the same sets of rainbow functions and obtain the approximate eigenvalue solution for the oscillator fields. Notably, we demonstrate that the relativistic approximate energy profiles of charge-free scalar particles and oscillator fields get influenced by the topology of the geometry and the cosmological constant. Furthermore, we show that the energy profiles of scalar particles receive modifications from the rainbow parameter and the quantum oscillator fields by both the rainbow parameter and the frequency of oscillation.

Creation of fermions in a two-dimensional de Sitter space via a quantum gravity approach

We discuss the production process of Dirac particles in a two-dimensional de Sitter geometry via the framework of rainbow gravity from the general relativity and the teleparallel theory perspectives. On this purpose, we find out the exact analytical solutions for the selected space-time model and then conclude that the general relativity and the teleparallel theory versions of the covariant Dirac equation in the (1+1) -dimensional deformed de Sitter space-time have the same exact solutions. In the subsequent step, making use of the explicit form of the Dirac spinor components and the Bogoliubov coefficients, we turn our attention to investigating the density of produced half-spin particles. Finally, we obtain two mathematical solutions for the fermionic energy spectrum.

Pair production by electromagnetic fields in a modified Robertson-Walker universe

We investigate the relativistic quantum dynamics of the spinless particles in a Robertson-Walker (RW) spacetime in the framework of gravity's rainbow (RG) when homogeneous electromagnetic fields exist. Exact solutions of the Klein-Gordon equation (KGE) are obtained and the amount of the created pairs is calculated by employing the Bogoliubov transformation method (BTM). The effects of homogeneous electromagnetic fields interacting with gravitational fields on particle production rate are discussed.

Effects of rainbow gravity on an electron confined to a triangular well and a periodic potential

We investigate quantum effects concerning the modification of the background via rainbow gravity on an electron. We employ the nonrelativistic approximation of the Dirac equation to analyze these effects in depth. We initially study the interaction between an electron and a uniform electric field, by exploring confinement of the particle to a triangular potential well. We find systematic alterations in the energy levels reliant on the rainbow parameter ϵ. Additionally, we investigate a particle in a periodic potential resembling a ring. We also find consistent alterations in energy levels due to changes in the background via rainbow functions. As in the previously analyzed scenario, the larger the rainbow parameter, the lower the obtained energy levels. These findings underscore a systematic influence of modified gravity on particle dynamics in quantum scenarios.

Investigating stable quark stars in Rastall-Rainbow gravity and their compatibility with gravitational wave observations

We present a stable model for quark stars in Rastall-Rainbow (R-R) gravity. The structure of this configuration is obtained by utilizing an interacting quark matter equation of state. The R-R gravity theory is developed as a combination of two distinct theories, namely, the Rastall theory and the gravity's rainbow formalism. Depending on the model parameters (λ¯,η,Σ,Beff), the mass-radius relations are numerically computed for modified Tolman-Oppenheimer-Volkoff (TOV) equations with proper boundary conditions. The stability of equilibrium configuration has been checked through the static stability criterion, adiabatic index and the sound velocity. Our calculations predict larger maximum masses for quark stars, and the obtained results are compatible with accepted masses and radii values, including constraints from GW190814 and GW170817 events in all the studied cases.

Van der Waals black holes in rainbow gravity

Recently, Rajagopal et al. presented an asymptotically AdS black hole metric whose thermodynamics qualitatively mimics the behavior of the Van der Waals fluid by treating the cosmological constant as a thermodynamic pressure. In some studies in the literature, authors have discussed the effects of deformed algebras such as generalized and extended uncertainty principles on the thermal quantities of these black holes. In this paper, we considered another deformation, the rainbow gravity formalism, and we investigated its impact on the Van der Waal black hole thermodynamics. To this end, we first generated the modified lapse and mass functions, and then we derived the modified thermal quantities such as thermodynamic volume, Hawking temperature, entropy, and specific heat functions. Finally, we explored the thermodynamics of a black hole, which mimics the thermodynamics of an ideal gas, under the influence of the rainbow gravity formalism.

Relativistic quantum motions of bosonic field under rainbow gravity's environment with point-like defect

In this paper, we focus on the relativistic quantum motions of spin-0 bosonic field in the background of a point-like global monopole taking into account the effects of background curvature. Moreover, we consider this quantum system in the presence of rainbow gravity's environment and analyze the influence on the behavior of scalar bosonic field. We solve the radial equation of the Klein-Gordon wave equation and present non-perturbative eigenvalue solutions for such a system by choosing well-known pair of rainbow functions, for examples, (i) f(χ)=1, h(χ)=1−β0χ; (ii) f(χ)=1, h(χ)=1−β0χ2; (iii) f(χ)=[exp⁡(β0χ)−1]/(β0χ), h(χ)=1, and (iv) f(χ)=(1−β0χ)−1=h(χ), where χ=|E|/Ep, and β0 is the rainbow parameter. In fact, it is shown that the energy eigenvalues and the wave functions of bosonic fields are influenced by the rainbow parameter β0. Furthermore, the eigenvalue solutions depend on the global monopole of the geometry characterized by the parameter α. The presence of a global monopole breaks the degeneracy of energy spectra and modifies the results compared to the flat space.

Noncommutative effects on wormholes in Rastall–Rainbow gravity

In this paper, we explore the physical properties and characteristics of static, spherically symmetric wormholes in the background of Rastall–Rainbow gravity. The Rastall–Rainbow gravity theory has recently been proposed as a combination of two theories, namely, the Rastall theory and the Rainbow description. We implemented noncommutativity by adopting two different distributions of energy density (Gaussian and Lorentzian) in the Morris and Thorne metric. We solve the field equations analytically and discuss all the properties of wormholes depending on the two model parameters. Notably, for specific parameter ranges, one can alleviate the violation of the WEC at the throat and its neighborhood.

Absorption cross section in gravity’s rainbow from confluent Heun equation

We investigate the scattering of a massless scalar field by a charged, non-rotating black hole in the presence of gravity’s rainbow. Using the connection coefficients of the confluent Heun equation expressed in terms of the semi-classical confluent conformal blocks and the instanton part of the Nekrasov–Shatashvili free energy, we obtain an asymptotic expansion for the low-energy absorption cross section. Furthermore, we consider the resummation of the instanton contributions to the absorption cross section, which gives the area of the black hole up to a factor of (4/3)2 .

Energy–Momentum distributions of cylindrical black hole in rainbow gravity

In this study, the energy–momentum localization problem is addressed within the framework of rainbow gravity. Considering the black string black hole, one of the cylindrical black hole models, energy–momentum distributions are obtained for Einstein, Bergmann–Thomson, and Landau–Liftshitz prescriptions in rainbow gravity. All prescriptions’ energy densities are non-zero and depend on the rainbow functions, while the momentum distributions are zero. It has been observed that space-time energy does not depend on the energy of the test particle for some particular choices of rainbow functions. The results obtained for all special cases are given in a table.

Relativistic quantum oscillator under rainbow gravity’s effects in traversable wormhole with disclination

In this paper, our principal objective is to investigate the impact of disclination and throat radius of a three-dimensional traversable wormhole on quantum oscillator fields. Specifically, we focus on Perry–Mann-type wormhole with disclination while also considering the influence of rainbow gravity’s. We derive the radial equation of the relativistic Klein–Gordon oscillator within this wormhole background under the effects of gravity’s rainbow and the analytical eigenvalue solution is obtained using the confluent Heun function. In fact, we show that the behavior of the oscillator fields is significantly influenced not only by the presence of disclination and the throat radius but also by the parameter of rainbow gravity’s. We choose various such rainbow functions to present and analyze the eigenvalue solutions of the quantum oscillator fields.