Gravity's Rainbow Research Articles

Rainbow gravity’s effects on scalar field in wormhole background with cosmic strings

Our primary focus is to investigate how the presence of cosmic strings affects a scalar field within the context of a static and circularly symmetric three-dimensional wormhole when subjected to the effects of rainbow gravity. To accomplish this, we address the relativistic Klein–Gordon wave equation and derive analytical solutions for the quantum system by employing the confluent Heun function. Significantly, our research reveals that the behavior of the scalar fields is notably influenced not only by the cosmic strings and wormhole throat radius but also by the parameter of rainbow gravity.

Effect of rainbow function on the structural properties of dark energy star

Confirming the existence of compact objects with a mass greater than 2.5M⊙ by observational results such as GW190814 makes that is possible to provide theories to justify these observational results using modified gravity. This motivates us to use gravity's rainbow, which is the appropriate case for dense objects, to investigate the dark energy star structure as a suggested alternative case to the mass gap between neutron stars and black holes in the perspective of quantum gravity. Hence, in the present work, we derive the modified hydrostatic equilibrium equation for an anisotropic fluid, represented by the extended Chaplygin equation of state in gravity's rainbow. Then, for two isotropic and anisotropic cases, using the numerical solution, we obtain energy-dependent maximum mass and its corresponding radius, and the other properties of the dark energy star including the pressure, energy density, stability, etc. In the following, using the observational data, we compare the obtained results in two frameworks of general relativity and gravity's rainbow.

Energy–momentum localization in rainbow gravity

Theoretical physicists generally prefer to modify the general theory of relativity rather than avoiding the successful approaches that have been offered to us. Hence, the rainbow formalism of gravity, which is one of the most studied quantum gravity candidates in literature, has recently gained importance in the field. In this study, the energy–momentum localization problem is discussed for the Taub universe within the framework of rainbow gravity. To achieve this goal, energy and momentum components are calculated by making use of diverse values of rainbow functions in the Einstein, Bergmann–Thomson, Landau–Lifshitz, and the Papapetrou prescriptions for the geometry under consideration. Except for the Landau–Lifshitz prescription, all prescriptions depend on the rainbow functions and the momentum components vanish. Graphical analysis is performed for all the energies obtained. Also, it is shown in limiting condition [Formula: see text] that the results are compatible with the ones obtained in the general relativity.

Theoretical information measures of a particle in a relativistic scenario of cosmic strings with a rainbow gravity structure

Theoretical information measures of a particle in a relativistic scenario of cosmic strings with a rainbow gravity structure

Massless KG-oscillators in Som-Raychaudhuri cosmic string spacetime in a fine tuned rainbow gravity

A fine tuned rainbow gravity describes both relativistic quantum particles and anti-particles alike. That is, the ratio y=E/EP in the rainbow functions g0(y) and g1(y) should be fine tuned into 0≤y=E/EP≤1⇒y=|E|/EP, otherwise rainbow gravity will only secure Planck's energy scale Ep as the maximal energy for relativistic particles and the anti-particles are left unfortunate (in the sense that their energies will be indefinitely unbounded). Using this fine tuning we discuss the rainbow gravity effect on Klein-Gordon (KG) oscillators in Som-Raychaudhuri cosmic string rainbow gravity spacetime background. We use the rainbow functions: (i) g0(y)=1, g1(y)=1−ϵyn,n=1,2, loop quantum gravity motivated pairs, (ii) g0(y)=g1(y)=(1−ϵy)−1, a horizon problem motivated pair, and (iii) g0(y)=(eϵy−1)/ϵy, g1(y)=1, a gamma-ray bursts motivated pair. We show that the energies obtained using the first two rainbow functions in (i) completely comply with the rainbow gravity model and secure Planck's energy Ep as the maximal energy for both particles and anti-particles. The rainbow function pair in (ii) has no effect on massless KG-oscillators. Whereas, the one in (iii) does not show any eminent tendency towards the Planck's energy as the maximal energy.

Thermal analysis of photon-like particles in rainbow gravity

This work is devoted to study the thermodynamic behavior of photon-like particles within the rainbow gravity formalism. To to do this, we chose two particular ansatzs to accomplish our calculations. First, we consider a dispersion relation which avoids UV divergences, getting a positive effective cosmological constant. We provide numerical analysis for the thermodynamic functions of the system and bounds are estimated. Furthermore, a phase transition is also expected for this model. Second, we consider a dispersion relation employed in the context of Gamma Ray Bursts. Remarkably, for this latter case, the thermodynamic properties are calculated in an analytical manner and they turn out to depend on the harmonic series Hn, gamma Γ(z), polygamma ψn(z) and zeta Riemann functions ζ(z).

Three-dimensional energy-dependent C-metric: Black hole solutions

Considering a three-dimensional C-metric and adding energy-dependent to this spacetime, we first create a three-dimensional energy-dependent C-metric. Then, we extract accelerating BTZ black hole solutions in gravity's rainbow. Besides, we show that (A)dS black holes cover by an event horizon that depends on all the parameters of this theory. Using the definition of Hawking temperature, we obtain the temperature of these black holes and study the effects of various parameters on this quantity. We find a critical radius in which the temperature is always positive (negative) before (after) it. Then, we obtain the entropy of such black holes. Our analysis indicates that there is the same behavior for entropy, similar to the temperature. Indeed, before (after) the critical radius, the entropy is positive (negative). In order to study the local stability of such black holes, we calculate the heat capacity. We find two different behaviors for the heat capacity, which depend on the cosmological energy-dependent constant. As a final result, accelerating AdS BTZ black holes can satisfy the physical condition and local stability at the same time.

Interaction of the DKP particle with the Coulomb-type potential and Aharonov–Bohm potential under the cosmic rainbow gravity

The Duffin–Kemmer–Petiau (DKP) particle with spin 0 interacts with the Aharonov–Bohm (AB) magnetic vector potential and scalar Coulomb-type potential in the cosmic string space–times under the framework of rainbow gravity (RG). By using Bethe–Ansatz method, we obtain the energy eigenvalue and approximate solution to the wave function of the DKP particle with spin 0. We select two sets of rainbow functions and analyze their influence on the energy eigenvalue and wave functions. We find that the energy eigenvalue is determined by the parameters of the rainbow function. It further shows that the rainbow function affects the properties of the space–time where the DKP particle located, and also affects the distribution probability of DKP particles in the space.

Black String Solutions in Rainbow Gravity

In this paper, we studied black string solutions under the consideration of rainbow gravity. We analytically obtained the solution for four-dimensional black strings in terms of the functions f(E/Ep) and g(E/Ep) that sets the energy scale where the rainbow gravity becomes relevant. We also obtained the Hawking temperature for the black string, from which we can see that the rainbow functions play the role of increasing or decreasing the Hawking temperature for a given horizon radius depending on the choice of such rainbow functions. We computed the entropy, specific heat and free energy for the black string. The entropy and specific heat exhibit a rainbow dependence, whereas the free energy is not modified by the rainbow functions. Finally, we studied the effects of rainbow gravity in the orbits of massive and massless particles around a black string. We could verify that neither massive nor massless particles exhibit stable orbits around a black string in the scenario of rainbow gravity for any configuration of rainbow functions.

CLOSED BKS-TYPE UNIVERSES AND DIRAC SPIN EFFECT IN THE RAINBOW GRAVITY

The result related to astrophysical datasets suggest that our universe has recently entered a phase of accelerated expansion. This accelerated expansion is not a situation predicted by the general theory of relativity. Therefore, the emergence of alternative approaches to general relativity has become inevitable. Modifying general relativity and absolute parallelism theory are just two of these theories. In addition, with the discovery of gravitational waves, the need for a view that includes gravitational quantum contributions arose. In this context, rainbow gravity has an approach that also offers quantum contributions to the theory of general relativity and absolute parallelism. In this study, axial vector torsion is calculated for BKS-type universe models using the rainbow gravity formalism. With the calculations made, the vector part and axial vector part components of the torsion tensor are obtained. The spin process, which contributes to the Dirac particles, is also investigated using the rainbow gravitational theory. However, since the obtained axial vector fragment is in time-like form, it is concluded that the spin vector of the Dirac particle is constant. The axial part of the torsion tensor for general BKS-type universe models is calculated and presented in a table for some well-known rainbow functions.

Traversable wormhole models supported by a string cloud in rainbow gravity

The traversable wormholes are fascinating as the shortcuts in space–time. This work discusses the geometry of a traversable wormhole with a string cloud as a source in rainbow gravity. The field equations are developed and solved to obtain the wormhole’s shape function, cloud’s mass density, and string tension. We have calculated the shape function and made it specific to study the dynamics for toy model. Based on the three well-known pairs of rainbow functions (mentioned by Ali and Khalil), the string cloud’s dynamical variables including mass density and string tension are graphically presented. The corresponding energy conditions are also visually depicted. It is found that the source matter (string cloud) of the traversable wormhole must be exotic. However, the positive values of the string tension led to the presence of Casimir and dark energy effects. It is found that the toy model respects the null energy condition for a single pair of rainbow functions, i.e., Rainbow Function Type II. We have concluded that in rainbow gravity theory, the traversable wormhole solutions originating from a string cloud requires the presence of exotic matter to achieve a stable structure.

Pair production in the rainbow dS2 space

The study is devoted to discuss the rate of pair production in a two-dimensional de Sitter (dS2) type manifold with the help of the rainbow gravity formalism and the method of the Bogoliubov transformations. After obtaining exact analytical solutions of the Dirac equation for the selected rainbow metric, we focus on the creation rate of massive spin-1/2 particles.

Thermodynamics of Schwarzschild black hole surrounded by quintessence in gravity's rainbow

According to some quantum gravity models, Lorentz invariance can be violated in the Planck energy scale. With this motivation, we analyze the thermal quantities and the stability of Schwarzschild black hole surrounded by quintessence in gravity's rainbow formalism. To do that, we consider the rainbow functions which are motivated by loop quantum gravity and gamma-ray bursts, and we derive Hawking temperature, specific heat, entropy and the equation of state function. We observe that the presence the quintessence matter field and rainbow gravity affect the stability of the black hole.

Revisiting f(R) gravity's rainbow: Inflation and primordial fluctuations

We study inflation and the generation of primordial fluctuations in f(R) gravity's rainbow. We calculate the cosmological perturbations and then the scalar and tensor primordial power spectrum. We contrast the predictions of the model with the current observational data from PLANCK and BICEP/Keck. Particularly, we found new results for the scalar spectral index ns and the tensor-to-scalar ratio r along with new observational constraints on the rainbow functions.

EFFECTS OF GRAVITY’S RAINBOW ON A RELATIVISTIC SPIN-1 OSCILLATOR

We consider a relativistic spin-1 particle with non-minimal coupling in the context of gravity’s rainbow in the three dimensional background spacetime spanned by static cosmic string. In this context, we acquire an exact solution of the associated spin-1 equation in the modified three dimensional static cosmic string-spanned background spacetime. This relativistic wave equation includes a reducible spinor and this allows us to acquire a non-perturbative expression including the modification functions in the energy domain. In the low energy limit, our results agree well with current literature and provide a basis to discuss the fundamental features of the relativistic spin-1 oscillator. Afterwards, we try to discuss the effects of gravity rainbow functions on the considered spin-1 oscillator in three different scenarios for the modification functions.

Entropy bound and EGUP correction of d-dimensional Reissner–Nordström black hole in rainbow gravity

Inspired by the pronounced effect of gravity’s Rainbow on black hole thermodynamics, entropy relations and bounds have been investigated for [Formula: see text]-dimensional Reissner–Nordström (RN) black hole in the framework of Rainbow gravity. Basic thermodynamic properties of the black hole have been derived for the event horizon and Cauchy horizon. Except for the horizon radius, they all crucially depend on the Rainbow functions. Bounds of the aforesaid thermodynamic quantities have been deduced for both horizons. Analyzing the specific heat capacity, stability conditions have been obtained. Also, the extremal phase of the black hole has been explored. Further, a comparative study has been carried out to distinguish between the effects of Rainbow gravity model parameters on the entropy bound by considering different Rainbow gravity functions. For massless scalar perturbation, quasinormal modes have been computed using modified WKB approach. We have investigated the quantum correction of the black hole in a Rainbow gravity background to obtain the effects of Extended Uncertainty Principle (EUP) and Generalized Uncertainty Principle (GUP) parameters. We have derived the Hawking temperature, specific heat, entropy and remnant masses of the black hole in the Extended General Uncertainty Principle (EGUP) framework, and with the help of graphical methods, we have compared our findings.

PDM KG-Coulomb particles in cosmic string rainbow gravity spacetime and a uniform magnetic field

Klein-Gordon (KG) particles in cosmic string rainbow gravity spacetime and a uniform magnetic field are studied in the context of the so called, effectively speaking, position-dependent mass (PDM) settings. We show that the corresponding KG-equation collapses into a two-dimensional radial Schrödinger-Coulomb like model. The exact textbook solution of which is used to find the energies and wave functions of KG-Coulomb particles (both constant mass and PDM ones). In so doing, we consider, with y=E/EP, four pairs of rainbow functions: (a) g0(y)=1, g1(y)=1−ϵy2, (b) g0(y)=1, g1(y)=1−ϵy, (c) g0(y)=g1(y)=(1−ϵy)−1, and (d) g0(y)=(eϵy−1)/ϵy, g1(y)=1. Interestingly, we observe that the first pair in (a) introduces the Planck energy Ep as a maximum possible KG-particle/antiparticle energy value.

Gravitational waves in f(R, T)-rainbow gravity: even modes and the Huygens principle

In the context of f(R, T)-gravity, propagation of gravitational waves (GWs) for even (or polar) modes is explored by using the Regge-Wheeler gauge in the conformally flat Friedman-Lemaitre-Robertson-Walker type rainbow (CFR) universe. Writing the perturbed field equations for the polar GWs in the CFR spacetime, we first acquire a second-order differential equation for one of the unknown perturbation factors and then get all other unknown perturbation functions. Withal, we reach a conclusion that both the four-velocity vector components except the third one and the corresponding matter distribution are affected by the polar perturbation. Furthermore, the effect of rainbow functions, which can change the geometry of space-time, on the polar GWs is also analyzed graphically. We achieve that the shape (wavelength and amplitude) of polar GWs is dramatically impressed by the alteration of rainbow functions. Lastly, we investigate whether the polar GWs satisfy the Huygens principle.

Wagner's Furious Host

Wagner's Furious Host

Energy‐Dependent Topological Black Holes in Massive Gravity Coupled to Double‐Logarithmic Electrodynamics

AbstractIn this paper, the nonlinear magnetized black holes of massive gravity's rainbow is investigated. In order to achieve this, the double‐logarithmic electromagnetic field is used as a matter source and the new anti‐de Sitter black hole solution is derived. The effects of the massive graviton, rainbow functions, and nonlinearity of the electromagnetic field on the black hole's inner and outer horizons are also studied. The black hole's thermodynamic properties are studied, and the mathematical expressions for temperature, heat capacity, and Gibbs free energy are found. The extended first law and Smarr's formula are derived as well. Using the behavior of thermodynamic quantities as a starting point, the local and global thermodynamic stabilities are also studied.