In this paper, we will analyze the gravitational collapse in the framework of gravity's rainbow. We will demonstrate that the position of the horizon for a particle inside the black hole depends on the energy of that particle. It will also be observe that the position of the horizon for a particle falling radially into the black hole also depends on its energy. Thus, it is possible for a particle coming from outside to interact with a particle inside the black, and take some information outside the black hole. This is because for both these particles the position of horizon is different. So, even though the particle from inside the black hole is in its own horizon, it is not in the horizon of the particle coming from outside. Thus, we will demonstrate that in gravity's rainbow information can get out of a black hole.
In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's rainbow. This will be done using the rainbow functions which are motivated from the results obtained in loop quantum gravity approach and non-commutative geometry. We will investigate the Gravitational collapse in this Galileon gravity's rainbow. We will discuss the behavior of singularities formed from the gravitational collapse in this rainbow deformed Galileon gravity.
In this paper, we will analyze the energy dependent deformation of massive gravity using the formalism of massive gravity's rainbow. So, we will use the Vainshtein mechanism and the dRGT mechanism for the energy dependent massive gravity, and thus analyze a ghost free theory of massive gravity's rainbow. We study the energy dependence of a time-dependent geometry, by analyzing the radiating Vaidya solution in this theory of massive gravity's rainbow. The energy dependent deformation of this Vaidya metric will be performed using suitable rainbow functions.
In this paper, we investigate the thermodynamic properties of black holes under the influence of rainbow gravity. In the metric of Schwarzschild, Reissner-Nordstrom and Reissner-Nordstrom-de-Sitter black hole surrounded by quintessence, we consider a rainbow function and derive the existence of remnant and critical masses of a black hole. Using the Hawking temperature relation we derive the heat capacity and the entropy of the rainbow gravity inspired black holes and closely study the relation between entropy and area of the horizon for different values of n of the rainbow function.
A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented.
Conformal transformation as a mathematical tool has been used in many areas of gravitational physics. In this paper, we would consider the gravity's rainbow, in which the metric could be treated as a conformal rescaling of the original metric. By using the conformal transformation technique, we get a specific form of modified Newton's constant and cosmological constant in gravity's rainbow, which implies that the total vacuum energy is dependent on probe energy. Moreover, the result shows that the Einstein gravity's rainbow could be described by an energy-dependent $f(E,\tilde R)$ gravity. At …
In this paper, we will generalize the Gauss-Bonnet gravity to an energy dependent Gauss-Bonnet theory of gravity, which we shall call as the Gauss-Bonnet gravity's rainbow. We will also couple this theory to a Maxwell's theory. We will analyze black hole solutions in this energy dependent Gauss-Bonnet gravity's rainbow. We will calculate the modifications to the thermodynamics of black holes in the Gauss-Bonnet's gravity's rainbow. We will demonstrate that even though the thermodynamics of the black holes get modified in the Gauss-Bonnet gravity's rainbow, the first law of thermodynamics still…
In this paper, by utilizing the rainbow functions that were proposed by Amelino-Camelia \emph{et al}., the information flux of rainbow Schwarzschild black hole and the sparsity of Hawking radiation in rainbow gravity are explored. The results show that the rainbow gravity has a very significant effect on the information flux. When the mass of rainbow Schwarzschild black hole approaches to the order of Planck scale, the Bekenstein entropy loss per emitted quanta in terms of the mass of Schwarzschild black hole reduces to zero. Furthermore, we also find the sparsity of Hawking radiation in rainb…
According to Verlinde's recent proposal, the gravity is originally an entropic force. In this work, we obtain the corrections to the entropy-area law of black holes within rainbow gravity. The corrected entropy-area law leads to the modifications of the number of bits $N$. Inspired by Verlinde's argument on the entropic force, and using the modified number of bits, we can investigate the effects of rainbow gravity on the modified Newtonian dynamics, Newton's law of gravitation, and Einstein's general relativity in entropic force approach.
In this letter, using the rainbow functions that were proposed by Magueijo and Smolin, we investigate the thermodynamics and the phase transition of rainbow Schwarzschild black hole. First, we calculate the rainbow gravity corrected Hawking temperature. From this modification, we then derive the local temperature, free energy, and other thermodynamic quantities in an isothermal cavity. Finally, we analyze the critical behavior, thermodynamic stability, and phase transition of the rainbow Schwarzschild black hole. The results show that the rainbow gravity can stop the Hawking radiation in the f…
We do a detailed study of the thermodynamics of black holes in Rainbow gravity in the framework of the Kiselev metric, taking into account different cosmic fluids which can mimic several kinds of dark energy scenarios. A discussion related to the appearance of black hole remnants is presented and, unlike other studies on the same topic, we found no evidence of the appearance of remnants in Rainbow gravity, except in peculiar cases.
In this paper we study the geodesic structure of the Schwarzschild black hole in rainbow gravity analyzing the behavior of null and time-like geodesic. We find that the structure of the geodesics essentially does not change when the semi-classical effects are included. However, we can distinguish different scenarios if we take into account the effects of rainbow gravity. Depending on the type of rainbow functions under consideration, inertial and external observers see very different situations in radial and non radial motion of a test particles.
In this letter, we analyze the modification to the thermodynamics of a Schwarzchild black hole and a Kerr black hole due to gravity's rainbow. The metric for these black holes will be made energy dependent. This will be done by using rainbow functions motivated from the hard spectra from gamma-ray bursters at cosmological distances. This modification of the metric by these rainbow functions will in turn modify the temperature and entropy of these black holes. We will also discuss how this effects the formation of virtual black holes.
We analyze the electrostatic self-energy of a point like electrically charged particle induced by a cosmic string in the context of gravity's rainbow, as well the electrostatic self-force on this particle. The possibility of the solution associated with a charged particle to be altered by modifications in dispersion relations of the space-time is discussed. We show that the self-energy depends on the rainbow functions and that this quantity can either increase or decrease depending on the rainbow function chosen, as compared with analogous result in the framework of general relativity. With re…
We consider the effects of Gravity's Rainbow on the computation of black hole entropy using a dynamical brick wall model. An explicit dependence of the radial coordinate approaching the horizon is proposed to analyze the behavior of the divergence. We find that, due to the modification of the density of states, the brick wall can be eliminated. The calculation is extended to include rotations and in particular to a Kerr black hole in a comoving frame.
We consider the effects of Gravity's Rainbow on the self-sustained equation which is responsible to find new traversable wormholes configurations powered by their own gravitational quantum fluctuations. The form of the shape function considered is obtained by imposing the equation of state $p_{r}=ωρ$. We investigate the size of the wormhole as a function of the parameter $ω$ in the phantom region. We discover that a wormhole which is traversable in principle, but not in practice, can be produced.
In this note we study an energy dependent deformation of a time dependent geometry in the background of Brans-Dicke gravity theory. The study is performed using the gravity's rainbow formalism. We compute the field equations in Brans-Dicke gravity's rainbow using Vaidya metric which is a time dependent geometry. We study a star collapsing under such conditions. Our prime objective is to determine the nature of singularity formed as a result of gravitational collapse and its strength. The idea is to test the validity of the cosmic censorship hypothesis for our model. We have also studied the ef…
In this paper, we proposed that at each point of spacetime, in addition to the Riemannian metric tensor which describes the geometry of spacetime and the gravitational field, there is an rainbow metric tensor which shows the geometry of spacetime depends on the energy of the test particle. Because Eddington-inspired Born-Infield(EiBI) gravity can be seen as a special bi-metric gravity, we research a varying speed of light theory for a bi-metric gravity corresponding to EiBI gravity. For FRW universe, we find the energy of test particle will increase with rising energy density of universe. We a…
Motivated by the violation of Lorentz invariancy in quantum gravity, we study black hole solutions in gravity's rainbow in context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered with an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally, we investigate thermal st…
We study the thermodynamics of modified black holes proposed in the context of gravity's rainbow. A notion of intrinsic temperature and entropy for these black holes is introduced. In particular for a specific class of modified Schwarzschild solutions, their temperature and entropy are obtained and compared with those previously obtained from modified dispersion relations in deformed special relativity. It turns out that the results of these two different strategies coincide, and this may be viewed as a support for the proposal of deformed equivalence principle.
In the context of gravity's rainbow, we study the deformed Starobinsky model in which the deformations take the form $f(R)\sim R^{2(1-α)}$, with $R$ the Ricci scalar and $α$ a positive parameter. We show that the spectral index of curvature perturbation and the tensor-to-scalar ratio can be written in terms of $N,\,λ$ and $α$, with $N$ being the number of {\it e}-foldings, $λ$ a rainbow parameter. We compare the predictions of our models with Planck data. With the sizeable number of {\it e}-foldings and proper choices of parameters, we discover that the predictions of the model are in excellen…
Quantum evolution of a scalar field's modes propagating on quantum spacetime of a collapsing homogeneous dust ball is written effectively, as an evolution of the same quantum modes on a (semiclassical) dressed geometry. When the backreaction of the field is discarded, the classical spacetime singularity is resolved due to quantum gravity effects and is replaced by a quantum bounce on the dressed collapse background. In the presence of backreaction, the emergent (interior) dressed geometry becomes mode dependent and the energy density associated with the backreaction of each mode scales as a ra…
Recently, O.B.Zaslavskii considers the collision near the horizon of the extremal Kerr black hole that produces two particles and one of two particles has divergent conserved killing energy(the so called super Penrose process). O.B.Zaslavskii shows this particle can not move in a asymptotic region in this universe. This means super Penrose process for extremal Kerr black hole is impossible. However, recently, Mandar Patil and Tomohiro Harada show this particle can enter event horizon, turns back and emerges through white hole event horizon into asymptotic region in other universe. This means s…
We obtain a (5+1)-dimensional global flat embedding of modified Schwarzschild black hole in rainbow gravity. We show that local free-fall temperature in rainbow gravity, which depends on different energy $ω$ of a test particle, is finite at the event horizon for a freely falling observer, while local temperature is divergent at the event horizon for a fiducial observer. Moreover, these temperatures in rainbow gravity satisfy similar relations to those of the Schwarzschild black hole except overall factor $g(ω)$, which plays a key role of rainbow functions in this embedding approach.
In this paper, we will analyze a five-dimensional Yang-Mills black hole solution in massive gravity's rainbow. We will also investigate the flow of such a solution with scale. Then, we will discuss the scale dependence of the thermodynamics for this black hole. Also, we study the criticality in the extended phase space by treating the cosmological constant as the thermodynamics pressure of this black hole solution. Moreover, we will use the partition function for this solution to obtaining corrections to the thermodynamics of this system and examine their key role on the behavior of corrected …
In this paper, the thermodynamic property of charged AdS black holes is studied in rainbow gravity. By the Heisenberg Uncertainty Principle and the modified dispersion relation, we obtain deformed temperature. Moreover, in rainbow gravity we calculate the heat capacity in a fixed charge and discuss the thermal stability. We also obtain a similar behaviour with the liquid-gas system in extending phase space (including \(P\) and \(r\)) and study its critical behavior with the pressure given by the cosmological constant and with a fixed black hole charge \(Q\). Furthermore, we study the Gibbs fun…
Motivated by the wide applications of BTZ black holes and interesting results of gravity's rainbow, we consider three dimensional rainbow solutions and investigate their thermodynamic properties. In addition to investigate black holes thermodynamics related to AdS/CFT correspondence, one may regard gravity's rainbow to to encode quantum gravity effects into the black hole solutions. We take into account the various models of linear and nonlinear electrodynamics and study their effects on the gravity's rainbow spacetime. We also examine thermal stability and find that obtained three dimensional…
In this paper, we investigate the thermodynamic properties of Reissner-Nordström black holes embedded in higher $(d)$ dimensions in the framework of rainbow gravity incorporating the effects of the generalized uncertainty principle. We also examine all the properties graphically by varying the rainbow gravity parameter $η$ and the generalized uncertainty principle parameter $α$. We find the existence of remnant and critical mass of the concerned black hole. We calculate the local temperature, local internal energy and hence we analyse the thermal stability of the black hole by computing the lo…
In this paper, we consider three-dimensional massive gravity's rainbow and obtain black hole solutions in three different cases of Born-Infeld, logarithmic, and exponential theories of nonlinear electrodynamics. We discuss the horizon structure and geometrical properties. Then, we study thermodynamics of these models by considering the first-order quantum correction effects, which appears as a logarithmic term in the black hole entropy. We discuss such effects on the black hole stability and phase transitions. We find that, due to the quantum corrections, the second-order phase transition happ…
Following an earlier study regarding Gauss-Bonnet-Maxwell black holes in the presence of gravity's rainbow [S. H. Hendi and M. Faizal, Phys. Rev. D 92, 044027 (2015)], in this paper, we will consider all constants as energy dependent ones. The geometrical and thermodynamical properties of this generalization are studied and the validation of the first law of thermodynamics is examined. Next, through the use of proportionality between cosmological constant and thermodynamical pressure, van der Waals-like behavior of these black holes in extended phase space is investigated. An interesting criti…
In this paper, we investigate the thermodynamic properties of the RN-AdS black hole with cloud of strings and quintessence in rainbow gravity with the stationary (ST) orthonormal frame and the free-fall (FF) orthonormal frame. After the SF and the FF rainbow metric is obtained, we get the Hawking temperature and the entropy, and their physical meanings are discussed. We find that, for the ST rainbow RN-AdS black hole with cloud of strings and quintessence, the effect of rainbow gravity is to increase the Hawking temperature but decrease the entropy of the black hole. However, for the FF rainbo…
In the context of a gravity's rainbow, the asymptotic quasinormal modes of the scalar perturbation in the quantum modified Schwarzschild black holes are investigated. By using the monodromy method, we calculated and obtained the asymptotic quasinormal frequencies, which are dominated not only by the mass parameter of the spacetime, but also by the energy functions from the modified dispersion relations. However, the real parts of the asymptotic quasinormal modes is still $T_H\ln 3$, which is consistent with Hod's conjecture. In addition, for the quantum corrected black hole, the area spacing i…
In this paper we study black string solutions under the consideration of rainbow gravity. We have analytically obtained the solution for four-dimensional black strings in terms of the functions $f(E/E_p)$ and $g(E/E_p)$ that sets the energy scale where the rainbow gravity becomes relevant. We have also obtained the Hawking temperature for the black string, from which we could 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 have computed the entropy, specific heat an…
We investigate the connection between Gravity's Rainbow and Horava-Lifshitz gravity, since both theories incorporate a modification in the UltraViolet regime which improves their quantum behavior at the cost of the Lorentz invariance loss. In particular, extracting the Wheeler-De Witt equations of the two theories in the case of Friedmann-Lemaitre-Robertson-Walker and spherically symmetric geometries, we establish a correspondence that bridges them.
In this paper, we study the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow. For this study, we consider that the background metric is Vaidya spacetime in massive gravity's rainbow. We show that the k-essence emergent gravity metric resembles closely to the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse where we consider the k-essence scalar field as a function solely of the advanced or the retarded time. The k-essence emergent Vaidya massive gravity rainbow mass function is…
In this work, we study the $f(R)$ models of inflation in the context of gravity's rainbow theory. We choose three types of $f(R)$ models: $f(R)=R+α(R/M)^{n},\,f(R)=R+αR^{2}+βR^{2}\log(R/M^{2})$ and the Einstein-Hu-Sawicki model with $n,\,α,\,β$ being arbitrary real constants. Here $R$ and $M$ are the Ricci scalar and mass scale, respectively. For all models, the rainbow function is written in the power-law form of the Hubble parameter. We present a detailed derivation of the spectral index of curvature perturbation and the tensor-to-scalar ratio and compare the predictions of our results with …
We explore a scenario of the general relativity determined by the framework of the rainbow gravity with the purpose of searching for analogues of the Aharonov-Bohm effect. By focusing on the confinement of the Dirac field and the scalar field to a hard-wall confining potential in a modified background of the cosmic string spacetime, we examine the effects of the rainbow gravity and the topology of the cosmic string spacetime. Then, we compare each spectrum of energy with the cases where the rainbow gravity is absent.
In this paper, we study the various cylindrical solutions (cosmic strings) in gravity's rainbow scenario. In particular, we calculate the gravitational field equations corresponding to energy-dependent background. Further, we discuss the possible Kasner, quasi-Kasner and non-Kasner exact solutions of the field equations. In this framework, we find that quasi-Kasner solutions can not be realized in gravity's rainbow. Assuming only time-dependent metric functions, we also analyse the time-dependent vacuum cosmic strings in gravity's rainbow, which are completely different than the other GR solut…
We present commutation relations depending on the rainbow functions which are slightly different from the well-known results. However, the advantage of these new commutation relations are compatible with the calculation of the Hawking temperature in the rainbow Schwarzschild black hole.
In this paper, we extend Joule-Thomson expansion to the low-dimensional regime in rainbow gravity by considering the rainbow rotating BTZ metric in the (2+1)-dimensional spacetime. After the metric of the black hole is obtained, we get the Joule-Thomson expansion of the black hole, including the Joule-Thomson coefficient, inversion curves, and isenthalpic curves. We find that a rainbow rotating BTZ black hole does not have $P-V$ critical behavior. The effects of rainbow gravity are to slow down the trend of the increase of the Joule-Thomson coefficient and make its zero point larger. Moreover,…
Planck scale corrections arising from deformed special relativity on Hawking radiation in Parikh and Wilczk's tunneling framework are studied. We calculate the emission rate of massless particles tunneling though the corrected horizon of modified black holes from gravity's rainbow. In the tunneling process, when a particle get across the quantum horizon, the metric fluctuation not only due to the energy conservation but also quantum effects of the space-time are taken into account. Our results show that, the emission rate is related to the changes of the black hole's quantum corrected entropy …
In this paper, we investigate the thermodynamic properties of black holes in the framework of rainbow gravity. By considering rainbow functions in the metric of Schwarzschild and Reissner-Nordström black holes, remnant and critical masses are found to exist. Demanding the universality of logarithmic corrections to the semi-classical area law for the entropy leads to constraining the form of the rainbow functions. The mass output and the radiation rate for these constrained form of rainbow functions have been computed for different values of the rainbow parameter $η$ and have striking similarit…
The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. One of these contexts is the gravity's rainbow formalism. We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativit…
In this work, we construct a new kind of rainbow functions, which has generalized uncertainty principle parameter. Then, we investigate modified thermodynamic quantities and phase transition of rainbow Schwarzschild black hole by employing this new kind of rainbow functions. Our results demonstrate that the rainbow gravity and generalized uncertainty principle have a great effect on the picture of Hawking radiation. They prevent black holes from total evaporation and cause a remnant. In addition, after analyzing the modified local thermodynamic quantities, we find that the effect of rainbow gr…
In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the rainbow gravity. Firstly, we focus on the non-relativistic regime by solving the corresponding Schrödinger equation, following by a complete relativistic treatment of the problem in which we considered the Klein-Gordon equation. In both cases we find exact expressions for the Landau levels in terms of the rainbow functions, used to characterize a rainbow gra…
Klein-Gordon oscillators in traversable wormhole rainbow gravity spacetime: Conditional exact solvability via a throat radius and oscillator frequency correlation
