Conformal transformation route to gravity’s rainbow

Conformal transformation as a mathematical tool has been used in many areas of gravitational physics. In this paper, we consider gravity’s rainbow, in which the metric can be treated as a conformal rescaling of the original metric. By using the conformal transformation technique, we get a specific form of a 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 Einstein gravity’s rainbow can be described by energy-dependent \(f(E,\tilde{R})\) gravity. At last, we study the f(R) gravity, when gravity’s rainbow is considered, which can also be described as energy-dependent \(\tilde{f}(E,\tilde{R})\) gravity.     

Exact Scalar Field Inflationary Solution in Rainbow Universe

Using the Friedmann equation in rainbow Universe, we obtain an exact scalar field Inflationary Solution, which is a modification of the exact scalar field with negative potential −V ₀+m ² φ ²/2. Because the rainbow metric is Finsler metric, the result in this paper implies that the research of Finsler geometry in Cosmology should lead to several new physics theories.     

An Inflationary Solution of Scalar Field in Finsler Universe

Using the energy-dependent rainbow metric, we investigate the rainbow universe metric as a Finsler metric, and obtain an inflationary solution of the universe. The theoretical results are in agreement with the astronomical observations.     

Hawking radiation and black hole entropy in a gravity’s rainbow

In the context of gravity’s rainbow, Planck scale correction on Hawking radiation and black hole entropy in Parikh and Wilczk’s tunneling framework is studied. We calculate the tunneling probability of massless particles in the modified Schwarzschild black holes from gravity’s rainbow. In the tunneling process, when a particle gets across the horizon, the metric fluctuation must be taken into account, not only due to energy conservation but also to spacetime Planck scale effect. Our results show that the emission rate is related to changes of the black hole’s quantum corrected entropies before and after the emission. In the same time, for the modified black holes, a series of correction terms including a logarithmic term to Bekenstein–Hawking entropy are obtained. Correspondingly, the spectrum of Planck scale corrected emission is obtained and it deviates from the thermal spectrum. In addition, a specific form of modified dispersion relation is proposed and applied.     

Mach's Principle and Model for a Broken Symmetric Theory of Gravity

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.     

Quantum gravity effects on spectroscopy of Kerr-Newman black hole in gravity’s rainbow

The effects of quantum gravity on spectroscopy for the charged rotating gravity’s rainbow are investigated in this paper. By utilizing an action invariant obtained from particles tunneling through the event horizon, the entropy and area spectrum for the modified Kerr-Newman black hole are derived. The equally spaced entropy spectrum characteristic of Bekenstein’s original derivation is recovered. And, the entropy spectrum is independent of the energy of the test particles, although the gravity’s rainbow itself is the energy dependent. Such that, the quantum gravity effects of gravity’s rainbow has no influence on the entropy spectrum. On the other hand, due to the spacetime quantum effects, the obtained area spectrum is different from the original Bekenstein spectrum. It is not equidistant and is dependent on the horizon area. And that, by analyzing the area spectrum from a specific rainbow function, a minimum area with a Planck scale is derived for the event horizon. At this point, the area quantum is zero and the black hole radiation stops. Thus, the black hole remnant for the gravity’s rainbow is obtained from the area quantization. In addition, the entropy for the modified Kerr-Newman black hole is calculated and the quantum correction to the area law is obtained and discussed.     

引力彩虹时空中Kerr黑洞的熵谱和面积谱

利用黑洞的绝热不变性,研究了引力彩虹时空中Kerr黑洞的熵谱和面积谱.首先,在引力彩虹时空背景下,计算了Kerr黑洞的绝热不变作用量,并将其与玻尔-索末菲量子化条件相结合,给出了黑洞的熵谱.得到的熵谱没有引力彩虹时空本身具有的粒子能量依赖性,且是与经典Kerr黑洞中原始贝肯斯坦熵谱相同的等间距熵谱.然后,根据黑洞热力学第一定律和黑洞熵谱,给出了与原始贝肯斯坦谱不同的面积谱.该面积谱是非等间距的,而且有对黑洞面积的依赖性,但不依赖于探测粒子的能量.面积谱表明,随着黑洞面积的减少,面积间隔逐步变小;当黑洞达到普朗克尺度时,面积量子可降为零.这表示黑洞面积不再减少,黑洞出现辐射剩余.而在忽略色散关系的修正效应或在大黑洞极限下,面积谱的修正项可以忽略,引力彩虹Kerr黑洞面积谱可以回归到原始贝肯斯坦谱.此外,对引力彩虹时空Kerr黑洞的熵进行了讨论,得到了带有面积倒数修正项的黑洞熵,分析了黑洞熵的量子修正与面积谱量子修正的一致性.     

Radiation Energy Flux and Radiation Power of Schwarzschild Black Hole

Applying the entropy density near the event horizon, we obtained the result that the radiation energy flux of the black hole is always proportional to the quartic of the temperature of its event horizon. That is to say, the thermal radiation of the black hole always satisfies the generalized Stefan–Boltzmann law. The derived generalized Stefan–Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient which is related to the black hole mass, the kinds of radiation particles and space–time metric near the event horizon. In this paper, we have put forward a thermal particle model in curved space–time. By this model, the result has been obtained that when the thin film thickness and the cut-off distance are both fixed, the radiation energy flux received by observer far away from the Schwarzschild black hole is proportional to the average radial effusion velocity of the radiation particles in the thin film, and inversely proportional to the square of the distance between the observer and the black hole.     

Charged Particle’s Tunneling in a Modified Reissner-Nordstrom Black Hole

In the tunneling framework of Hawking radiation, charged particle’s tunneling in the modified Reissner-Nordstrom black hole from gravity’s rainbow is investigated. To this end, following the Schwarzschild solution in gravity’s rainbow, the metric of the modified Reissner-Nordstrom black hole is given. In the tunneling process, the metric fluctuation is taken into account, due to not only the energy conservation and electric charge conservation, but also the spacetime quantum effects. The calculation shows out that the emission rate satisfies the first law of black hole thermodynamics and is consistent with an underlying unitary theory. In addition, it is found that the entropy of the modified black hole is different to the Benkestein-Hawking entropy and the quantum corrections of the entropy appears.     

Extended general relativity: Large-scale antigravity and short-scale gravity with from five-dimensional vacuum

Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we obtain in the framework of the induced matter theory an effective 4D static and spherically symmetric metric which give us ordinary gravitational solutions on small (planetary and astrophysical) scales, but repulsive (anti gravitational) forces on very large (cosmological) scales with ω=−1. Our approach is an unified manner to describe dark energy, dark matter and ordinary matter. We illustrate the theory with two examples, the solar system and the great attractor. From the geometrical point of view, these results follow from the assumption that exists a confining force that make possible that test particles move on a given 4D hypersurface.     

On the origin of cosmic rays and the value of fundamental length

It is suggested that the physical mechanism responsible for the acceleration of cosmic rays is due to the stochastic (or fluctuational) structure of space-time at small distances. A method of introducing fluctuations in a conformally flat Riemannian space-time metric due to ultrahigh energy particles is presented, from which a nonlinear dynamics of particles and equations for the electromagnetic field are obtained. The former admits the acceleration mechanism for cosmic-ray particles and the extreme energy increases during the evolution of the Universe. In our model the energy of the cosmic-ray particle and its radius (the effective Schwarzschild), the age of the universe, and the value of the fundamental length are connected with one another and are determined by a unified formula, Einstein's relation for the relativistic particle energy. It allows one to define experimentally the value of the fundamental length, which is l=1.56×10 ^–33 cm for the maximum proton energy observed in cosmic rays. The problem of the energy spectrum of the cosmic rays and the ratio of intensities of the electron component to the proton component at the same energy level are also discussed.On leave of absence from the Academy of Sciences, Mongolian People's Republic, Ulan-Bator, Mongolia.     

On the motion of particles in covariant Ho?ava-Lifshitz gravity and the meaning of the A-field

We studied the low energy motion of particles in the general covariant version of Ho?ava-Lifshitz gravity proposed by Ho?ava and Melby-Thompson. Using a scalar field coupled to gravity according to the minimal substitution recipe proposed by da Silva and taking the geometrical optics limit, we could write an effective relativistic metric for a general solution. As a result, we discovered that the equivalence principle is not in general recovered at low energies, unless the spatial Laplacian of A vanishes. Finally, we analyzed the motion on the spherical symmetric solution proposed by Ho?ava and Melby-Thompson, where we could find its effective line element and compute spin-0 geodesics. Using standard methods we have shown that such an effective metric cannot reproduce Newton?s gravity law even in the weak gravitational field approximation.     

The collisional Penrose process

Shortly after the discovery of the Kerr metric in 1963, it was realized that a region existed outside of the black hole’s event horizon where no time-like observer could remain stationary. In 1969, Roger Penrose showed that particles within this ergosphere region could possess negative energy, as measured by an observer at infinity. When captured by the horizon, these negative energy particles essentially extract mass and angular momentum from the black hole. While the decay of a single particle within the ergosphere is not a particularly efficient means of energy extraction, the collision of multiple particles can reach arbitrarily high center-of-mass energy in the limit of extremal black hole spin. The resulting particles can escape with high efficiency, potentially serving as a probe of high-energy particle physics as well as general relativity. In this paper, we briefly review the history of the field and highlight a specific astrophysical application of the collisional Penrose process: the potential to enhance annihilation of dark matter particles in the vicinity of a supermassive black hole.     

Delta-Gravity

We present a model of the gravitational field based on two symmetric tensors. The equations of motion of test particles are derived: Massive particles do not follow a geodesic but massless particles trajectories are null geodesics of an effective metric. Outside matter, the predictions of the model coincide exactly with General Relativity, so all classical tests are satisfied. In Cosmology, we get accelerated expansion without a cosmological constant. Additionally, we study the quantization of the model. The main result being that the Effective Action is finite and receives one loop corrections only.     

Exact relativistic models of conformastatic charged dust thick disks

We construct relativistic models of charged dust thick disks for a particular conformastatic spacetime through a Miyamoto–Nagai transformation used in Newtonian gravity to model disk like galaxies. Two simple families of thick disk models and a family of thick annular disks based on the field of an extreme Reissner–Nordström black hole and a Morgan–Morgan-like metric are considered. The electrogeodesic motion of test particles around the structures are analyzed. Also the stability of the particles against radial perturbation is studied using an extension of the Rayleigh criteria of stability of a fluid in rest in a gravitational field. The models built satisfy all the energy conditions.     

Cosmological Model Universe Consisting of Two Forms of Dark Energy

Considering a spatially flat FRW metric we obtain a model universe consisting partly of quintessence form of dark energy and partly of cosmological constant form of dark energy; and after studying their physical,dynamical and kinematical properties it is found that our model is a new and viable form of model universe containing dark energy.     

Quantum corrections to the spacetime metric from geometric phase space quantization

We consider the possibility that the physical spacetime of a quantum particle may be regarded as a four-dimensional hypersurface locally embedded in eightdimensional phase space. We show that, as a consequence, accelerated particles are seen to live in a curved spacetime, and, in the particular case of uniform acceleration, we are led to a generalization of the Rindler metric which implies, for a uniformly accelerated particle, a discrete energy spectrum.     

Geometric Conditions on the Type of Matter Determining the Flat Behavior of the Rotational Curves in Galaxies

In an arbitrary axisymmetric stationary spacetime, we determine the expression for the tangential velocity of test objects following a circular stable geodesic motion in the equatorial plane, as function of the metric coefficients. Next, we impose the condition, observed in large samples of disks galaxies, that the magnitude of such tangential velocity be radii independent in the dark matter dominated region, obtaining a constraint equation among the metric coefficients, and thus arriving to an iff (iff means: if and only if.) condition: The tangential velocity of test particles is radii independent iff the metric coefficients satisfied the mentioned constraint equation. Furthermore, for the static case, the constraint equation can be easily integrated, leaving the spacetime at the equatorial plane essentially with only one independent metric coefficient. With the geometry thus fixed, we compute the Einstein tensor and equate it to an arbitrary stress energy tensor, in order to determine the type of energy-matter which could produce such a geometry. Within an approximation, we deduce a constraint equation among the components of the stress energy tensor. We test in that constraint equation several well known types of matter, which have been proposed as dark matter candidates and are able to point for possible right ones. Finally, we also present the spherically symmetric static case and apply the mentioned procedure to perfect fluid stress energy tensor, recovering the Newtonian result as well as the one obtained in the axisymmetric case. We also present arguments on the need to use GR to study types of matter different than the dust one.     

Holographic Ricci Dark Energy Model with Non-constant c 2 Term

In this paper, we study holographic Ricci dark energy model with non-constant c ² term in dark energy density formula. We consider FRW metric in flat space-time and calculate density. Also we find scale factor and Hubble expansion parameter.     

Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.