Evolution of primordial black holes in a radiation and phantom energy environment

In this work we extend previous work on the evolution of a primordial black hole (PBH) to address the presence of a dark energy component with a super-negative equation of state as a background, investigating the competition between the radiation accretion, the Hawking evaporation and the phantom accretion, the latter two causing a decrease on black hole mass. It is found that there is an instant during the matter-dominated era after which the radiation accretion becomes negligible compared to the phantom accretion. The Hawking evaporation may become important again depending on a mass threshold. The evaporation of PBHs is quite modified at late times by these effects, but only if the generalized second law of thermodynamics is violated.     

Phantom energy accretion and primordial black holes evolution in Brans–Dicke theory

In this work, we study the evolution of primordial black holes within the context of Brans–Dicke theory by considering the presence of a dark energy component with a super-negative equation of state, called phantom energy, as a background. Besides Hawking evaporation, here we consider two types of accretion—radiation accretion and phantom energy accretion. We found that radiation accretion increases the lifetime of primordial black holes whereas phantom accretion decreases the lifespan of primordial black holes. Investigating the competition between the radiation accretion and phantom accretion, we found that there is an instant during the matter-dominated era beyond which phantom accretion dominates radiation accretion. So the primordial black holes which are formed in the later part of radiation-dominated era and in matter-dominated era are evaporated at a quicker rate than by Hawking evaporation. But for presently evaporating primordial black holes, radiation accretion and Hawking evaporation terms are dominant over the phantom accretion term and hence presently evaporating primordial black holes are not much affected by phantom accretion.     

Accretion,primordial black holes and standard cosmology

Primordial black holes evaporate due to Hawking radiation. We find that the evaporation times of primordial black holes increase when accretion of radiation is included. Thus, depending on accretion efficiency, more primordial black holes are existing today, which strengthens the conjecture that the primordial black holes are the proper candidates for dark matter.     

The Evolution of Primordial Black Hole Masses in the Radiation-Dominated Era

We discuss in this work the behaviour of primordial black holes (PBHs) in the radiation era. Taking into account the Hawking evaporation and the absorption of energy we revisit the complete differential equation for the evolution of the mass of a PBH. We show that the mass can grow in this cosmological phase in a very slow fashion (even when considering the very high temperature of the radiation) if at all, and give a strong upper limit to the maximum accretion of mass. We evaluate relativistic effects due to the peculiar motion relative to the CMBR and show that the existence of relativistic black holes with very high mass absorption is highly unlikely. Finally we demonstrate that thermodynamic equilibrium between black holes and the cosmic radiation can not exist for finite times, and therefore initially non-evaporating PBHs must jump to the evaporating regime. This analysis supports the several efforts performed to look for signatures of evaporating holes.     

Primordial braneworld black holes: Significant enhancement of lifetimes through accretion

The Randall-Sundrum (RS-II) braneworld cosmological model with a fraction of the total energy density in primordial black holes is considered. Due to their 5d geometry, these black holes undergo modified Hawking evaporation. It is shown that during the high-energy regime, accretion from the surrounding radiation bath is dominant compared to evaporation. This effect increases the mass of the black holes till the onset of matter (or black hole) domination of the total energy density. Thus black holes with even very small initial masses could survive till several cosmologically interesting eras.     

Primordial black holes in phantom cosmology

We investigate the effects of accretion of phantom energy onto primordial black holes. Since Hawking radiation and phantom energy accretion contribute to a decrease of the mass of the black hole, the primordial black hole that would be expected to decay now due to the Hawking process would decay earlier due to the inclusion of the phantom energy. Equivalently, to have the primordial black hole decay now it would have to be more massive initially. We find that the effect of the phantom energy is substantial and the black holes decaying now would be much more massive—over ten orders of magnitude! This effect will be relevant for determining the time of production and hence the number of evaporating black holes expected in a universe accelerating due to phantom energy.     

Baryon production by primordial black holes

The evaporation of primordial black holes (PBH's) by the Hawking process can produce an excess of baryons over anti-baryons. Assuming a power-law form of the initial mass spectrum of PBH's and taking into account the observational constraints on that spectrum we calculate the baryon excess produced. We find that if the spectrum is steep ($\text{α?3.5}$) or cut off for masses above ～ 10⁹ g, the observed baryon/photon ratio of ～ 10^?9 can be produced by PBH evaporations.     

A New Proposal for Galactic Dark Matter: Effect of f(T) Gravity

It is still a challenging problem to the theoretical physicists to know the exact nature of the galactic dark matter which causes the galactic rotational velocity to be more or less a constant. We have proposed that the dark matter as an effect of f(T) gravity. Assuming the flat rotation curves as input we have shown that f(T) gravity can explain galactic dynamics. Here, we don’t have to introduce dark matter. Spacetime metric inspired by f(T) gravity describes the region up to which the tangential velocity of the test particle is constant. This inherent property appears to be enough to produce stable circular orbits as well as attractive gravity.     

Gauss-bonnet black holes and possibilities for their experimental search

Corollaries of gravity models with second-order curvature corrections in the form of a Gauss-Bonnet term and possibilities (or impossibilities) for their experimental search or observations are discussed. The full version of the four-dimensional Schwarzschild-Gauss-Bonnet black hole solution and the constraint on the possible minimal black hole mass following from this model are considered. Using our solution as a model for the final stages of Hawking evaporation of black holes with a low initial mass (up to 10¹⁵ g) whose lifetime is comparable to that of our Universe, we have revealed differences in the patterns of evaporation: we have obtained high values of the emitted energy and showed the impossibility of an experimental search for primordial black holes by their evaporation products. Scenarios for the evaporation of Gauss-Bonnet black holes in multidimensional gravity models and possibilities for their experimental search are also discussed.     

Effect of vacuum energy on evolution of primordial black holes in Einstein gravity

We study the evolution of primordial black holes by considering present universe is no more matter dominated rather vacuum energy dominated. We also consider the accretion of radiation, matter and vacuum energy during respective dominance period. In this scenario, we found that radiation accretion efficiency should be less than 0.366 and accretion rate is much larger than previous analysis by Nayak et al. (2009) [1]. Thus here primordial black holes live longer than previous works Nayak and Singh (2011) [1]. Again matter accretion slightly increases the mass and lifetime of primordial black holes. However, the vacuum energy accretion is slightly complicated one, where accretion is possible only up to a critical time. If a primordial black hole lives beyond critical time, then its? lifespan increases due to vacuum energy accretion. But for presently evaporating primordial black holes, critical time comes much later than their evaporating time and thus vacuum energy could not affect those primordial black holes.     

Domination of black hole accretion in brane cosmology

We consider the evolution of primordial black holes formed during the high energy phase of the braneworld scenario. We show that the effect of accretion from the surrounding radiation bath is dominant compared to evaporation for such black holes. This feature lasts till the onset of matter (or black hole) domination of the total energy density which could occur either in the high energy phase or later. We find that the black hole evaporation times could be significantly large even for black holes with small initial mass to survive until several cosmologically interesting eras.     

Late-time cosmological approach in mimetic <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

In this paper, we investigate the late-time cosmic acceleration in mimetic f(R, T) gravity with the Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations the main equation that can describe the cosmological evolution. Then, with several models from \(\mathcal {Q}(z)\) and the well-known particular model f(R, T), we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and in each case we compare the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic f(R, T) gravity. The results obtained are in good agreement with the observational data and show that in the presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped.     

Charged Fermions Tunnel from the Kerr-Newman Black Hole Influenced by Quantum Gravity Effects

Taking into account quantum gravity effects, we investigate the tunnelling radiation of charged fermions in the Kerr-Newman black hole. The result shows that the corrected Hawking temperature is determined not only by the parameters of the black hole, but also by the energy, angular momentum and mass of the emitted fermion. Meanwhile, an interesting found is that the temperature is affected by the angle ??. The quantum gravity correction slows down the evaporation.     

Fermions Tunnelling with Quantum Gravity Correction

Based on the generalized uncertainty principle (GUP), we investigate the correction of quantum gravity to Hawking radiation of black hole by utilizing the tunnelling method. The result tells us that the quantum gravity correction retards the evaporation of black hole. Using the corrected covariant Dirac equation in curved spacetime, we study the tunnelling process of fermions in Schwarzschild spacetime and obtain the corrected Hawking temperature. It turns out that the correction depends not only on the mass of black hole but also on the mass of emitted fermions. In our calculation, the quantum gravity correction slows down the increase of Hawking temperature during the radiation explicitly. This correction leads to the remnants of black hole and avoids the evaporation singularity.     

Accretion of radiation and rotating primordial black holes

We consider rotating primordial black holes (PBHs) and study the effect of accretion of radiation in the radiation-dominated era. The central part of our analysis deals with the role of the angular momentum parameter on the evolution of PBHs. We find that both the accretion and evaporation rates decrease with an increase in the angular momentum parameter, but the rate of evaporation decreases more rapidly than the rate of accretion. This shows that the evaporation time of PBHs is prolonged with an increase in the angular momentum parameter. We also note that the lifetime of rotating PBHs increases with an increase in the accretion efficiency of radiation as in the case of nonrotating PBHs.     

Violation of causality in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

In the standard formulation, the f(T) field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. Actually, even locally violation of causality can occur in this formulation of f(T) gravity. A locally Lorentz covariant f(T) gravity theory has been devised recently, and this local causality problem seems to have been overcome. The non-locality question, however, is left open. If gravitation is to be described by this covariant f(T) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality on non-local scale. Here, to look into the potentialities and difficulties of the covariant f(T) theories, we examine whether they admit Gödel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Gödel-type solution, which contains special solutions in which the essential parameter of Gödel-type geometries, \(m^2\), defines any class of homogeneous Gödel-type geometries. We show that solutions of the trigonometric and linear classes (\(m^2 < 0\) and \(m=0\)) are permitted only for the combined matter sources with an electromagnetic field matter component. We extended to the context of covariant f(T) gravity a theorem which ensures that any perfect-fluid homogeneous Gödel-type solution defines the same set of Gödel tetrads \(h_A^{~\mu }\) up to a Lorentz transformation. We also showed that the single massless scalar field generates Gödel-type solution with no closed time-like curves. Even though the covariant f(T) gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Gödel-type solutions makes apparent that the covariant formulation of f(T) gravity does not preclude non-local violation of causality in the form of closed time-like curves.     

The simplest non-minimal matter–geometry coupling in the <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) cosmology

f(R, T) gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar R and the trace of the energy-momentum tensor T. In this way, f(R, T) models are capable of describing a non-minimal coupling between geometry (through terms in R) and matter (through terms in T). In this article we construct a cosmological model from the simplest non-minimal matter–geometry coupling within the f(R, T) gravity formalism, by means of an effective energy-momentum tensor, given by the sum of the usual matter energy-momentum tensor with a dark energy contribution, with the latter coming from the matter–geometry coupling terms. We apply the energy conditions to our solutions in order to obtain a range of values for the free parameters of the model which yield a healthy and well-behaved scenario. For some values of the free parameters which are submissive to the energy conditions application, it is possible to predict a transition from a decelerated period of the expansion of the universe to a period of acceleration (dark energy era). We also propose further applications of this particular case of the f(R, T) formalism in order to check its reliability in other fields, rather than cosmology.     

Wormhole Geometries in f(R,T) Gravity

We study wormhole solutions in the framework of f(R,T) gravity where R is the scalar curvature, and T is the trace of the stress-energy tensor of the matter. We have obtained the shape function of the wormhole by specifying an equation of state for the matter field and imposing the flaring out condition at the throat. We show that in this modified gravity scenario, the matter threading the wormhole may satisfy the energy conditions, so it is the effective stress-energy that is responsible for violation of the null energy condition.     

Pilgrim dark energy in f(T) gravity

We discuss the interacting f(T) gravity with pressureless matter in an FRW spacetime. We construct an f(T) model by following the correspondence scheme incorporating a recently developed pilgrim dark energy model and taking the Hubble horizon as the IR cutoff. We use constructed model to discuss the evolution trajectories of the equation-of-state parameter, the ω _T -ω′ _T phase plane, and state-finder parameters in the evolving universe. It is found that the equation-of-state parameter gives a phantom era of the accelerated universe for some particular range of the pilgrim parameter. The ω _T -ω′ _T plane represents freezing regions only for an interacting framework, while the ΛCDM limit is attained in the state-finder plane. We also investigate the first and second laws of thermodynamics assuming equal temperatures at and inside the horizon in this scenario. Due to the violation of the first law of thermodynamics in f(T) gravity, we explore the behavior of the entropy production term. The validity of a generalized second law of thermodynamics depends on the present-day value of the Hubble parameter.     

Birkhoff’s theorem in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

Generalized from the so-called teleparallel gravity, which is exactly equivalent to general relativity, f(T) gravity has been proposed as an alternative gravity model to account for the dark energy phenomena. In this letter we prove that the external vacuum gravitational field for a spherically symmetric distribution of source matter in the f(T) gravity framework must be static. The conclusion is independent of the radial distribution and spherically symmetric motion of the source matter, that is, whether it is in motion or static. As a consequence, the Birkhoff’s theorem is valid in the general nonsingular f(T) theory at the un-perturbative level. We also discuss its application in the de Sitter spacetime evolution phase as preferred by present dark energy observations.