General Relativity And Quantum Cosmology

In this paper, we have used the extended generalized uncertainty principle to investigate the Unruh temperature and thermodynamic properties of a black hole. We started with a brief perusal of the Heisenberg uncertainty principle and continue with some physical and mathematical discussion for obtaining the generalized and the extended generalized uncertainty principle. Then, we obtained the Unruh temperature, mass-temperature, specific heat, and entropy functions of a black hole. We enriched the paper with graphical analysis as well as their comparisons.

In this work we have obtained a charged black hole solution in the presence of perfect fluid dark matter (PFDM) and discuss its energy conditions. The metric corresponding to the rotating avatar of this black hole solution is obtained by incorporating the Newman-Janis algorithm. We then compute two types of circular geodesics, namely, the null geodesics and time-like geodesics for this rotating spacetime geometry. For the case of time-like geodesics, we consider both neutral as well as charged massive particles. The effective potentials of the corresponding circular geodesics has also been studied. We then present our results by graphically representing the collective effects of the black hole parameters, namely, the charge of the black hole ( Q ), spin parameter ( a ) and the PFDM parameter ( α ) on the energy ( E ), angular momentum ( L ) and effective potential ( V eff ) of the concerned particle. Finally, we discuss the Penrose process in order to study the negative energy particles having possible existence within the ergosphere, and which in turn leads to the energy gain of the emitted particle.

For horizonless spherical stars with uniform charge density, the hoop conjecture was tested based on the interior solution. In this work, we are interested in more general horizonless spherical charged stars. We test hoop conjecture using the exterior solution since all types of interior solutions correspond to the same exterior Reissner-Nordsr o ¨ m solution. Our analysis shows that the hoop conjecture is violated for very compact stars if we express the conjecture with the total ADM mass. And the hoop conjecture holds if we express the conjecture using the mass in the sphere.

We explore the cosmological viability of a theory of gravity defined by the Lagrangian f(R)= R n(R) in the Palatini formalism, where n(R) is a dimensionless function of the Palatini scalar curvature R that interpolates between general relativity when n(R)=1 and a locally scale-invariant and superficially renormalizable theory when n(R)=2 . We refer to this model as asymptotically Weyl-invariant gravity (AWIG). We analyse perhaps the simplest possible implementation of AWIG. A phase space analysis yields three fixed points with effective equation of states corresponding to de Sitter, radiation and matter-dominated phases. An analysis of the deceleration parameter suggests our model is consistent with an early and late period of accelerated cosmic expansion, with an intermediate period of decelerated expansion. We show that the model contains no obvious curvature singularities. Therefore, AWIG appears to be cosmologically viable, at least for the simple implementation explored.

Recently, based on swampland considerations in string theory, the (no) eternal inflation principle has been put forward. The natural question arises whether similar conditions hold in other approaches to quantum gravity. In this article, the asymptotic safety hypothesis is considered in the context of eternal inflation. As exemplary inflationary models the SU(N) Yang-Mills in the Veneziano limit and various RG-improvements of the gravitational action are studied. The existence of UV fixed point generically flattens the potential and our findings suggest no tension between eternal inflation and asymptotic safety, both in the matter and gravitational sector in contradistinction to string theory. Moreover, the eternal inflation cannot take place in the range of applicability of effective field quantum gravity theory. We employ the analytical relations for eternal inflation to some of the models with single minima, such as Starobinsky inflation, alpha-attractors, or the RG-improved models and verify them with the massive numerical simulations. The validity of these constraints is also discussed for a multi-minima model.

We propose to reinterpret Einstein's field equations as a nonlinear eigenvalue problem, where the cosmological constant ? plays the role of the (smallest) eigenvalue. This interpretation is fully worked out for a simple model of scalar gravity. The essential ingredient for the feasibility of this approach is that the classical field equations be nonlinear, i.e., that the gravitational field is itself a source of gravity. The cosmological consequences and implications of this approach are developed and discussed.

In this paper, we study the Joule-Thomson expansion for RN-AdS black holes immersed in perfect fluid dark matter. Firstly, the negative cosmological constant could be interpreted as thermodynamic pressure and its conjugate quantity with the volume gave us more physical insights into the black hole. We derive the thermodynamic definitions and study the critical behaviour of this black hole. Secondly, the explicit expression of Joule-Thomson coefficient is obtained from the basic formulas of enthalpy and temperature. Then, we obtain the isenthalpic curve in T?�P graph and demonstrate the cooling-heating region by the inversion curve. At last, we derive the ratio of minimum inversion temperature to critical temperature and the inversion curves in terms of charge Q and parameter λ .

The kinematics on spatially flat FLRW space-times is presented for the first time in co-moving local charts with physical coordinates, i. e. the cosmic time and Painlev\' e-type Cartesian space coordinates. It is shown that there exists a conserved momentum which determines the form of the covariant four-momentum on geodesics in terms of physical coordinates. Moreover, with the help of the conserved momentum one identifies the peculiar momentum separating the peculiar and recessional motions without ambiguities. It is shown that the energy and peculiar momentum satisfy the mass-shell condition of special relativity while the recessional momentum does not produce energy. In this framework, the measurements of the kinetic quantities along geodesic performed by different observers are analysed pointing out an energy loss of the massive particles similar to that giving the photon redshift. The examples of the kinematics on the de Sitter expanding universe and a new Milne-type space-time are extensively analysed.

We study the propagation of a massless scalar wave in de Sitter spacetime perturbed by an arbitrary central mass. By focusing on the late time limit, this probes the portion of the scalar signal traveling inside the null cone. Unlike in asymptotically flat spacetimes, the amplitude of the scalar field detected by an observer at timelike infinity does not decay back to zero but develops a spacetime constant shift - both at zeroth and first order in the central mass M. This indicates that massless scalar field propagation in asymptotically de Sitter spacetimes exhibits both linear and nonlinear tail-induced memories. On the other hand, for sufficiently late retarded times, the monopole portion of the scalar signal measured at null infinity is found to be amplified relative to its timelike infinity counterpart, by its nonlinear interactions with the gravitation field at first order in M.

In this work by using a numerical analysis, we investigate in a quantitative way the late-time dynamics of scalar coupled f(R,G) gravity. Particularly, we consider a Gauss-Bonnet term coupled to the scalar field coupling function ξ(?) , and we study three types of models, one with f(R) terms that are known to provide a viable late-time phenomenology, and two Einstein-Gauss-Bonnet types of models. Our aim is to write the Friedmann equation in terms of appropriate statefinder quantities frequently used in the literature, and we numerically solve it by using physically motivated initial conditions. In the case that f(R) gravity terms are present, the contribution of the Gauss-Bonnet related terms is minor, as we actually expected. This result is robust against changes in the initial conditions of the scalar field, and the reason is the dominating parts of the f(R) gravity sector at late times. In the Einstein-Gauss-Bonnet type of models, we examine two distinct scenarios, firstly by choosing freely the scalar potential and the scalar Gauss-Bonnet coupling ξ(?) , in which case the resulting phenomenology is compatible with the latest Planck data and mimics the ? -Cold-Dark-Matter model. In the second case, since there is no fundamental particle physics reason for the graviton to change its mass, we assume that primordially the tensor perturbations propagate with the speed equal to that of light's, and thus this constraint restricts the functional form of the scalar coupling function ξ(?) , which must satisfy the differential equation ξ ¨ =H ξ ? .