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We consider the third law of thermodynamics for families of 4- and n-dimensional Vaidya black holes, including many of interest. Since there are several versions of the definition of surface gravity as well as the extremality condition for dynamical black holes, we first show that for the considered 4- and n-dimensional Vaidya families, these definitions are consistent with each other. We assume, first, that a non-extremal black hole evolves to an extremality state after a finite time and second, that the weak energy condition for the source holds at all times. We then compare the results of these assumptions and investigate whether there are ranges of black hole parameters where these two assumptions are in conflict., Comment: 21 pages, 8 figures

We introduce an ingenious approach to explore cosmological implications of higher-derivative gravity theories. The key novelty lies in the characterization of the additional massive spin-0 modes constructed from Hubble derivatives as an effective density, with the corresponding pressure uniquely determined by energy conservation, while terms with no Hubble derivatives directly alter Friedmann equations. This classification of the various high-derivative contributions to Friedmann equations develops insight about their cosmological impacts and is essential for understanding the universe's evolution across energy scales. Various examples of higher-derivative gravity theories illustrate the power of this method in efficiently solving Friedmann equations and exploring new phenomena. Using CMB and BAO data, we apply this method to assess the observational feasibility of wall-bouncing universes, as predicted by scenarios with, e.g., certain third order modifications to general relativity. These models also provide an inflationary phase without the need to introduce extra scalar fields., Comment: 9 pages, 1 table

Here we consider the generalized Oppenheimer-Snyder collapse of a star into a four-dimensional Einstein-Gauss-Bonnet black hole as well as a class of regular black holes labeled by the polytropic index of the stellar matter. We then analyze the nature of the horizon and the corresponding surface gravity outside and inside the star. The Hayward and Nielsen-Visser dynamical surface gravity are in agreement with the one resulting from the Killing vector of the outer static metric. However, these two definitions inside the star do not coincide with the Killing surface gravity outside the star when the star crosses the event horizon. This motivates us to study the surface gravity using Fodor's approach to have a unique surface gravity at the mentioned moment. Then the extremality condition and the first law of thermodynamics are discussed at the trapping horizon of the star., Comment: 13 pages, 2 figures, accepted for publication in EPJC

We investigate various cosmological aspects of a 4-Dimensional Gauss-Bonnet Lagrangian, which is integrated into the Einstein Lagrangian with an arbitrary sign, using the Friedman-Lema\^itre-Robertson-Walker (FLRW) metric. We consider a general potential term, $V(a)$, that depends on the scale factor $a$, and we analyze several scenarios by investigating the critical points of the dynamical equations and stability conditions to understand how the universe's behavior is affected by the Gauss-Bonnet term. Our research suggests that choosing the negative sign, this integration allows for the spontaneous breaking of time reflection symmetry. This can lead to the generation of a bounce universe even with a normal matter sector, marking a significant departure from traditional theories. Furthermore, we examine the possibility of a time-crystal universe, showing that under certain circumstances, the theory might give rise to cyclic universes., Comment: 24 pages, 8 figures, 2 tables

Apart from the assumption that the inflation started at an infinite time in the past, the more realistic initial state of the quantum fluctuations is described by a mixed quantum state imposed at a finite value of the initial time. One of the most important non-trivial vacua is the $\alpha$-vacuum, which is specified by a momentum cutoff $\Lambda$ \cite{Danielsson:2002kx}. As a consequence, the initial condition is imposed at different initial times for the different $k$-modes. This modifies the amplitude of the quantum fluctuations, and thus the corresponding power spectra. In this paper, we consider the imprint of the $\alpha$-vacuum state on the power spectrum of scalar perturbations in a generic $f(R)$ gravity by assuming an ultraviolet cutoff $\Lambda$. As a specific model, we consider the Starobinsky model and find the trans-Planckian power spectrum. We find that the leading order corrections to the scalar power spectra in $f(R)$ gravity have an oscillatory behavior as in general relativity \cite{Lim}, and furthermore, the results are in sufficient agreement with the $\Lambda$CDM model., Comment: 21 pages, 5 figures, 1 table

In this paper, we treat 4-dimensional Einstein-Gauss-Bonnet gravity as general relativity with an effective stress-energy tensor. We will study the modified Oppenheimer-Snyder-Datt model of the gravitational collapse of a star in a 4-dimensional Einstein-Gauss-Bonnet black hole. The inside geometry of the star is described by the spatially flat Friedmann-Robertson-Walker metric and the matter is distributed uniformly without any pre-assumption about its equation of state. The exterior Einstein-Gauss-Bonnet black hole is smoothly matched to the interior geometry without the requirement of any thin shell. This gives the energy density, pressure, and the equation of state of collapsing matter. At the end, we study the time evolution of event and apparent horizons., Comment: 9 pages, 2 figures

We shall study the formation of a particular class of regular black holes from the gravitational collapse of a massive star. The inside geometry is described by spatially flat Friedmann-Robertson-Walker metric and the stellar matter is distributed uniformly without any pre-assumption about its equation of state. Our model is a generalization of Oppenheimer-Snyder collapse for regular black holes. We have obtained the density and pressure of star by applying the condition of smooth joining of metrics at the freely falling surface of star. Specifying the regular black holes to Hayward and Bardeen cases, we see that the stellar matter is described by a polytropic equation of state and moreover, for the radius smaller than a certain value, the strong energy condition becomes invalid. Then for both black holes, the interior apparent and event horizons and also the stellar surface are obtained as functions of the proper time of star. At the end, we have constructed a new two parametric family of regular black holes jointed smoothly to the flat Friedmann-Robertson-Walker interior metric of a polytropic star with an arbitrary index., Comment: To appear in Class. Quant. Grav

In this paper, we study the geodesic deviation equation (GDE) within the context of the Brans-Dicke (BD) theory in $D$ dimensions. Then, we restrict our attention to the GDE for the fundamental observers and null vector field past directed. Concerning the latter, in order to apply the retrieved GDE for the cosmological models as well as examining exact solutions, we study some cosmological models in general relativity (GR) and in the context of the BD theory. For the BD framework, we provide two appropriate settings for dynamical system, which can be considered as the most extended case scenarios with respect to those studied previously. Then, we investigate a few well-known BD cosmological models, for which we present the modified and corrected exact solutions. Moreover, we show that the retrieved formalism of the GDE can also be properly applicable for the modified BD theory (MBDT), whose matter and potential emerge from the geometry. For all of our herein cosmological models, we investigate the energy conditions and depict the behavior of the deviation vector and observer area distance. We demonstrate that why the MBDT can be considered as a more appropriate candidate to describe the universe in accordance with the observational data as well as from theoretical viewpoint., Comment: 34 pages, 7 figures

We present some new aspects of Kiselev black hole and then study the null and timelike thin shell collapse in this spacetime. For the latter, we show that Kiselev black hole can be matched to de Sitter core with a thin timelike dust shell to produce a non-singular black hole space-time. It is argued that for timelike hypersurface, the equation of state parameter must be non-negative. Using Barrabes-Israel junction conditions, the equation of motion of the shell is obtained. The stability of stationary solutions of the shell is discussed and some appropriate ranges for the parameters of shell and Kiselev geometry are found for which a stable stationary black hole is constructed., Comment: 21 pages, 8 figures

Using some probes, the violation of cosmic censorship conjecture in a general Kerr-Newman black hole is investigated. The result depends on many factors, like the relative sign of charge and rotation direction of the probe and black hole. Moreover the comparison of the angular momentum of the black hole and its charge has an impressive effect. Considering all these together, we have found the range of the angular momentum, energy and charge of the probe for which the event horizon disappears. We have found that cosmic censorship conjecture violation is possible only for near extremal black hole if the parameters of the probe are too large and fine tuned. Taking into account the hoop conjecture, we see that the cosmic censorship conjecture is respected for a general Kerr-Newman black hole subject to a large enough number of falling particles and also field quanta., Comment: 19 pages

It is well-known that in order to make the action well defined, one may employ different kinds of boundary conditions (BCs) accompanied by the appropriate Gibbons-Hawking-York (GHY) terms. In this paper we investigate the role of the selected BC and the corresponding GHY terms on the black hole (BH) entropy. Our result shows, regardless of the kind of BC, the BH entropy in all cases is the same as one obtained under Dirichlet BC from Wald formula or semi-classical approximation method. We considered the Schwarzschild solution for $f(R)$-gravity and general relativity (GR) in standard dimensions as special models., Comment: 22 pages, To appear in Phys. Rev. D

As a local effect of dynamical dark energy, bending of light in the presence of a spherically symmetric and static black hole surrounded by quintessence has been studied. Having in mind recent observational data, we have treated the problem as a deviation from Kottler space-time. This deviation is measured by a perturbation parameter $\varepsilon$ included in the equation of state parameter of quintessence as $\omega_q=-1+\frac{1}{3}\varepsilon$. Here, the deflection angle is calculated and then the result is compared with \cite{Arakida:2011th} in the limit $\varepsilon\rightarrow 0$ where the quintessence behaves like the cosmological constant. It is shown that unlike the cosmological constant, the effect of quintessence on the photon energy equation can not be absorbed into the definition of impact parameter. Moreover in this paper, we generalize the Kiselev black hole to the case that there is a modified Chaplygin gas as the dark energy component of the universe and show that the resulted metric can be reduced to the Kiselev metric by adjusting some arbitrary parameters., Comment: 14 pages, Accepted for publication in Phys. Rev. D

In this article we study the gauge invariant effective energy momentum tensor for cosmological perturbations in f(R) gravity during the inflationary epoch. Considering the super-horizon regime, we derive the effective energy density up to the one-loop corrections. It describes the back-reaction effect of the fluctuations on the background space-time., Comment: 18 pages, Accepted for publication in Phys. Rev. D

We study the effect of a non-trivial vacuum prescription on warm inflation observables, namely the power spectrum of the comoving curvature perturbation. Non-trivial choice of vacuum, can provide information about trans-Planckian physics. Traditionally, the initial condition for inflation is chosen to be the usual Bunch-Davies vacuum. Another more reasonable choice of vacuum is the so-called $\alpha$-vacua. Because the duration of inflation is not infinite, as it is assumed in the Bunch-Davies case, imposing the initial condition at infinite past is not sensible and one must utilize another vacuum prescription. In this paper, working in the slow-roll regime during warm inflation, the initial condition for inflaton fluctuations is imposed at finite past, i.e. the $\alpha$-vacua. We show that this non-trivial vacuum prescription results in oscillatory correction to the comoving curvature power spectrum, which is scale dependent both in amplitude and frequency. Having obtained this scale dependent power spectrum, we consider its late time footprints and compare our results with observational data and other proposed models for the comoving curvature power spectrum., Comment: 29 pages, 5 figures

Using a completely covariant approach, we discuss the role of boundary conditions (BCs) and the corresponding Gibbons--Hawking--York (GHY) terms in $ \mathit{f}(\mathit{R}) $-gravity in arbitrary dimensions. We show that $ f(\mathit{R}) $-gravity, as a higher derivative theory, is not described by a degenerate Lagrangian, in its original form. Hence, without introducing additional variables, one can not obtain consistent BCs, even by adding the GHY terms (except for $f(\mathit{R})=R$). However, following the Ostrogradsky approach, we can introduce a scalar field in the framework of Brans-Dicke formalism to the system to have consistent BCs by considering appropriate GHY terms. In addition to the Dirichlet BC, the GHY terms for both Neumann and two types of mixed BCs are derived. We show the remarkable result that the $f(\mathit{R})$-gravity is itself compatible with one type of mixed BCs, in $D$ dimension, i.e. it doesn't require any GHY term. For each BC, we rewrite the GHY term in terms of Arnowit-Deser-Misner (ADM) variables., Comment: 21 pages

We have considered the perturbation equations governing the growth of fluctuations in generalized scalar tensor theory during inflation. we have found that the scalar metric perturbations at very early times are negligible compared with the scalar field perturbation, just like general relativity. At sufficiently early times, when $q/a\gg H$, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov-Sasaki equation. And a similar procedure is performed for the case of tensor metric perturbation., Comment: 11 pages

Since the duration of inflation is finite, imposing the initial condition in infinite past, i.e. the Bunch-Davies vacuum, is inherently ambiguous. In this paper, we resort to the mixed states as initial condition which are called the $\alpha$-vacua and then introduce a physical momentum cutoff $\Lambda$ [Danielsson:2002kx], in which the evolution of perturbations begins. We show that the initial time $t_i$, when the initial condition is imposed, depends on the wave number of fluctuation, as it is for the time of horizon crossing, $t_q$. Then we calculate the corrections to the scalar and tensor power spectra and their corresponding spectral indices. Throughout this work, the calculation is done up to the first order in slow-roll parameters. We indicate that the leading order corrections to the spectral indices have a $q$-dependent amplitude, $2\epsilon_{f}[2\epsilon_{f}(\frac{q}{q_{f}})^{4\epsilon+4\eta}-\eta_{f}(\frac{q}{q_{f}})^{3\epsilon+\xi}]$ times a $q$-dependent oscillatory part, $\cos(\frac{2\Lambda(q/q_{f})^{\epsilon}}{H_{f}})$, where $H$, $\epsilon$, $\eta$, and $\xi$ are the Hubble and slow-roll parameters respectively, and the subscript $f$ denotes that these quantities are evaluated at the time when the first scale, $q_{f}$, satisfies the initial condition, i.e. $q=a(t_i)\Lambda$., Comment: 32 pages, 4 figure

In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov (TOV) equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behaviour of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed., Comment: 4 figures

Cosmological models may result in future singularities. We show that, in the framework of dynamical varying speed of light theories, it is possible to regularize those singularities.

In this paper we explicitly show that in general relativity, the relative velocity of two local inertial frames is always less than the velocity of light. This fact is a by-product of the equivalence principle. The general result is then illustrated within two examples, the FLRW cosmological model and the Schwarzschild metric., Comment: 1 Figure

In this paper we are concerned with the effects of anisotropic pressure on the boundary conditions of anisotropic Lane-Emden equation and homology theorem. Some new exact solutions of this equation are derived. Then some of the theorems governing the Newtonian perfect fluid star are extended taking the anisotropic pressure into account.

There should be two ways to describe the flat rotation curves of galaxies and cluster of galaxies. Either one can introduce a dark matter component for the matter filling the halo, or by modifying the gravity theory and give the flat rotation curve a geometrical nature. Here we adopt an f(R) model suitable for describing the effect. After matching the solution with the exterior solution, the effective density, radial and tangential pressures are obtained. Then the energy conditions and lensing effect is investigated.

Some theorems for a static prefect fluid sphere, i.e. a star, in the presence of a positive cosmological constant are proved. These theorems put bounds on the pressure profile and internal compactness of the star., Comment: 2 figures

Observational data for type Ia supernovae, shows that the expansion of the universe is accelerated. This accelerated expansion can be described by a cosmological constant or by dark energy models like quintessence. An interesting question may be raised here. Is it possible to describe the accelerated expansion of universe using varying--$G$ cosmological models? Here we shall show that the price for having accelerated expansion in slow--varying--$G$ models (in which the dynamical terms of $G$ are ignored) is to have highly non--conserved matter and also that it is in contradiction with other data.

In this paper two tracker solutions for conformally coupled quintessence model is obtained. The first solution is determined by dividing the evolution of the universe to matter and dark energy dominated epochs and then the allowed bound on the equation of state parameter is obtained, such that a tracker behaviour is resulted. For the other solution, the quintessence potential is assumed to be a linear combination of two exponential functions. Then we have found an exact solution which can be tracker by adjusting some parameters., Comment: 8 figures

Non-minimally coupled scalar field models of dark energy are equivalent to an interacting quintessence in the Einstein's frame. Considering two special important choices of the potential of the scalar field, i.e. nearly flat and thawing potential, one has an analytical expression for the equation of state parameter as a function of the density parameter of the scalar field for any choice. Here we investigate the non-minimal quintessence model by applying the method of statefinder diagnosis to it and plotting the evolutionary trajectories of the statefinder parameters., Comment: 8 figures. To appear in Euro. Phys. Lett. 2009

The classical trajectories for FLRW universe with varying speed of light are obtained for the cases in which the cosmological constant depends or not depend on the velocity of light. The theory is then quantized and the corresponding WDW equation is solved. It is shown that the method of causal interpretation of Bohm can be applied successfully to the theory. Finally the Bohmian trajectories are obtained and compared with the classical ones.

We shall in the framework of Bohmian quantum gravity show that it is possible to find a {\it pure} quantum state which leads to the static Einstein universe whose classical counterpart is flat space--time. We obtain the solution not only in the long--wavelength approximation but also exactly., Comment: to appear in Int. J. Mod. Phys. A

In this paper we have investigated the classical limit in Bohmian quantum cosmology. It is observed that in the quantum regime where the quantum potential is greater than the classical one, one has an expansion in terms of negative powers of the Planck constant. But in the classical limit there are regions having positive powers of the Planck constant, and regions having negative powers and also regions having both. The conclusion is that the Bohmian classical limit cannot be obtained by letting the Planck constant goes to zero., Comment: to appear in Int. J. Mod. Phys. D