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This paper deals with the study of quasi-spherical gravitational collapse in the framework of f (R , T) theory. We will divide geometry of the star into two distinct portions i.e. interior portion and exterior portion. In the interior portion, we consider quasi-spherical Szekeres line element and in the exterior portion we take Vaidya line element. The interior and exterior portions will be glued by using Israel's junction conditions [W. Israel, Il Nuovo Cimento B (1965–1970) 44, 1 (1966); W. Israel, Phys. Lett. A 24, 184 (1967)]. The field equations will be derived in the context of f (R , T) theory for a particular model. Apparent horizons and their time configuration for various desirable cases will also be discussed. [ABSTRACT FROM AUTHOR]

In spirit of the recently proposed four-parameter generalized entropy of apparent horizon, we investigate inflationary cosmology where the matter field inside of the horizon is dominated by a scalar field with a power law potential (i.e., the form of ϕ n where ϕ is the scalar field under consideration). Actually without any matter inside of the horizon, the entropic cosmology leads to a de-Sitter spacetime, or equivalently, an eternal inflation with no exit. Thus in order to achieve a viable inflation, we consider a minimally coupled scalar field inside the horizon, and moreover, with the simplest quadratic potential. It is well known that the ϕ 2 potential in standard scalar field cosmology is ruled out from inflationary perspective as it is not consistent with the recent Planck 2018 data; (here it may be mentioned that in the realm of "apparent horizon thermodynamics", the standard scalar field cosmology is analogous to the case where the entropy of the apparent horizon is given by the Bekenstein–Hawking entropy). However, the story becomes different if the horizon entropy is of generalized entropic form, in which case, the effective energy density coming from the horizon entropy plays a significant role during the evolution of the universe. In particular, it turns out that in the context of generalized entropic cosmology, the ϕ 2 potential indeed leads to a viable inflation (according to the Planck data) with a graceful exit, and thus the potential can be made back in the scene. [ABSTRACT FROM AUTHOR]

Momentum is characterized in terms of inertial mass for particles moving at less than the speed of light, but entirely in terms of their energy for those lacking inertia. Does this difference suggest a physically distinct origin of momentum in the two cases and, if so, what is actually being conserved in interactions involving both types of particle? In this paper, we consider a recently proposed gravitational origin for rest-mass energy to demonstrate that a single definition of momentum applies to all particles, massless or otherwise. When introduced into this description, inertial mass is merely a surrogate for the particle's 'free' energy, but does not imply an origin of momentum different from that of particles without mass. [ABSTRACT FROM AUTHOR]

In this paper, the different properties of generalized Vaidya spacetime are considered. We define the location of horizons. We show that the apparent horizon can contain the event horizon. The locations of all types of horizons are compared with the ones in the usual Vaidya spacetime. We investigate the time-like geodesics in this spacetime. New corrections to Schwarzschild and Vaidya cases appear and we give conditions when these corrections are not negligible. Also, we consider the conformal Killing vector and transform the metric to conformally static coordinates. We introduce a new constant of motion along null and time-like geodesics, which is generated by a homothetic Killing vector. The conformally static coordinates allow diagonalizing of the generalized Vaidya spacetime. The surface gravity has been calculated for the dust and stiff fluid cases. [ABSTRACT FROM AUTHOR]

The investigation of modifications to the FLRW cosmology resulting from the consideration of a general entropy for the cosmological apparent horizon is the subject of this study. Building upon the work of Nojiri and colleagues in 2022, who introduced a class of generalized entropies with four parameters capable of converging to familiar entropies and addressing specific cosmological issues, our research explores the impact of correcting the entropy on the energy-momentum tensor of the cosmic fluid from the outset. Our calculations demonstrate that, by employing a correction function f(ρ) to modify the energy-momentum density tensor, the entropic area law (Bekenstein-Hawking entropy) can still be regarded as a general entropy. The construction of the function f(ρ) is facilitated through considerations of the thermodynamics associated with the apparent horizon. Additionally, we investigate the first and second laws of thermodynamics within this framework and illustrate how the limitations imposed on the equation of state of the cosmic fluid can be resolved through the incorporation of this correction function. Finally, we compute cosmography parameters to analyze the kinematics of the universe, with particular attention given to the notable influence of the correction function f(ρ) on these parameters. This paper provides valuable insights into the application of general entropies to the apparent horizon of the universe.

In this work, new Tsallis holographic dark energy with apparent horizon as IR-cutoff is constructed in a non-flat Friedmann–Lemaitre–Robertson–Walker Universe. The accelerating expansion phase of the Universe is described by using deceleration parameter, equation of state parameter and density parameter by using different values of new Tsallis holographic dark energy (NTHDE) parameter " δ ". The NTHDE Universe's transition from a decelerated to an accelerated expanding phase is described by the smooth graph of deceleration parameter. Depending on distinct values of Tsallis parameter " δ ", we have explored the quintessence behavior of the equation of state parameter. We used Hubble data sets obtained using Cosmic Chronometric methods and distance modulus measurement of Type Ia Supernova to fit the NTHDE parameters. Stability of our model by analyzing the squared speed of sound is investigated as well. [ABSTRACT FROM AUTHOR]

Gaspard Monge has received undue credit for his observations of mirages in 1798 in Egypt. He did not discover inferior mirages; they were known to sailors before 1687, and the term mirage had entered the French literature in 1753. Monge’s “total reflection” explanation for them was seriously flawed; it had already been considered and rejected by Gruber and by Büsch, and was promptly criticized by others. Yet he continues to be given credit for the first scientific explanation of mirages; and his false total-reflection mechanism survives today in some textbooks. Apparently this is due to its superficial simplicity, which appeals to novices.

Hawking radiation as a quantum phenomenon is generally attributed to the existence of the event horizon of a black hole. However, we demonstrate in this paper that there is indeed ingoing Hawking-like radiation associated with apparent horizons of the first cosmological black hole solution in the framework of Scalar–Tensor–Vector Gravity (STVG) theory living in the Friedmann–Lemaître–Robertson–Walker (FLRW) background. Such radiation can be attributed also to the cosmological apparent horizon of the FLRW universe and even to the cosmological event horizon of de Sitter spacetime. We see how STVG theory as a successful theory for explaining black holes both on local and global scales affects the Hawking effect. Based on semiclassical approximation, we follow Hamilton–Jacobi and Parikh–Wilczek tunneling methods respectively with and without back-reaction effects. We find out that back-reaction effects make a correlation between the emission modes in Parikh–Wilczek tunneling formalism, which can address the information paradox. We obtain the corresponding Hawking-like temperature as a function of inverse powers of apparent horizons radiuses of the cosmological black hole in STVG theory. Due to non-equilibrium situation, the definition of such time-dependent temperature is effectively valid at near horizon, since Hawking (-like) radiation is a near-horizon effect. We analyze the influence of the STVG parameter associated with a deviation of the STVG theory from General Theory of Relativity (GR) on both apparent horizons and the Hawking-like temperature of the cosmological black hole. We show that increasing the STVG parameter results in appearing the Hawking-like temperature in later cosmic times with some smaller values. Also, we follow the Hamilton–Jacobi approach beyond semiclassical approximation to involve all quantum correction terms in the deduced semiclassical outcomes for the cosmological black hole in the STVG theory. Also, we prove that all results of the paper satisfy the correspondence principle so that eliminating the STVG parameter leads to achieve the corresponding results in the McVittie spacetime. [ABSTRACT FROM AUTHOR]

To investigate the relationship between gravity and thermodynamics in the case of dynamic systems, we interpret the apparent horizon of the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime as a thermodynamic system. We derive the corresponding fundamental equation in the entropy representation and explore the consequences of demanding the fulfillment of the classical laws of thermodynamics. We investigate in detail the case of an FLRW spacetime with and without cosmological constant. We show that the interpretation of the apparent horizon as an isolated thermodynamic system is possible only under certain conditions because the analogy is not always valid for all the values of the parameters entering the dynamics of the horizon and certainly not for its entire evolution. Nevertheless, we show that the generalized second law of thermodynamics remains valid.

In spirit of the recently proposed four-parameter generalized entropy of apparent horizon, we investigate inflationary cosmology where the matter field inside of the horizon is dominated by a scalar field with a power law potential (i.e., the form of ϕn where ϕ is the scalar field under consideration). Actually without any matter inside of the horizon, the entropic cosmology leads to a de-Sitter spacetime, or equivalently, an eternal inflation with no exit. Thus in order to achieve a viable inflation, we consider a minimally coupled scalar field inside the horizon, and moreover, with the simplest quadratic potential. It is well known that the ϕ2 potential in standard scalar field cosmology is ruled out from inflationary perspective as it is not consistent with the recent Planck 2018 data; (here it may be mentioned that in the realm of “apparent horizon thermodynamics”, the standard scalar field cosmology is analogous to the case where the entropy of the apparent horizon is given by the Bekenstein–Hawking entropy). However, the story becomes different if the horizon entropy is of generalized entropic form, in which case, the effective energy density coming from the horizon entropy plays a significant role during the evolution of the universe. In particular, it turns out that in the context of generalized entropic cosmology, the ϕ2 potential indeed leads to a viable inflation (according to the Planck data) with a graceful exit, and thus the potential can be made back in the scene.

We continue a study by Adler and Ramazanoǧlu (AR) of "black" holes as modified by a scale invariant dark energy action. For the spherically symmetric Schwarzschild-like case, AR found that there is no event horizon; hence spacetime is not divided by the "black" hole into causally disconnected regions. We review the formalism for locating trapped surfaces and apparent horizons, and show that the modified "black" hole has no trapped surfaces. Thus, one suspects that it is "leaky," and that there will be a "black hole wind" of particles streaming out from the location of the nominal horizon. This will have astrophysical consequences, for example, the wind may feed and stabilize star formation in the vicinity of the "black" hole. We initiate a study of the stationary axially-symmetric rotating "black" hole as modified by a scale invariant dark energy action, i.e. one that is Kerr-like. To set-up the axial case, we note that the conserving completion of the dark energy stress-energy tensor can be calculated algebraically by solving a 2 × 2 matrix equation. Using Mathematica we calculate and simplify the modified system of Einstein equations for the axial case in quasi-isotropic coordinates, and give appropriate boundary conditions. Solution of these equations, which may require developing a special purpose numerical program, is rendered tricky by a residual general coordinate invariance of quasi-isotropic coordinates. This leads to the interesting mathematical question of representing a positive planar function as the gradient squared of a harmonic function. [ABSTRACT FROM AUTHOR]

For distant observers, black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely, that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which manifests itself in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects. [ABSTRACT FROM AUTHOR]

We study the evolution of some simple cosmological black holes in the framework of the generalized Lemaitre-Tolman-Bondi (LTB) model developed by Lasky and Lun, which includes the effects of nonzero pressure. A small Gaussian overdensity is introduced into the LTB solutions, and an equation of state is assumed in order to fix the relation between the pressure and the density. Numerical solutions are calculated, which simulate the dynamical effects of the pressure field on the formation of a black hole as the end state of the collapse. The influence of the pressure effects on the behavior of the solutions is measured by comparing the development of the generalized LTB model with that of the corresponding pressure-free LTB model. Finally, we plot the location of the apparent horizon on each shell and examine the differences in the locations between the cases with and without pressure. The evidence indicates that the apparent horizon forms later in the presence of pressure. [ABSTRACT FROM AUTHOR]

The present paper deals with the gravitational collapse of shear-free inhomogeneous spherical star consisting of dust fluid (ρ) in the background of dark energy components ( p DE , ρ DE ) with equation of state p DE = ω ρ DE (ω being a nonzero constant parameter describing dark energy component). We discussed the development of apparent horizon to investigate the black hole formation in gravitational collapsing process. The collapsing process is examined first separately for dust cloud and dark energy and then under the combined effect of dust interacting with dark energy. It is obtained that when only dust cloud or dark energy is present the collapse leads to the formation of black hole under certain conditions. When both of them are present, the collapsing star does not form black hole. However, when dark energy is considered as cosmological constant (ω = − 1) , the collapse leads to black hole formation. [ABSTRACT FROM AUTHOR]

From a fractal perspective, the entropy bound of gravitational systems undergoes changes. Furthermore, in the cosmological setting, the conservation law of a perfect fluid is also altered in such systems, affecting spatial elements like volume, area, and radius. By applying the first law of thermodynamics and deriving the Friedmann equations, we can gain insight into the evolution of such a fractal cosmos. However, observations continue to necessitate the existence of a dark energy source. To address this, in this article, we have created a novel fractal Λ CDM cosmological model and determined the fractal cosmological observables. We show that the spatial fractal dimension is two, and the age of the Universe is 13.91 Gyr, by fitting the model's parameters to cosmological data. [ABSTRACT FROM AUTHOR]

We show that the recipe for computing the expansions ℓ and n of outgoing and ingoing null geodesics normal to a surface admits a covariance group with nonconstant scalar κ (x) , corresponding to the mapping ℓ → κ ℓ , n → κ − 1 n . Under this mapping, the product ℓ n is invariant, and thus the marginal surface computed from the vanishing of ℓ , which is used to define the apparent horizon, is invariant. This covariance group naturally appears in comparing the expansions computed with different choices of coordinate system. [ABSTRACT FROM AUTHOR]

We review the basic definitions and properties of trapped surfaces and discuss them in the context of Kerr–Vaidya line element. Our study shows that the apparent horizon does not exist in general for axisymmetric space–times. The reason being the surface at which the null tangent vectors are geodesics and the surface at which the expansion of such vectors vanishes do not coincide. The calculation of an approximate apparent horizon for space–times that ensure its existence seems to be the only way to get away with this problem. The approximate apparent horizon, however, turned out to be non-unique. The choice of the shear-free null geodesics, at least in the leading order, seems to remove this non-uniqueness. We also propose a new definition of the black hole boundary. [ABSTRACT FROM AUTHOR]

In this short note, we show how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8. [ABSTRACT FROM AUTHOR]

In this paper, we compare the force expressions in both comoving synchronous and Ellis coordinate systems in Friedman-Robertson-Walker spacetime in order to understand how the coordinate transformation affects the inertial forces. We also studied the negative energy problem in Ellis system. The Penrose process is possible outside the apparent horizon due to the fact that the line element has off-diagonal term. However, only the movement towards infinity is possible; we offer the way how one can ascertain that this effect took place outside the apparent horizon.

In this work, we consider gravitationally induced particle creation scenario to discuss the validity of thermodynamic laws in the context of cubic gravity which is based on an invariant term and constructed from cubic contraction of the Riemann tensor. We consider spatially flat FRW universe filled with a perfect fluid assuming an equation of state p = (γ − 1) ρ with 2 3 ≤ γ ≤ 2. By taking the Hubble horizon as the boundary of the universe, we investigate the first and generalized second law of thermodynamics along with thermodynamic equilibrium in the presence of Bekenstein entropy. In order to view the clear picture of these laws, we take into account two models of particle creation rate Γ which are constrained with recent observational data. It is found that the validity of these laws holds for the suitable values of model parameters in the specific ranges of redshift parameter for both models. [ABSTRACT FROM AUTHOR]

Although it is not a fundamental question, determining exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting the integration of the General Relativity Theory field equations for the Kantowski–Sachs spacetime describes a homogeneous but anisotropic universe whose spatial section has the topology of R × S 2 , we integrate the equations for arbitrary curvature parameter and write the solutions considering the process of gravitational collapse. We took the opportunity and made some comments involving some features of the model such as energy density, shear, viscosity and the production of gravitational waves via Petrov classification. [ABSTRACT FROM AUTHOR]

We discuss the thermodynamical behavior of homogeneous and isotropic universe (flat and non-flat) in the framework of f (R , T ϕ) gravity, where R stands for Ricci scalar and T ϕ signifies the trace of energy–momentum tensor of a scalar field ϕ. We follow through the first-order formalism that specifies the scalar field to the Hubble parameter which becomes H = W (ϕ). By using Bekenstein–Hawking entropy, we analyze the validity of generalized second law of thermodynamics at apparent horizon for different values of W (ϕ) and evaluate the equilibrium condition for all cases as well. [ABSTRACT FROM AUTHOR]

A new perspective toward Einstein's theory of general relativity, called mimetic gravity, was suggested in [A. H. Chamseddine and V. Mukhanov, J. High Energy Phys.1311 (2013) 135] by isolating the conformal degree of freedom in a covariant fashion through a re-parametrization of the physical metric in terms of an auxiliary metric and a mimetic field. In this paper, we first derive the Friedmann equations of the Friedmann–Robertson–Walker (FRW) universe with any spatial curvature in mimetic gravity. Then, we disclose that one can always rewrite the Friedmann equations of mimetic cosmology in the form of the first law of thermodynamics, d E eff = T h d S h + W d V , on the apparent horizon. We confirm that the entropy associated with the apparent horizon in mimetic cosmology still obeys the area law of entropy which is useful in studying the thermodynamical properties of the black holes in mimetic gravity. We also examine the time evolution of the total entropy in mimetic cosmology and show that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon. Our study further supports the viability of the mimetic gravity from a thermodynamic viewpoint and provides a strong consistency check of this model. [ABSTRACT FROM AUTHOR]

The investigation of modifications to the FLRW cosmology resulting from the consideration of a general entropy for the cosmological apparent horizon is the subject of this study. Building upon the work of Nojiri and colleagues in 2022, who introduced a class of generalized entropies with four parameters capable of converging to familiar entropies and addressing specific cosmological issues, our research explores the impact of correcting the entropy on the energy-momentum tensor of the cosmic fluid from the outset. Our calculations demonstrate that, by employing a correction function f (ρ) to modify the energy-momentum density tensor, the entropic area law (Bekenstein-Hawking entropy) can still be regarded as a general entropy. The construction of the function f (ρ) is facilitated through considerations of the thermodynamics associated with the apparent horizon. Additionally, we investigate the first and second laws of thermodynamics within this framework and illustrate how the limitations imposed on the equation of state of the cosmic fluid can be resolved through the incorporation of this correction function. Finally, we compute cosmography parameters to analyze the kinematics of the universe, with particular attention given to the notable influence of the correction function f (ρ) on these parameters. This paper provides valuable insights into the application of general entropies to the apparent horizon of the universe. [ABSTRACT FROM AUTHOR]