Apparent Horizon Research Articles

Cooling-heating properties of the FRW universe in gravity with a generalized conformal scalar field

In this paper, within the framework of modified gravity involving a conformal scalar field, we investigate the Joule-Thomson expansion of the Friedmann-Robertson-Walker (FRW) universe to identify cooling and heating regions. We observe a divergence in the Joule-Thomson coefficient (μ), precisely at the apparent horizon (RA=−2α) of the FRW universe, under conditions of negative gravitational coupling (α<0), which aligns with a thermodynamic singularity. Furthermore, we determine the inversion temperature and pressure for the FRW universe, and elucidate the salient features of inversion and isenthalpic curves in the temperature-pressure (T-P) plane. We compare these findings with results obtained under Einstein gravity, discussing the influence of the modification term on the cooling and heating properties of the FRW universe. This work presents insights into the formation of cooling and heating regions within the FRW universe, contributing to a deeper understanding of the physical mechanisms behind cosmic expansion history.

Traces of Quantum Gravity Effects at Late-time Cosmological Dynamics via Distance Measures

Inspired by the entropy–area relation of black hole thermodynamics, we study the thermodynamics of the cosmological apparent horizon in a spatially flat Friedmann–Robertson–Walker universe in the framework of an extended uncertainty principle (EUP). The adopted EUP naturally admits a minimal measurable momentum (equivalently a maximal measurable length), as an infrared cutoff in the theory. We derive the modified Friedmann equations in this setup and explore some predictions of these equations for the late-time universe via distance measures. We show that in this framework it is possible to realize the late-time cosmic speedup and transition to the phantom phase of the equation-of-state parameter of the effective cosmic fluid without recourse to any dark energy component or modified gravity. Inspection of various distance measures in this framework shows that an EUP with a negative deformation parameter suffices for the interpretation of the late-time asymptotically de Sitter universe with standard nonrelativistic matter.

A new perspective on gravitational collapse: a comprehensive analysis using Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document} parametrization

In this article, we have studied some new facets of gravitational collapse, beyond conventional notions of black holes, and naked singularities. The present work is focused on the unresolved problems of theoretical physics concerning the final fate of the gravitational collapse of any massive star. By generalizing the foundational work of Oppenheimer and Snyder (Phys Rev 56:455, 1939), we have considered the homogeneous gravitational collapsing system filled with perfect fluid distributions (devoid of dust fluid) within the framework of GR theory. The article investigates a homogeneous gravitational collapsing system using a parametrization scheme for the expansion-scalar (Θ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\Theta )$$\\end{document} and determining the exact solution of field equations. Further, by employing the known Darmois–Israel boundary condition, we have discussed the solution in more detail, and the model’s physical and geometrical quantities are obtained in terms of stellar mass (M), making it crucial for astrophysical applications. To assess the astrophysical viability of our model, we consider a massive star-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}Canis Majoris and throughout this study we have presented a detailed numerical and graphical analysis of our model. The analysis of singularities in the models is conducted through the examination of the apparent horizon. Our findings demonstrate that the star continues to collapse indefinitely in co-moving time, ultimately leading to a space-time singularity-this represents a case of continuous gravitational collapse. We propose that this scenario describes an “Eternal Collapsing Object,” which may be treated as a “mathematical black hole without any finite equilibrium state.” Our presented models undergo rigorous physical tests to ensure their regularity, causality, and stability, and to satisfy the necessary energy conditions.

The analytical approach in testing the Kaniadakis cosmology

Abstract We know that a quantum-corrected cosmological scenario can emerge based on its corrected Friedmann equations corresponding to the corrected entropy of cosmic-horizon using the gravity-thermodynamics conjecture in deriving those equations. In this right, the Kaniadakis entropy associated with the apparent horizon of Friedmann-Robertson-Walker(FRW) Universe leads to a corrected Friedmann equation which contains a correction term as $\Omega_{Ka}=\frac{\alpha\left(H^2+\frac{k}{a^2}\right)^{-1}}{H^{2}}$ where $\alpha\equiv\frac{K^2 \pi^2}{2 G^2}$ ($K$ is the Kaniadakis parameter). Here, we derive the analytical relations between the energy density parameters $\Omega_{m},\Omega_{\Lambda}$ (and the ratio density $\Omega_{Ka}$ of correction term) and the geometrical cosmological parameters $\{q, j\}$. This leads to getting $\Omega_{Ka}=\frac{j-1}{4(q+1)^{2}-(j-1)}$ which enables us to put constrains on $\Omega_{Ka_{0}}$ using the measurable parameters $\{q_{0},j_{0}\}$ and $H_{0}$. It also reveals some interesting aspects of the Kaniadakis cosmology by explaining that the correction term plays different roles both in the presence and in the absence of the cosmological constant $\Lambda$.&amp;#xD;This term plays the role of dark energy in the absence of the cosmological constant $\Lambda$, while in the presence of this component, it plays the role of a small correction to dark energy. The value of $\Omega_{Ka}$ then determines the amount of the deviation of Kaniadakis model from the concordance $\Lambda CDM$ model. As a result, the value of $j_{0}$ is found to be close to unit for vanishing cosmological constant $\Lambda=0$ and the maximum value of $\Omega_{Ka0}$; thereby we get $(j_{0}-1)\simeq 0.137$ and $(j_{0}-1)\simeq&lt; 10^{-3}$ for the case of $\Lambda=0$ and $\Lambda\neq0$, respectively&amp;#xD;

No drama in two-dimensional black hole evaporation

We numerically calculate the spacetime describing the formation and evaporation of a regular black hole in 2D dilaton gravity. The apparent horizons evaporate smoothly in finite time to form a compact trapped region. We nevertheless see rich dynamics: an antitrapped region forms alongside the black hole and additional compact trapped and antitrapped regions are formed by backreaction effects as the mass radiates away. The spacetime is asymptotically flat at future null infinity and is free of singularities and Cauchy horizons. These results suggest that the evaporation of regular 2D black holes is unitary. Published by the American Physical Society 2024

Different Aspects of Entropic Cosmology

We provide a short review of the recent developments in entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change in entropy of the apparent horizon during the cosmic evolution of the universe; in particular, it is expressed by TdS=−d(ρV)+WdV (where W is the work density and other quantities have their usual meanings). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question—“What is the form of the horizon entropy corresponding to a general modified theory of gravity?”. The second law of horizon thermodynamics states that the change in total entropy (the sum of horizon entropy + matter fields’ entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of a generalised entropy function.

Apparent horizon tracking in supercritical solutions of the Einstein-scalar field equations in spherical symmetry in affine-null coordinates

Apparent horizon tracking in supercritical solutions of the Einstein-scalar field equations in spherical symmetry in affine-null coordinates

The exact relativistic scalar quasibound states of the dyonic Kerr–Sen black hole: quantized energy, and Hawking radiation

We consider Klein–Gordon equation in the Dyonic Kerr–Sen black hole background, which is the charged rotating axially symmetric solution of the Einstein–Maxwell–Dilaton–Axion theory of gravity. The black hole incorporates electric, magnetic, dilatonic and axionic charges and is constructed in 3+1 dimensional spacetime. We begin our investigations with the construction of the scalar field’s governing equation, i.e., the covariant Klein–Gordon equation. With the help of the ansatz of separation of variables, we successfully separate the polar part, and find the exact solution in terms of Spheroidal Harmonics, while the radial exact solution is obtained in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that gives rise to discrete complex-valued energy levels for massive scalar fields. The real part is the scalar field relativistic quantized energy, while the imaginary part represents the quasibound states’s decay. We present all of the sixteen possible exact energy solutions for both massive and massless scalars. We also present the investigation the Hawking radiation of the Dyonic Kerr–Sen black hole’s apparent horizon, via the Sigurd–Sannan method by making use of the obtained exact scalar wave functions. The radiation distribution function, and the Hawking temperature are also obtained.

Emergence of cosmic space and horizon thermodynamics from Kaniadakis entropy

Abstract Utilizing Kaniadakis entropy associated with the apparent horizon of the Friedmann-Robertson-Walker (FRW) Universe and applying the emergence of cosmic space paradigm, we deduce the modified Friedmann equation for a non-flat (n+1)-dimensional universe. Employing the first law of thermodynamics, we arrive at the same modified Friedmann equation, showing the connection between emergence of cosmic space and first law of thermodynamics. We also establish the condition to satisfy the Generalized second law of thermodynamics within the Kaniadakis framework. Our study illuminates the intricate connection between the law of emergence and horizon thermodynamics, offering a deeper insight through the lens of Kaniadakis entropy.

Dynamical Black holes in the FLRW universe

Observations show that massive black holes, thought to be at the center of galaxies and galaxy clusters, are dynamical objects and interact with their environments. Black holes are characterized by their mass and angular momentum, and they are time-varying objects embedded in the cosmological Friedman-Lemaitre-Robertson-Walker (FLRW) universe. Finding analytical solutions for the dynamical black holes with all these properties is very important in theoretical physics. In the present work, we obtain Einstein’s field equations for our predicted dynamical black hole geometry and obtain analytical solutions using the energy-momentum tensor obeying imperfect fluid dynamics. Misner-Sharp-Hernandez mass, turnaround radius, and apparent horizon are analyzed and compared with the recent observations.

Barrow entropic cosmology with exponential potential field

In this paper, we consider an exponential potential [Formula: see text] in the framework of Barrow entropy under the constant-roll inflation and check their viability in the light of observable Planck 2020 data. By applying the first law of thermodynamics to the apparent horizon of the Universe, a modification of the Friedmann–Robertson–Walker (FRW) metric is derived in the context of Barrow entropy. We consider the early inflationary period of the universe to consist phenomenologically of a single inflationary state, that is, a state of the costant-roll inflation in which inflation is driven by an exponential potential field function. By fitting the constant-roll inflationary models to the observations, we examined the effect of the Barrow parameter [Formula: see text] on the inflation mechanism with the constant-roll parameter [Formula: see text]. As a result, we concluded that for a viable inflation, the observation limits of the inflation parameters determine that the constant-roll parameter is in the range [Formula: see text].

Dynamics of Apparent Horizon and a Null Comparison Principle

Dynamics of Apparent Horizon and a Null Comparison Principle

Entropy of dynamical black holes

We propose a new formula for the entropy of a dynamical black hole—valid to leading order for perturbations off of a stationary black hole background—in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in n dimensions. In stationary eras, this formula agrees with the usual Noether charge formula, but in nonstationary eras, we obtain a nontrivial correction term. In particular, in general relativity, our formula for the entropy of a dynamical black hole differs from the standard Bekenstein-Hawking formula A/4 by a term involving the integral of the expansion of the null generators of the horizon. We show that, to leading perturbative order, our dynamical entropy in general relativity is equal to 1/4 of the area of the apparent horizon. Our formula for entropy in a general theory of gravity is obtained from the requirement that a “local physical process version” of the first law of black hole thermodynamics hold for perturbations of a stationary black hole. It follows immediately that for first order perturbations sourced by external matter that satisfies the null energy condition, our entropy obeys the second law of black hole thermodynamics. For vacuum perturbations, the leading-order change in entropy occurs at second order in perturbation theory, and the second law is obeyed at leading order if and only if the modified canonical energy flux is positive (as is the case in general relativity but presumably would not hold in more general theories of gravity). Our formula for the entropy of a dynamical black hole differs from a formula proposed independently by Dong and by Wall. We obtain the general relationship between their formula and ours. We then consider the generalized second law in semiclassical gravity for first order perturbations of a stationary black hole. We show that the validity of the quantum null energy condition (QNEC) on a Killing horizon is equivalent to the generalized second law using our notion of black hole entropy but using a modified notion of von Neumann entropy for matter. On the other hand, the generalized second law for the Dong-Wall entropy is equivalent to an integrated version of QNEC, using the unmodified von Neumann entropy for the entropy of matter. Published by the American Physical Society 2024

Holographic vacuum energy regularization and corrected entropy of de Sitter space

Abstract We propose that the spectrum of the surface area of the apparent horizon (AH) of de Sitter (dS) spacetime leads to corrected temperature and entropy of the dS spacetime, offering new insights into its thermodynamic properties. This is done by employing the spectrum of the AH radius, acquired from the Wheeler--DeWitt (WDW) equation, together with the Stefan--Boltzmann law, the time-energy uncertainty relation, and the unified first law of thermodynamics.

Investigation of generalised uncertainty principle effects on FRW cosmology

Based on the entropy-area relation from Nouicer's generalised uncertainty principle (GUP), we derive the GUP modified Friedmann equations from the first law of thermodynamics at apparent horizon. We find a minimum apparent horizon due to the minimal length notion of GUP. We show that the energy density of universe has a maximum and finite value at the minimum apparent horizon. Both minimum apparent horizon and maximum energy density imply the absence of the Big Bang singularity. Moreover, we investigate the GUP effects on the deceleration parameter for flat case. Finally, we examine the validity of generalised second law (GSL) of thermodynamics. We show that GSL always holds in a region enclosed by apparent horizon for the GUP effects. We also investigate the GSL in ΛCDM cosmology and find that the total entropy change of universe has a maximum value in the presence of GUP effects. To better grasp the effects of Nouicer's GUP on cosmology, we compare our results with those obtained from quadratic GUP (QGUP).

Exponential correction to Friedmann equations

In this paper, employing the exponential corrected entropy (Chatterjee and Ghosh in Phys Rev Lett 125:041302, 2020), we derive the modified Friedmann equations from the first law of thermodynamics at apparent horizon and Verlinde’s entropic gravity scenario. First, we derive the modified Friedmann equations from the first law of thermodynamics. We investigate the validity of generalised second law (GSL) of thermodynamics and find that it is always satisfied for the all eras of universe. Moreover, we investigate the deceleration parameter for the case k=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=0$$\\end{document} in two frameworks. Finally, we numerically study the bouncing behaviour for the modified Friedmann equations obtained from entropic gravity. The results indicate that the bouncing behaviour is possible for the cases k=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=1$$\\end{document} and k=-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=-1$$\\end{document}.

Self-similar collapse in Painlevé–Gullstrand coordinates

We report a family of self-similar exact solutions in General Relativity. The solutions are found in a Painleve-Gullstrand coordinate system but can also be transformed smoothly into a diagonal form. The solutions represent a gravitational collapse leading to three possible outcomes, depending on the parameter space: (i) a collapse followed by a bounce and dispersal of the clustered matter distribution, (ii) a rapid collapse followed by a bounce and an eventual re-collapse, and (iii) a standard collapse leading to zero proper volume. Profiles of the energy conditions are studied for all of the scenarios, and it is noted that a bounce is usually associated with a violation of the Null Energy Condition. It is found that more than one null surfaces (apparent horizons) can develop during the collapse. We also discuss that for a general metric tensor having a conformal symmetry, some regions of the parameter space allows a formation of null throat, much like a wormhole. Matching the metric with a Schwarzschild metric in Painleve–Gullstrand form leads to the geodesic equation for a zero energy falling particle in the exterior.

Gravitational wave probes of Barrow cosmology with LISA standard sirens

We study the Barrow cosmological model, which proposes that quantum gravity effects create a complex, fractal structure for the universe's apparent horizon. We leverage the thermodynamics-gravity conjecture. By applying the Clausius relation to the apparent horizon of the Friedmann-Lemaître-Robertson-Walker universe within this framework, we derive modified field equations where the Barrow entropy is linked to the horizon. We assess the Barrow cosmology against current observations — cosmic microwave background, supernovae, and baryon acoustic oscillations data — and include projections for future Laser Interferometer Space Antenna (LISA) standard sirens (SS). Our numerical results suggest a modest improvement in the Hubble tension for Barrow cosmology with phantom dark energy behavior, compared to the standard cosmological model. Furthermore, incorporating simulated LISA SS data alongside existing observational constraints tightens the limitations on cosmological parameters, particularly the deformation exponent.

Cosmology of Barrow holographic QCD ghost dark energy and a look into the thermodynamics

The present study endeavours to study the cosmology of QCD ghost dark energy based on Barrow holographic fluid, a particular example of Nojiri-Odintsov holographic dark energy (2006, General Relativity and Gravitation, 38, 1285–1304); (2017, The European Physical Journal C, 77, 1–8). The Hubble parameter is reconstructed and according the equation of state parameter is reconstructed for the Barrow holographic QCD ghost dark energy. It is observed that the effective equation of state parameter has a transition from quintessence to phantom and for the current universe the equation of state parameter is very close to −1. The deceleration parameter is computed based on the reconstructed Hubble parameter and it is observed that the model can have a transition from decelerated to accelerated universe. The statefinder trajectories are plotted and an interpolation between dust and ΛCDM phases is observed. Finally, the thermodynamics is studied considering apparent horizon as the enveloping horizon of the Universe.

Closed FRW holography: a time-dependent ER=EPR realization

We extend a recent de Sitter holographic proposal and entanglement entropy prescription to generic closed FRW cosmologies in arbitrary dimensions, and propose that for large classes of bouncing and Big Bang/Big Crunch cosmologies, the full spacetime can be encoded holographically on two holographic screens, associated to two antipodal observers. In the expanding phase, the two screens lie at the apparent horizons. In the contracting phase, there is an infinite number of possible trajectories of the holographic screens, which can be grouped in equivalence classes. In each class the effective holographic theory can be derived from a pair of “parent” screens on the apparent horizons. A number of cases including moduli dominated cosmologies escape our discussion, and it is expected that two antipodal observers and their associated screens do not suffice to reconstruct these cosmologies. The leading contributions to the entanglement entropy between the screens arise from a minimal extremal trapped or anti-trapped surface lying in the region between them. This picture entails a time-dependent realization of the ER=EPR conjecture, where an effective geometrical bridge connecting the screens via the minimal extremal surface emerges from entanglement. For the Big Crunch contracting cases, the screens disentangle and the geometrical bridge closes off when the minimal extremal trapped sphere hits the Big Crunch singularity at a finite time before the collapse of the Universe. Semiclassical, thermal corrections are incorporated in the cases of radiation dominated cosmologies.