Apparent Horizon Research Articles

Kaniadakis entropy-based characterization of IceCube PeV neutrino signals

Kaniadakis κ-thermostatistics is by now recognized as an effective paradigm to describe relativistic complex systems obeying power-law tailed distributions, as opposed to the classical (exponential-type) decay. It is founded on a non-extensive one-parameter generalization of the Bekenstein-Hawking entropy, which, in the cosmological framework, gives rise to modified Friedmann equations on the basis of the gravity-thermodynamic conjecture. Assuming the entropy associated with the apparent horizon of the Friedmann–Robertson–Walker (FRW) Universe follows Kaniadakis prescription, in this work we analyze the observed discrepancy between the present bound on the Dark Matter relic abundance and the IceCube high-energy (∼1PeV) neutrinos. We show that this tension can be alleviated in the minimal model of Dark Matter decay with Kaniadakis-governed Universe evolution, while still considering the 4-dimensional Yukawa coupling between Standard Model and Dark Matter particles. This argument phenomenologically supports the need for a Kaniadakis-like generalization of the Boltzmann–Gibbs–Shannon entropy in the relativistic realm, opening new potential scenarios in high-energy astroparticle physics.

Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.

Signature flip in deceleration parameter: a thermodynamic phase transition?

Using the Hayward–Kodama temperature for the apparent horizon, it is found that matter content in the Universe is not thermodynamically stable, and the entry to the late accelerated expansion is actually a second order phase transition. The cosmological model used for the purpose is one that imitates the varLambda CDM model, the favoured model for the present Universe.

Schrödinger and Klein–Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse

The Schrödinger equation of the Schwarzschild black hole (BH) has been recently derived by the author and collaborators. The BH is composed of a particle, the ‘electron’, interacting with a central field, the ‘nucleus’. Via de Broglie’s hypothesis, one interprets the ‘electron’ in terms of BH horizon’s modes. Quantum gravity effects modify the BH semi-classical structure at the Schwarzschild scale rather than at the Planck scale. The analogy between this BH Schrödinger equation and the Schrödinger equation of the s states of the hydrogen atom permits us to solve the same equation. The quantum gravitational quantities analogous of the fine structure constant and of the Rydberg constant are not constants, but the dynamical quantities have well-defined discrete spectra. The spectrum of the ‘gravitational fine structure constant’ is the set of non-zero natural numbers. Therefore, BHs are well-defined quantum gravitational systems obeying Schrödinger’s theory: the ‘gravitational hydrogen atoms’. By identifying the potential energy in the BH Schrödinger equation as being the gravitational energy of a spherically symmetric shell, a different nature of the quantum BH seems to surface. BHs are self-interacting, highly excited, spherically symmetric, massive quantum shells generated by matter condensing on the apparent horizon, concretely realizing the membrane paradigm. The quantum BH described as a ‘gravitational hydrogen atom’ is a fictitious mathematical representation of the real, quantum BH, a quantum massive shell having a radius equal to the oscillating gravitational radius. Nontrivial consequences emerge from this result: (i) BHs have neither horizons nor singularities; (ii) there is neither information loss in BH evaporation, nor BH complementarity, nor firewall paradox. These results are consistent with previous ones by Hawking, Vaz, Mitra and others. Finally, the special relativistic corrections to the BH Schrödinger equation give the BH Klein–Gordon equation and the corresponding eigenvalues.

Modified Friedmann equations from fractional entropy

Based on the fractional black-hole entropy (Jalalzadeh S. et al., Eur. Phys. J. C, 81 (2021) 632), we derive the modified Friedmann equations from two different frameworks. First, we consider the modifications of Friedmann equations from the first law of thermodynamics at the apparent horizon. We show that the generalized second law (GSL) of thermodynamics always holds in a region bounded by the apparent horizon. Then, we obtain Friedmann equations from Verlinde's entropic gravity framework. We also compute the fractional corrections to the deceleration parameter q in the flat case k = 0 for both frameworks. Furthermore, we consider the time to reach the initial singularity for the two frameworks. The results indicate that the initial singularity is accessible for both frameworks. However, fractional effects may provide a constraint on the equation-of-state parameter in the entropic gravity scenario since the time is imaginary for .

Modified cosmology from quantum deformed entropy

Jalalzadeh (2022), established that the thermodynamical entropy of a quantum-deformed black hole with horizon area A can be written as Sq=πsinA8GN/sinπ2N, where N=Lq2/LP2, LP being the Planck length and Lq denoting, generically, the q-deformed cosmic event horizon distance Lq. Motivated by this, we now extend the framework constructed in Jalalzadeh (2022) towards the Friedmann and Raychaudhuri equations describing spatially homogeneous and isotropic universe dynamics. Our procedure in this paper involves a twofold assumption. On the one hand, we take the entropy associated with the apparent horizon of the Robertson–Walker universe in the form of the aforementioned expression. On the other hand, we assume that the unified first law of thermodynamics, dE=TdS+WdV, holds on the apparent horizon. Subsequently, we find a novel modified cosmological scenario characterized by quantum-deformed (q-deformed) Friedmann and Raychaudhuri equations containing additional components that generate an effective dark energy sector. Our results indicate an effective dark energy component, which can explain the Universe’s late-time acceleration. Moreover, the Universe follows the standard thermal history, with a transition redshift from deceleration to acceleration at ztran=0.5. More precisely, according to our model, at a redshift of z=0.377, the effective dark energy dominates with a de Sitter universe in the long run. We include the evolution of luminosity distance, μ, the Hubble parameter, H(z), and the deceleration parameter, q(z), versus redshift. Finally, we have conducted a comparative analysis of our proposed model with others involving non-extensive entropies.

Generalized Vaidya spacetime: Horizons, conformal symmetries, surface gravity and diagonalization

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.

Magnetic string matter collapse in rainbow gravity

This work investigates the dynamics of a collapsing magnetic string dust and string fluid in the Plank Era via spherically symmetric rainbow geometry. The field equations are modified and solved to obtain the dynamical quantities, including mass density, pressure, string tension, and magnetic field strength. These quantities are presented graphically. The energy conditions are computed showing that all the dynamical quantities are associated with physical matter. The distance and moment of apparent horizon formation are computed. The magnetic field is found to affect the distance and moment of the apparent horizon’s formation. It accelerates the collapsing process. Further, the dynamical variables are maximum in the collapsing configuration’s center leading to compact object (black hole) formation. The probing particle’s energy affects all the dynamical variables of the fluid in a direct proportion. This resolves the information paradox as a particle with greater energy grasps the information from a particle with lesser energy and takes it out in the real world.

First law of thermodynamics and entropy of FLRW universe in modified gravity

We investigate the first law of thermodynamics and entropy associated to the apparent horizon of (non-flat) FLRW space–time in different theories of modified gravity and in the presence of a perfect fluid of matter. We pose our attention on those theories which lead to second order differential field equations on FLRW background. In this way, we observe that one may obtain a formula for entropy in terms of the radius of the apparent horizon only. Thus, when considering a modification to the area law of General Relativity, it is possible to reconstruct the gravitational lagrangian consistent with the corresponding first law.

Exploring modifications to FLRW cosmology with general entropy and thermodynamics: A new approach

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.

Canonical quantization of modified non-gauge invariant Einstein-Maxwell gravity and stability of spherically symmetric electrostatic stars

We consider a non-minimally coupled Einstein-Maxwell gravity with no U(1) symmetry property to study stability of an electrostatic star via canonical quantization approach and obtain that the stability is free of gauge field effects. By calculating the Hamiltonian density of the stellar system we show that the corresponding Wheeler-DeWitt wave functional is similar to a simple harmonic quantum Oscillator for which a non zero ADM mass of the system causes a quantization condition on the metric fields. Probability wave packets are described by the Hermit polynomials. Our mathematical calculations show that in this approach of quantum gravity the metric fields are regular for all values of the electric potential and so the quantized spacetime has not both of event and apparent horizons. The most probability of the quantized line element is for ground state of the system. To check validation of the model we use Bohr's correspondence principal and generate directly semi classical approach of the quantized metric states at large quantum numbers where they reach to Schwarzschild like metric according to the Birkhoff’s theorem. Also we check that the generated semi classical solutions are satisfied exact classical metric solutions which are obtained from Euler–Lagrange equations. We show that ‘charge to mass ratio’ of the electrostatic star is a constant defined by the coupling constant of the model and it is in accord to other alternative approaches.

Perturbative Solution of the Einstein Constraints with Spin and Momentum Far Away From a Binary Source in the Bowen‐York Formalism

AbstractThe momentum and Hamiltonian constraints of vacuum Einstein equations, within the Bowen‐York formalism, for two interacting black holes in close separation, with anti‐parallel spins and anti‐parallel linear momenta is studied. An analytical solution using perturbation theory is given. The location and the shape of the apparent horizon which generically depend on all the parameters, angles, and the separation between the black holes are also computed. The solution only works for distances far away from the black holes. To gain more insight close into the black holes, one has to go to the higher orders in perturbation theory, which is a rather cumbersome process. But the solution presented here can be of some use for numerical computations as the latter should match our result for the described problem.

Thermodynamics and Perturbative Analysis of Some Newly Developed F(R,Lm,T)$\mathcal {F}(R,L_m, T)$ Theories Under the Scenario of Conserved Energy‐momentum Tensor

AbstractThe present work is devoted to explore some interesting cosmological features of a newly proposed theory of gravity namely theory, where R and T represent the Ricci scalar and trace of energy momentum‐tensor, respectively. First, a non‐equilibrium thermodynamical description is considered on the apparent horizon of the Friedmann's cosmos. The Friedmann equations are demonstrated to be equivalent to the first law of thermodynamics, i.e., , where refers to entropy production term. The constraint for validity of generalized second law of thermodynamics is also formulated and checked it for some simple well‐known forms of generic function . Next, the energy bounds for this framework and constraint the free variables by finding the validity regions for NEC and WEC are developed. Furthermore, some interesting cosmological solutions namely power law, ΛCDM, and de Sitter models in this theory are reconstructed. The reconstructed solutions are then examined by checking the validity of GSLT and energy bounds. Lastly, the stability of all reconstructed solutions by introducing suitable perturbations in the field equations is analyzed. It is concluded that obtained solutions are stable and cosmologically viable.

Astrophysical implications of an eternal homogeneous gravitational collapse model with a parametrization of expansion scalar

In this study, we continue our previous work (Annu et al. 2023) by introducing a novel parametrization of the expansion scalar Theta as a rational function of time t. The paper provides a comprehensive analysis of a homogeneous gravitational collapsing system, wherein the exact solutions of the Einstein field equations (EFEs) are determined using a new parametrization of Theta in a model-independent way. The model is especially significant for the astrophysical applications because we have addressed the physical and geometrical quantities of the model in terms of Schwarzschild mass M. We have estimated the numerical value of the model parameter involved in the functional form of Theta -parametrization using the masses and radii data of some massive stars namely, Westerhout 49-2, BAT99-98, R136a1, R136a2, WR 24, Pismis 24-1, lambda Cephei, alpha Camelopardalis, beta Canis Majoris. We have presented theoretical investigations about such astrophysical stellar systems. The formation of an apparent horizon is also studied for the collapsing system, and it has been shown that our model produces a continuing collapsing scenario of star (an eternal collapsing object).

Black Hole Spectra from Vaz's Quantum Gravitational Collapse

AbstractIn 2014, in a famous paper Hawking strongly criticized the firewall paradox by claiming that it violates the equivalence principle and breaks the CPT invariance of quantum gravity. He proposed that the final result of the gravitational collapse should not be an event horizon, but an apparent horizon instead. On the other hand, Hawking did not give a mechanism for how this could work. In the same year, Vaz endorsed Hawking's proposal in a quantum gravitational model of dust collapse by winning the Second Prize in the 2014 Gravity Research Foundation Essay Competition. He indeed showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler‐DeWitt equation. Vaz's interpretation of the paradox was in terms of simply forbidding such a combination. This leads naturally to matter condensing on the apparent horizon during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. In this work we derive the BH mass and energy spectra via a Schrodinger‐like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact “dark star”. This “gravitational atom” is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, by evoking the generalized uncertainty principle, the maximum value of the density of Vaz's shell will be estimated.

Islands in proliferating de Sitter spaces

We study two-dimensional de Sitter universe which evolves and proliferates according to the Ginsparg-Perry-Bousso-Hawking mechanism, using Jackiw-Teitelboim gravity coupled to conformal matter. Black holes are generated by quantum gravity effects from pure de Sitter space and then evaporate to yield multiple disjoint de Sitter spaces. The back-reaction from the matter CFT is taken into account for the dilaton as a function of the temperature of the CFT. We discuss the evaporation of black holes and calculate the finite temperature entropy of an inflating region using the island formula. We find that the island moves towards the apparent horizon of the black hole as the temperature increases. The results are applied to the case of multiple evaporating black holes, for which we suggest multiple islands.

Constraining barrow entropy-based cosmology with power-law inflation

We study the inflationary era of the Universe in a modified cosmological scenario based on the gravity-thermodynamics conjecture with Barrow entropy instead of the usual Bekenstein–Hawking one. The former arises from the effort to account for quantum gravitational effects on the horizon surface of black holes and, in a broader sense, of the Universe. First, we extract modified Friedmann equations from the first law of thermodynamics applied to the apparent horizon of a Friedmann–Robertson–Walker Universe. Assuming a power-law behavior for the scalar inflaton field, we then investigate how the inflationary dynamics is affected in Barrow cosmological setup. We find that the inflationary era may phenomenologically consist of the slow-roll phase, while Barrow entropy is incompatible with kinetic inflation. By demanding observational consistency of the scalar spectral index and tensor-to-scalar ratio with recent Planck data, we finally constrain Barrow exponent to Delta lesssim mathcal {O}(10^{-4}), which is the most stringent bound in so-far literature.

A new constraint on the Hawking evaporation of primordial black holes in the radiation-dominated era

In this paper, we revisit the evaporation and accretion of primordial black holes (PBHs) during cosmic history and compare them to see if both of these processes are constantly active for PBHs or not. Our calculations indicate that during the radiation-dominated era, PBHs absorb ambient radiation due to accretion, and their apparent horizon grows rapidly. This growth causes the Hawking radiation process to practically fail and all the particles that escape as radiation from PBHs to fall back into them. Nevertheless, our emphasis is that the accretion efficiency factor also plays a very important role here and its exact determination is essential. We have shown that the lower mass limit for PBHs that have not yet evaporated should approximately be 10^{14}g rather than 10^{15}g. Finally, we study the effects of Hawking radiation quiescence in cosmology and reject models based on the evaporation of PBHs in the radiation-dominated era.

Spatial curvature and thermodynamics

ABSTRACTReasonable parametrizations of the current Hubble data set of the expansion rate of our homogeneous and isotropic universe, after suitable smoothing of these data, strongly suggest that the area of the apparent horizon increases irrespective of whether the spatial curvature of the metric is open, flat, or closed. Put in another way, any sign of the spatial curvature appears consistent with the second law of thermodynamics.

Holographic Dark Energy in Modified Barrow Cosmology

Thermodynamics-gravity conjecture implies that there is a deep connection between the gravitational field equations and the first law of thermodynamics. Therefore, any modification to the entropy expression directly modifies the field equations. By considering the modified Barrow entropy associated with the apparent horizon, the Friedmann equations are modified as well. In this paper, we reconsider the holographic dark energy (HDE) model when the entropy is in the form of Barrow entropy. This modification to the entropy not only changes the energy density of the HDE but also modifies the Friedmann equations. Therefore, one should take into account the modified HDE in the context of modified Friedmann equations. We study the Hubble horizon and the future event horizon as IR cutoffs and investigate the cosmological consequences of this model. We also extend our study to the case where dark matter (DM) and dark energy (DE) interact with each other. We observe that Barrow exponent δ significantly affects the cosmological behavior of HDE, and in particular, the equation of state (EoS) parameter can cross the phantom line (wde<-1). Additionally, adding δ remarkably affects the deceleration parameter and shifts the time of universe phase transition.