Black hole thermodynamics from logotropic fluids

We assume the negative cosmological constant as a thermodynamic pressure and the anti-de Sitter (AdS) black hole thermodynamics with modified Chaplygin gas. We write the mass, volume, entropy and temperature of the black hole due to the thermodynamic system. We find a new solution of the Einstein’s field equations of AdS black hole with modified Chaplygin gas as a thermodynamic system. We examine the weak, strong and dominant energy conditions for the source fluid of black hole. We also show that the thermodynamic black hole with Chaplygin gas can be considered as a heat engine, and then we calculate work done and its efficiency by this system.

Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois–Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows us to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild–de Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analysed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild–anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a0 ⩽ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild–anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild–de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.

Locally Rotationally Symmetric (LRS) Bianchi type-I metric is examined in the presence of perfect fluid. Exact solutions of Einstein’s field equations (EFE) have been studied by taking into account a hyperbolic scale factor. We observed that the model has initial singularity. It is found that the Universe approaches isotropy at late times. Through state finder pair [Formula: see text], it is observed that at late cosmic time, the model behaves analogous to [Formula: see text]CDM model. Energy conditions of the model are studied and it is found that null energy condition (NEC), weak energy condition (WEC) and dominant energy conditions (DEC) are satisfied for our model while SEC is violated. We investigate some physically and geometrically realistic models in order to develop a viable cosmological model.

The study of energy conditions has many significant applications in general relativistic and cosmological contexts. This paper explores the energy conditions in the framework of the most general scalar-tensor theory with field equations involving second-order derivatives. For this purpose, we use flat FRW universe model with perfect fluid matter contents. By taking power law ansatz for scalar field, we discuss the strong, weak, null, and dominant energy conditions in terms of deceleration, jerk, and snap parameters. Some particular cases of this theory likek-essence model, modified gravity theories and so forth. are analyzed with the help of the derived energy conditions, and the possible constraints on the free parameters of the presented models are determined.

In isotropic loop quantum cosmology, non-perturbatively modified dynamics of a minimally coupled scalar field violates weak, strong and dominant energy conditions when they are stated in terms of the equation-of-state parameter. The violation of the strong energy condition helps to have non-singular evolution by evading singularity theorems thus leading to a generic inflationary phase. However, the violation of weak and dominant energy conditions raises concern, as in general relativity these conditions ensure causality of the system and stability of vacuum via the Hawking–Ellis conservation theorem. It is shown here that the non-perturbatively modified kinetic term contributes negative pressure but positive energy density. This crucial feature leads to the violation of energy conditions but ensures the positivity of energy density, as the scalar matter Hamiltonian remains bounded from below. It is also shown that the modified dynamics restricts group velocity for inhomogeneous modes to remain sub-luminal thus ensuring causal propagation across spatial distances.

In this study, we investigate anisotropic Bianchi Type VI cosmological model within the framework of fractal universe. By utilizing the energy–momentum tensor for a perfect fluid, we solve the corresponding field equations. In this study, we derive leading cosmological parameters, including the hubble parameter H and deceleration parameter q in terms of cosmic time and redshift also. To determine the model parameters such as k, [Formula: see text] and the hubble constant [Formula: see text], the hubble dataset was analyzed using the [Formula: see text] test. This analysis reveals the best-fit values of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] match with the [Formula: see text]CDM model. We carry blow-by-blow analysis of the model’s characteristics via energy density [Formula: see text], pressure p and EoS parameter. We examine whether the energy conditions — null energy condition (NEC), strong energy condition (SEC), weak energy condition (WEC) and dominant energy condition (DEC) — are satisfied. Furthermore, the diagnostic parameters are analyzed to evaluate the deviation of the obtained model from the [Formula: see text]CDM model and to classify various dark energy models during the universe’s expansion. The om diagnostic is depicted as a function of redshift for [Formula: see text] and [Formula: see text] revealing that [Formula: see text] settles around [Formula: see text] with slight deviation in the range [Formula: see text]. The model closely aligns with [Formula: see text]CDM at higher redshifts. The pair of statefinder diagnostics r versus s is also discussed, and our model for [Formula: see text] represents the [Formula: see text]CDM model.

The present research paper discusses the derivation for the change in entropy of Non- spinning black holes with respect to the change in the radius of event horizon applying the first law of black hole mechanics (\(\delta M = \frac{\kappa}{8\pi} \delta A + \varOmega\delta J - \upsilon\delta Q\)) with the relation for the change in entropy δS=8πMδM. When the work is further extended with proper operation, the entropy of black hole is obtained almost the same as the Bekenstein-Hawking entropy of black hole. This is the entirely new method to obtain the change in entropy of Non-spinning black holes w.r.t. the radius of event horizon and Hawking entropy of black hole. We have also calculated their values for different types of test non-spinning black holes having masses 5–20M⊙ found in X-ray binaries (Narayan, gr-qc/0506078v1, 2005).

In the context of current scenario, it is crucial to look beyond Einstein’s theory, which opens the door to certain modified theories of gravity. So, present study is devoted to investigate the various energy conditions, particularly, strong energy condition (SEC), weak energy condition (WEC), null energy condition (NEC) and dominant energy condition (DEC) corresponding to different functional forms of f(R) gravity. We have studied for flat, isotropic and homogeneous FLRW cosmological model filled with interacting field i.e., perfect fluid is coupled with mass less scalar field for different models of modified f(R) gravity in which R is the Ricci scalar. We have observed, the accelerated expansion of the Universe which exact match with recent observational evidences.

We obtain Traversable Wormholes in the 4D Einstein-Gauss-Bonnet (4D-EGB) gravity with phenomenological Bose-Einstein Condensates (BEC) dark matter. The 4D-EGB gravity considered here results from a regularization of the higher-dimensional EGB gravity in the limit $D \to 4$. The rescaled Gauss-Bonnet coupling parameter ($\alpha$) plays an important role to admit spherically symmetric traversable wormholes (TW). Considering the energy density profile of non-relativistic BEC matter, the shape function of the TW geometry is determined. Thereafter, all the energy conditions namely, Null energy condition (NEC), Strong energy condition, Weak energy condition, and Dominant energy condition are analyzed for a constant redshift function. The flaring-out and asymptotic flatness conditions are probed for a realistic scenario. The embedding diagram of the TW is also analyzed along with proper radial distance, volume integral quantifier, and pressure anisotropy. TW obtained here are found stable at the throat when $\alpha = - 0.0512471$ with a set of model parameters, which are determined from the acceptable sound speed measurement. In the 4D Einstein-Gauss-Bonnet (EGB) gravity, all the energy conditions are satisfied for $\alpha \in [-4.222,-4]$ with a set of model parameters. There is a range of $\alpha$ for which exotic properties of the BEC DM is not needed to sustain the TW throat, which is a new observation in modified 4D EGB gravity with BEC Dark Matter profile.

Tsallis holographic dark energy model in an anisotropic universe with linearly varying deceleration parameter and its correspondence with phantom

In this paper, we study a spatially homogeneous and anisotropic Bianchi type-III universe containing cold dark matter and Barrow holographic dark energy within the framework of General Relativity. We assume the cold dark matter and Barrow holographic dark energy to be non-interacting and obtain exact solutions of the Einstein field equations by considering a hybrid expansion law and assuming that the expansion scalar is proportional to the shear scalar. We examine the physical and kinematical properties of the resulting model using parameters such as the Hubble parameter, the anisotropic parameter, the deceleration parameter, the equation of state parameter, the jerk parameter etc. We also examine whether the energy conditions are violated or validated. We find that the Null, Weak, and Dominant energy conditions are fulfilled, while the Strong Energy Condition is violated, which supports the accelerated expansion of the universe. The Statefinder diagnostics have been conducted based on recent cosmological observations. In addition, wereformulated the correspondence between quintessence scalar field and Barrow holographic dark energy model.

This research work discusses the energy bounds in [Formula: see text] gravity with an anisotropic background, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of the energy–momentum tensor. For our study, we consider the locally rotationally symmetric Bianchi Type-I space-time. Moreover, we calculate the field equations and find exact solutions by considering different [Formula: see text] gravity models. We investigate the graphical behavior of energy density and pressure components by considering these distinct gravity models. We further use Hubble, deceleration, jerk, and snap parameters to evaluate the viability of our models. We also perform the graphical analysis to observe the behavior of energy conditions especially null energy conditions, weak energy conditions, strong energy conditions, and dominant energy conditions. It can be noticed that all considered [Formula: see text] gravity models support the idea of the presence of exotic matter, which justifies the phenomenon of expansion of the universe.

In this paper, we study the traversable wormhole solutions for a logarithmic corrected [Formula: see text] model by considering two different statements of shape [Formula: see text] and redshift [Formula: see text] functions. We calculate the parameters of the model including energy density [Formula: see text], tangential pressure [Formula: see text] and radial pressure [Formula: see text] for the corresponding forms of the functions. Then, we investigate different energy conditions such as null energy condition, weak energy condition, dominant energy condition and strong energy condition for our considered cases. Finally, we explain the satisfactory conditions of energy of the models by related plots.

We study the behavior of a massless, quantized, scalar field on a two-dimensional cylinder spacetime as it responds to the time-dependent evolution of a Mamev-Trunov potential of the form $V(x,t) = 2 \xi \delta(x) \theta(-t)$. We begin by constructing mode solutions to the classical Klein-Gordon-Fock equation with potential on the whole spacetime. For a given eigen-mode solution of the IN region of the spacetime ($t<0$), we determine its evolution into the OUT region ($t>0$) through the use of a Fourier decomposition in terms of the OUT region eigen-modes. The classical system is then second quantized in the canonical quantization scheme. On the OUT region, there is a unitarily equivalent representation of the quantized field in terms of the OUT region eigen-modes, including zero-frequency modes which we also quantize in a manner which allows for their interpretation as particles in the typical sense. After determining the Bogolubov coefficients between the two representations, we study the production of quanta out of the vacuum when the potential turns off. We find that the number of "particles" created on the OUT region is finite for the standard modes, and with the usual ambiguity in the number of particles created in the zero frequency modes. We then look at the renormalized expectation value of the stress-energy-tensor on the IN and OUT regions for the IN vacuum state. We find that the resulting stress-tensor can violate the null, weak, strong, and dominant energy conditions because the standard Casimir energy-density of the cylinder spacetime is negative. Finally, we show that the same stress-tensor satisfies a quantum inequality on the OUT region.

In this paper, the dissipative mechanism (bulk viscosity and matter creation) is introduced to describe the effects of cosmic non-perfect fluid on the Ricci dark energy (RDE) model. We consider matter creation and bulk viscosity as two independent irreversible processes. Assuming suitable forms of the bulk viscous coefficient and matter creation rate, we find the exact solution of the field equations. We carry out fitting analysis on the cosmological parameters in the model by using Type Ia supernovae data, observational Hubble data and baryon acoustic oscillation (BAO) data with cosmic microwave background. We plot the trajectory of cosmological parameters with the best-fit values of model parameters and discuss all possible (deceleration, acceleration and their transitions) evolutions of the model. The current values of deceleration parameter and equation of state parameter are found to be $$q_0=-0.362$$ and $$\omega _{\mathrm {eff}}=-0.575$$ , respectively. The age of the Universe is found to be $$t_0\simeq 13.397$$ Gyr, which is very close to the $$\Lambda $$ CDM model. We further discuss the geometrical diagnostic parameters such as statefinder and Om to distinguish the model with $$\Lambda $$ CDM model. Finally, we discuss the behaviour of energy conditions for our model and find that the model satisfies the null energy condition (NEC), weak energy condition (WEC) and dominant energy condition (DEC) while it violates strong energy condition (SEC).