International Journal of Geometric Methods in Modern Physics

Thermodynamic extrinsic curvature is a new mathematical tool in thermodynamic geometry. By using the thermodynamic extrinsic curvature, one may obtain a more complete geometric representation of the critical phenomena and thermodynamics. We introduce nonperturbative thermodynamic extrinsic curvature of an ideal two-dimensional gas of anyons. Using extrinsic curvature, we find new fixed points in nonperturbative thermodynamics of the anyon gas that particles behave as semions. Here, we investigate the critical behavior of thermodynamic extrinsic curvature of two-dimensional Kagome Ising model near the critical point ${\beta }_c={(k_B{T}_c)}^{-1}$ in a constant magnetic field and show that it behaves as $|\beta -{\beta }_c{|}^{\alpha }$ with $\alpha =0$, where $\alpha$ denotes the critical exponent of the specific heat. Then, we consider the three-dimensional spherical model and show that the scaling behavior is $|\beta -{\beta }_c{|}^{\alpha }$, where $\alpha =-1$. Finally, using a general argument, we show that extrinsic curvature $K$ has two different scaling behaviors for positive and negative $\alpha$. For $\alpha >0$, our results indicate that $K\sim |\beta -{\beta }_c{|}^{\frac{1}{2}(\alpha -2)}$. However, for $\alpha <0$, we found a different scaling behavior, where $K\sim |\beta -{\beta }_c{|}^{\alpha }$.

The development and stability of acoustic thin-shell wormholes (WHs) within the context of acoustic black holes are examined in this paper. Utilizing linearized radial perturbations, the stability of these WHs is examined. In this study, a variety of equations of state are taken into account, including barotropic, variable Chaplygin, and phantom-like equations of state. According to the findings, the acoustic black hole structure has an unstable configuration for barotropic fluid. However, as the parameter ${ℰ}$ gets closer to zero, it does not show any stable or unstable configurations at the event horizon position. For higher values of $n$ and $\xi$, the resulting structure for the phantom-like variable equation of state (EoS) displays stable behavior away from the horizon while presenting unstable configurations close to the event horizon. The possibility of a stable structure rises as $n$ is increased. Additionally, the constructed structure exhibits stable behavior for $n=1$ under extreme acoustic black holes, whereas thin-shell topologies demonstrate unstable behavior outside the event horizon for the generalized Chaplygin variable EoS. However, the structure stabilizes for $n=1$ at higher values of $\xi$. The stability of acoustic thin-shell WHs is higher than that of Schwarzschild thin-shell WHs for smaller values of $n$, indicating that the acoustic black hole parameter greatly influences the stable configurations of thin-shell WHs.

This study investigated the formation and evolution of a strange star known as SAX.J1808.4–3658 in the Krori–Barua Rainbow spacetime, resulting from the collapse of string fluid. The study examined the dynamical variables derived from the field equations, taking into consideration the influence of the particle’s energy on the mass density, pressure, and string tension. Additionally, various techniques were employed to analyze the physical properties, including gradients, energy conditions, anisotropy, stability, the Tolman–Oppenheimer–Volkoff equation, mass function, compactness, and red-shift. The study’s findings revealed that the strange star SAX.J1808.4–3658 satisfies all the conditions necessary for its evolution from an anisotropic string fluid. This discovery suggests that strange stars might have emerged during the string-oriented quark era of the Universe. The researchers presented all the physical quantities within the frameworks of both rainbow gravity and general relativity, while also utilizing graphical representations to aid in comprehending the study’s findings. The energy conditions and anisotropy were found to be fulfilled, indicating the stability of the strange star. Furthermore, the Tolman–Oppenheimer–Volkoff equation was employed to determine the maximum mass of the strange star, which was found to align with observational data.

Observational evidence revealed that in the composition of the Universe, the dark energy is in heap proportion which is mainly responsible for the accelerated expansion of the Universe. The astrophysicists hypothesized that every astrophysical object is likely interact with the dark energy Sakti and Sulaksono [Phys. Rev. D 103 (2021) 084042]. Therefore, researchers are intended to study the astrophysical objects with dark energy interaction. In this paper, we proposed a dark energy stars (composed of with dark matter and ordinary matter) model in the Rastall theory of gravity. The Rastall field equations are obtained in the Tolman–Kuchowicz-type metric. To solve the field equations, the arbitrary constants involved in the field equations (due to Tolman–Kuchowicz ansatz) are obtained by matching the interior geometry with the exterior Schwarzschild geometry. The obtained solution is tested physically by computing some analytical results and plotting graphs of different physical parameters like pressure, density for ordinary matter, density for dark matter, mass function, compactness and surface redshift. Stability of the model is also analyzed by different tests like velocity of sound, adiabatic index and TOV equations. The influence of the Rastall parameter on the model has been studied by plotting graphs and computing numerical values of model’s physical parameters for different values of the Rastall parameter. We infer that our propounded model fulfills all the necessary requirements for a physically plausible model.

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Robertson Walker mini-superspace in $R^2$ gravity. Quantum wormhole satisfies Hawking Page wormhole boundary condition in the Euclidean background of mini-superspace, however, in the Lorentzian background wave functional turns to the usual oscillatory function. The Euclidean field equations for $\kappa =0,\pm 1$ lead to the wormhole configuration, as well as oscillating universe in Euclidean time $\tau$. The oscillating universe in Euclidean time $\tau$ transforms to an expanding universe only for $\kappa =1$ in Lorentz time $t$ under analytic continuation $\tau =it$ and asymptotically leads to an exponential solution. An Euclidean wormhole in the very early era evolves to an oscillating universe in $\tau$, thereafter crossing deSitter radius transition to an inflationary era is evident at later epoch only for $\kappa =1$.

This paper aims to provide a consistent, finite-valued, and mathematically well-defined reformulation of Feynman’s path-integral measure for quantum fields obtained by studying the Wiener stochastic process in the infinite-dimensional Hilbert space of quantum states. This reformulation will undoubtedly have a crucial role in formulating quantum gravity within a mathematically well-defined framework. In fact, this study is fundamentally different from any previous research on the relationship between Feynman’s path-integral and the Wiener stochastic process. In this research, we focus on the fact that the classic Wiener measure is no longer applicable in infinite-dimensional Hilbert spaces due to fundamental differences between displacements in low and extremely high dimensions. Thus, an analytic norm motivated by the role of the fractal functions in the Wilsonian renormalization approach is worked out to properly characterize Brownian motion in the Hilbert space of quantum states on a compact flat manifold. This norm, the so-called fractal norm, pushes the rougher functions (physically the quantum states with higher energies) to the farther points of the Hilbert space until the fractal functions as the roughest ones are moved to infinity. Implementing the Wiener stochastic process with the fractal norm, results in a modified form of the Wiener measure called the Wiener fractal measure, which is a well-defined measure for Feynman’s path-integral formulation of quantum fields. Wiener fractal measure has a complicated formula of non-local terms but produces the Klein–Gordon action at the first order of approximation. Using complex integrals to compensate for the removal of non-local terms appearing in higher orders of approximation, the Wiener fractal measure turns into a complex measure and generates Feynman’s path-integral formulation of scalar quantum fields. This brings us to the main objective of this study. Finally, some various significant aspects of quantum field theory (such as renormalizability, RG flow, Wick rotation, regularization, etc.) are revisited by means of the analytical aspects of the Wiener fractal measure.

In this study, our main focus is to investigate the mass–radius relation and several important properties of massive neutron stars to realize the nature, behavior and evolution of these kinds of compact objects at present time. Also, we want to understand the equation-of-state of the core nuclear matter precisely with their stable equilibrium configuration. We have chosen a few massive binary pulsars and investigated on maximum attainable mass and lowest possible radius of them. We have considered Einstein–Hilbert action as $f(R,T)=R+\alpha T$, where $R$ is the Ricci scalar and $T$, the trace of energy–momentum tensor with $\alpha$ as the coupling parameter and also used modified TOV equations. The interior space-time of the spherical neutron star is matched to the exterior Schwarzschild line element at the surface of the star. The $M$–$R$ curve can predict the maximum achievable mass is about $3.51M_{\odot }$ with lowest possible radius of around $10.5$ km for the massive compact stars under stable equilibrium. We have obtained a clear picture of structural evolution of massive neutron stars through accelerating space-time and can put some constraints on several quantities related to them. It is depicted from our present investigation that all the derived outcomes are compatible with physically adopted regimes which reveal the viability of our current model in the context of $f(R,T)$ modified gravity.

This research investigates the impact of modified gravity on cosmic scales, focusing on $f(Q)$ cosmology. By applying energy conditions, the study reconstructs various $f(Q)$ models, considering an accelerating Universe, quintessence, and a cosmological constant $\mathrm{\Lambda }$. Using up-to-date observational data, including the Supernova Pantheon sample and cosmic chronometer data, Hubble constants $H_0$ are estimated as $70.37_{-0.92}^{+0.84}$ km/s/Mpc (from $H(z)$ data) and $70.02_{-0.25}^{+0.44}$ km/s/Mpc (from pantheon compilation of SN Ia data). The matter energy density parameter (${\mathrm{\Omega }}_{0m}$) is calculated as $0.26_{-0.010}^{0.015}$ (OHD) and $0.27_{-0.014}^{0.025}$ (SN Ia). Furthermore, as a function of red-shift $z$, explicit expressions of $f(Q)$ and the EOS parameter $\omega$ are produced, and their graphical analysis describes the late time acceleration of the Universe without the usage of dark energy.

In this paper, we derive the Darboux solutions of Ito-type coupled KdV equation in Darboux framework which is associated with Hirota Satsuma systems. One of the main results is the generalization of $N$th-fold Darboux solutions in terms of Wronskians. We also derive the exact multi-soliton solutions for the coupled field variables of that system in the background of zero seed solutions. With the addition of these findings, we also enrich our results with the graphical interpretations of interacting solitons which preserve their profiles after the collision as usually solitons possess such property intrinsically. Subsequently, we construct the equation of continuity that yields the infinite conserved quantities associated with interacting phenomenon of multi-solitons.

The concept of wormholes is still hypothetical in physics but attractive among researchers. In this work, motivated by the important effect of $f(R,T)$ gravity theory, we seek the existence of wormhole solutions. We consider the field equations that can be derived from two different choices of matter Lagrangian density and utilize them to find the possibility of having some wormhole geometry. This procedure is based on the specific choice of an equation-of-state that obeys a certain physical requirement on the matter stress-energy [S. Kar and D. Sahdev, Restricted class of traversable wormholes with traceless matter, Phys. Rev. D 52 (1995) 2030]. For this purpose, the functional form of the redshift function is taken into consideration, and the possible existence of wormhole solutions is proven. Finally, the work examines the energy conditions and shows that violations of null energy conditions hold throughout spacetime.

In this work, we study the Chafee–Infante differential equation (CIDE) for various types of nonlinear waves (NW) like breather waves (BW), periodic cross-kink (PCKW), lump waves (LW), rogue waves (RW), periodic wave (PW), lump soliton (LS) with one kink, LS with two kink and periodic-cross lump waves (PCLW). The CIDE is a nonlinear evolution equation (NLEE) introduced by Nathaniel Chafee and Ettore Infante. This equation has been widely investigated in the context of pattern generation and soliton solutions, and it plays an essential role in understanding the complex nonlinear dynamics across a wide range of scientific fields. BW is a localized, non-dispersive solution to NW equations, maintaining shape and amplitude during travel. An LS is a type of solitary wave solution in NLEEs. In mathematics, RW refers to rare and unusually large solutions of NW equations. These waves have garnered significant attention due to their unpredictable and extreme nature. A PW is a type of wave that repeats its shape and behavior at regular intervals in both time and space. These waves are characterized by their periodicity, which means that they have a consistent and predictable pattern of oscillation. We’ll offer a graphical explanation of our newly discovered answers toward the conclusion.

This study explores the generalized embedded wormhole (WH) solutions in the background of $f({ℛ},{𝒢})$ gravity, where ${ℛ}$ represents the Ricci scalar and ${𝒢}$ denotes the Gauss–Bonnet invariant. To investigate the necessary structures of the WH solutions we thoroughly analyzed the energy conditions under $f({ℛ},{𝒢})$ gravity within the anisotropic source of matter. To meet this aim, we consider spherically symmetric geometry with the most generic gravity model of the gravity. A modified version of the field equations is calculated for two different embedded WH solutions. All the energy conditions are calculated and shown graphically with the regional ranges of the model parameter. Further, the invalid region of the energy conditions confirms the presence of exotic matter. Finally, we have concluding remarks.

In this paper, we present comparisons of the deflection angles of massless and massive particles in the Schwarzschild space-time. For the case of photons in a general static space-time, we construct a spatial 3D equation of motion for their path that leads to an implicit formula for the deflection angle. We then compare our results with well-known results of the literature in the Schwarzschild space-time. For the case of massive particles, we calculate the deflection angle only in the Schwarzschild space-time. The end result is that as the velocity of any massive particle diminishes, the deflection angle increases. To show the relevance of these comparisons, we constructed different black hole shadows for massive particles in order to be compared with a shadow made by photons.

This paper is an investigation of dark energy cosmological models in non-coincident gauge formulation of non-metricity gravity with boundary term. We have considered an arbitrary function $f(Q,C)=Q+\lambda C^m$, where $Q$ is the non-metricity scalar, $C$ is the boundary term derived by $C=\mathring{R}-Q$, and $\lambda ,m$ are the model parameters, to obtain the modified field equations from action. We have parameterized the Hubble function as $H(a)=k_0(a{(t)}^{-n}+k_1)$ with $n,k_0,k_1$ are arbitrary constants and $a(t)$ is the scale-factor depending upon cosmic time. We have compared this Hubble function with $H(z)$ datasets and obtained best fit values of model parameters using likelihood analysis. Using these best fit values of model parameters, we have done our result analysis and discussion with cosmological parameters viz effective equation of state parameter, energy density, energy conditions, deceleration parameter, om diagnostic analysis and age of the universe. We have found a transit phase universe model with effective EoS parameter $-1.18<{\omega }^{\mathrm{\text{eff}}}<-0.2$ over redshift $-1<z<3$.

The ambiguity of the Weitzenböck connection is investigated from the perspective of frames. In doing so, the pure-tetrad formalism and the formalism with an affine connection are compared with each other; it is shown that the ambiguity in the affine connection is equivalent to that of the frame. The role played by the regularization procedure is discussed, and it is argued that the frame approach gives better results than any regularization procedure, including those that make use of a suitable choice of the affine connection. It is also argued that, for consistency, the Weitzenböck torsion must be either manifesting only gravitational effects or gravitational effects plus accelerations. Two possible interpretations for the torsion tensor are present, and an application to a frame that accelerates along the same direction as that of a $pp$-wave is used to show the consistence of these interpretations. Finally, some possible solutions to the well-known problems of the $f(T)$ theories are proposed.

In this work, we investigate the behavior of non-relativistic quantum particles immersed in a cosmic string space-time background. Our study involves the examination of these particles as they interact with a range of influences, including potential, magnetic, and quantum flux fields. We employ analytical methods to solve the associated wave equation, leading to the derivation of eigenvalue solutions for this quantum system. Subsequently, we leverage these eigenvalue solutions to scrutinize several potential models. For each model, we present and engage in a thorough discussion of the corresponding eigenvalue solutions. In an extension of our investigation, we explore the thermodynamic and magnetic properties of the quantum system when it is exposed to non-zero temperature conditions, denoted by $T\ne 0$. Our analysis encompasses the calculation of essential parameters such as the partition function for the system and other pertinent functions. Following these calculations, we meticulously examine and interpret the outcomes, shedding light on the system’s behavior and characteristics in the presence of temperature variations. Furthermore, we calculate entropic information to investigate the location of particles in the system.

In this paper, we establish a connection between Sisyphus dynamics and the Liénard-II equation through branched Hamiltonians. Sisyphus dynamics stem from a higher-order Lagrangian. Surprisingly, when expressed in terms of velocity, the Sisyphus dynamical equations align closely with the Liénard-II equation. Sisyphus dynamics introduces velocity-dependent “mass functions”, a departure from conventional position-dependent mass, potentially linked to cosmological time crystals. Additionally, we demonstrate that spontaneously broken time translational symmetry results in a deformed symplectic structure, resembling the classical counterpart of the Generalized Uncertainty Principle (GUP).

The novel forms of the split octonionic Dirac equation and its corresponding Lagrangian are derived using symbolic computing techniques.