General Relativity and Quantum Cosmology (gr-qc)

Abstract: The current study examines the geometry of static wormholes with anisotropic matter distribution in context of modified $f(\mathcal{G})$ gravity. We consider the well known Noether and conformal symmetries, which help in investigating wormholes in $f(\mathcal{G})$ gravity. For this purpose, we develop symmetry generators associated with conserved quantities by taking into consideration the $f(\mathcal{G})$ gravity model. Moreover, we use the conservation relationship gained from the classical Noether method and conformal Killing symmetries to develop the metric potential. These symmetries provide a strong mathematical background to investigate wormhole solutions by incorporating some suitable initial conditions. The obtained conserved quantity performs a significant role in defining the essential physical characteristics of the shape-function and energy conditions. Further, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition in modified $f(\mathcal{G})$ gravity. It is observed from graphical representation of obtained wormhole solutions that Noether and conformal Killing symmetries provide the results with physically accepted patterns.

Abstract: We argue that, as long as relativistic quantum particles are in point, the variable $y=E/E_p$ of the rainbow functions pair $g_{_{0}} (y)$ and $g_{_{1}} (y)$ should be fine tuned into $y=|E|/E_p$, where $E_p$ is the Planck's energy scale. Otherwise, the rainbow functions will be only successful to describe the rainbow gravity effect on relativistic quantum particles and the anti-particles will be left unfortunate. Under such fine tuning, we consider Klein-Gordon (KG) particles in cosmic string rainbow gravity spacetime in a non-uniform magnetic field (i.e., $\mathbf{B}=\mathbf{\nabla }\times \mathbf{A}=\frac{3}{2}B_{\circ }r\,\hat{z}$ ). Then we consider KG-particles in cosmic string rainbow gravity spacetime in a uniform magnetic field (i.e., $\mathbf{B}=\mathbf{\nabla }\times \mathbf{A}=\frac{1}{2}B_{\circ }\,\hat{z}$ ). Whilst the former effectively yields KG-oscillators, the later effectively yields KG-Coulombic particles. We report on the effects of rainbow gravity on both KG-oscillators and Coulombic particles using four pairs of rainbow functions: (i) $% g_{_{0}}\left( y\right) =1$, $g_{_{1}}\left( y\right) =\sqrt{1-\epsilon y^{2}% }$, (ii) $g_{_{0}}\left( y\right) =1$, $g_{_{1}}\left( y\right) =\sqrt{% 1-\epsilon y}$, (iii) $g_{_{0}}\left( y\right) =g_{_{1}}\left( y\right) =\left( 1-\epsilon y\right) ^{-1}$, and (iv) $g_{_{0}}\left( y\right) =\left( e^{\epsilon y}-1\right) /\epsilon y$, $g_{_{1}}\left( y\right) =1$, where $y=|E|/E_p$ and $\epsilon$ is the rainbow parameter. It is interesting to report that, all KG particles' and anti-particles' energies are symmetric about $E=0$ value (a natural relativistic quantum mechanical tendency), and a phenomenon of energy states to fly away and disappear from the spectrum is observed for the rainbow functions pair (iii) at $\gamma=\epsilon m/E_p=1$.

Abstract: The Bardeen and Hayward spacetimes are here considered as standard configurations of spherically symmetric regular black holes. Assuming the thermodynamics of such objects to be analogous to standard black holes, we compute the island formula in the regime of small topological charge and vacuum energy, respectively for Bardeen and Hayward spacetimes. Late and early-time domains are separately discussed, with particular emphasis on the island formations. We single out conditions under which it is not possible to find out islands at early-times and how our findings depart from the standard Schwarzschild case. Motivated by th fact that those configurations extend Reissner-Nordstr\"{o}m and Schwarzschild-de Sitter metrics through the inclusion of regularity behavior at $r=0$, we show how the effects of regularity induces modifications on the overall entanglement entropy. Finally, the Page time is also computed and we thus show which asymptotic values are expected for it, for all the configurations under exam. The Page time shows slight departures than the Schwarzschild case, especially for the Hayward case, while the Bardeen regular black hole turns out to be quite indistinguishable from the Schwarzschild case.

Abstract: In this study, we consider dark matter and dark energy as grand-canonical systems which are open, non-equilibrium coupled, and interacting systems. It is the first time, we propose a new more realistic interaction schema to explain dynamics between coupled interacting thermodynamic systems. Based on this new interaction schema, we propose new theorems to define the interactions. We proved the theorems based on the energy conservation law of thermodynamics. Furthermore, we obtain new coupled equations using the theorems. We numerically solve the interaction equations and obtained phase space diagrams and Lyapunov exponents. We show that the interaction between dark matter and dark energy is chaotic. We conclude that these theorems and results can be generalized to all coupled interacting non-equilibrium systems. Finally, we give a new definition of chaos.

Abstract: We build an analytical framework to study the observability of anisotropies and a net chiral polarization of the Stochastic Gravitational Wave Background (SGWB) with a generic network of ground-based detectors. We apply this formalism to perform a Fisher forecast of the performance of a network consisting of the current interferometers (LIGO, Virgo and KAGRA) and planned third-generation ones, such as the Einstein Telescope and Cosmic Explorer. Our results yield limits on the observability of anisotropic modes, spanning across noise- and signal-dominated regimes. We find that if the isotropic component of the SGWB has an amplitude close to the current limit, third-generation interferometers with an observation time of $10$ years can measure multipoles (in a spherical harmonic expansion) up to $\ell = 8$ with ${\cal O }\left( 10^{-3} - 10^{-2} \right)$ accuracy relative to the isotropic component, and an ${\cal O }\left( 10^{-3} \right)$ amount of net polarization. For weaker signals, the accuracy worsens as roughly the inverse of the SGWB amplitude.

Abstract: In recent few years, the Gauss-Bonnet $f(\mathcal{G},\mathrm{\textit{T}})$ theory of gravity has fascinated considerable researchers owing to its coupling of trace of the stress-energy tensor $T$ with the Gauss-Bonnet term $\mathcal{G}$. In this context, we focuss ourselves to study bouncing universe with in $f(\mathcal{G},\mathrm{\textit{T}})$ gravity background. Some important preliminaries are presented along with the discussion of cosmological parameters to develop a minimal background about $f(\mathcal{G},\mathrm{\textit{T}})$ theory of gravity. The exact bouncing solutions with physical analysis are provided with the choice of two equation of state parameters. It is shown that the results do agree with the present values of deceleration, jerk and snap parameters. Moreover, it is concluded that the model parameters are quite important for the validity of conservation equation (as the matter coupled theories do not obey the usual conservation law).