General Relativity and Quantum Cosmology (gr-qc)

Abstract: The investigation of the anisotropy of the stochastic gravitational wave background (SGWB) using the TianQin detector plays a crucial role in studying the early universe and astrophysics. In this work, we examine the response of the $AET$ channel of the TianQin Time Delay Interferometry (TDI) to the anisotropy of the SGWB. We calculate the corresponding angular sensitivity curves and find that TianQin is capable of detecting the anisotropy of the SGWB, with an angular sensitivity reaching $10^{-10}$ for quadrupoles. Due to the fixed $z$-axis of TianQin pointing towards J0806, its overlap reduction functions (ORFs) exhibit specific symmetries, enabling the resolution of different multipole moments $\ell m$. The detection sensitivity is optimal for the $(2, 0)$ mode, with a sensitivity reaching $10^{-10}$. Using the Fisher matrix approach, we estimate the parameters and find that in the power-law spectrum model, higher logarithmic amplitudes lead to more effective reconstruction of the spectral index for all multipole moments. Under the optimal scenario with a signal amplitude of $\Omega_{\mathrm{GW}} (f = f_{\mathrm{c}}) h^2 = 10^{-9}$, the spectral indices can be reconstructed with uncertainties of $10^{-3}$, $10$, and $10^{-3}$ for $\ell = 0$, $1$, and $2$ multipole moments, respectively. For the cases of $(\ell, m) = (0, 0)$, $(1, 1)$, $(2, 0)$, and $(2, 2)$, the spectral indices can be reconstructed with uncertainties of $10^{-3}$, $10$, $10^{-3}$, and $10$, respectively.

Abstract: We describe charged BHs, Penrose process for energy extraction from Kerr BHs and Wald's proposal concerning a Kerr BH slowly becoming a Kerr-Newman BH in the presence of a uniform magnetic field. In the context of BHs bearing magnetic charge, we discuss both magnetic monopoles as well as dyons, and their emergence from various models like string theory, GUTs and electroweak theories, etc. In the later portions, we concentrate on our recent research work pertaining to the non-relativistic dynamics of dyon-dyon interaction that includes mutual gravitational attraction. From the derived classical equations of motion, we obtain not only the well known Schwinger-Zwanziger quantization condition for dyons using Saha's argument based on quantized angular momentum of electromagnetic field but also a scalar virial theorem for an astrophysical system consisting of point particles, some of which carry both electric and magnetic charges. In the final sections, we obtain expressions for the generated electromagnetic wave as well as gravitational wave amplitudes, and the corresponding luminosities due to dyon-dyon interactions. Lastly, we discuss the results after computing these quantities using a range of values for the mass, electric and magnetic charges, etc. of the dyonic BHs.

Abstract: In this paper, we present an accelerating cosmological model by constraining the free parameters using the cosmological datasets in an extended symmetric teleparallel gravity for the flat and anisotropic space-time. We employ a time variable deceleration parameter that behaves early deceleration and late time acceleration in the form of Hybrid Scale Factor (HSF). We obtain the present values of deceleration parameter and analyse the late time behavior of the Universe based on the best-fit values of free parameters. We derive the dynamical parameters of the model and obtain the equation of state parameter at present in the quintessence region; however at late time it approaches to $\Lambda$CDM. The energy conditions are also analysed to validate the modified gravity and we find that strong energy condition is violating. We establish the importance of hybrid scale factor in the late time cosmic phenomena issue.

Abstract: In this paper, we construct exact rotating wormholes using Ehlers solution-generating technique. This is based on the Ernst description of four-dimensional, stationary, and axially symmetric solutions of the Einstein-Maxwell theory. We adopt the static Barcel\'o-Visser wormhole derived from the Einstein-Maxwell-conformal-scalar theory as a seed, and demonstrate, through the Ernst approach, how to construct two novel geometries of rotating wormholes. These geometries correspond to the Barcel\'o-Visser wormhole embedded within a rotating and a magnetic background, respectively. In the first case, the rotation is a result of a dragging force (due to the rotating background) acting on the initial static wormhole, while in the second case it is caused by the electromagnetic interaction between the electric charge of the static wormhole and the external magnetic field. We conduct a comprehensive analysis of the geometric properties of these configurations, and examine the new features introduced by rotation, such as the emergence of ergoregions. Recent evidence suggests that incorporating slow rotation can stabilise wormholes, rendering these exact, fully rotating solutions particularly appealing.

Abstract: In this paper, via a covariant semitetrad spacetime decomposition, we present a novel geometrical classification of shear-free Locally Rotationally Symmetric (LRS-II) perfect fluid self-gravitating systems, in terms of the covariantly defined fluid acceleration and the fluid expansion. We further analyze the interesting class of these systems that are dynamic, necessarily inhomogeneous with tidal deformations and yet shear-free. We deduce the governing highly non-linear differential equation that gives the possible equations of state of matter that can lead to such a scenario. We find that the possible equations of state are very limited.

Abstract: The cores of neutron stars (NS) reach densities several times the nuclear saturation density and could contain strangeness containing exotic particles such as hyperons. During the binary inspiral, viscous processes inside the NS matter can damp out the tidal energy induced by the companion and convert this to thermal energy to heat up the star. We demonstrate that the bulk viscosity originating from the non-leptonic weak interactions involving hyperons is several orders of magnitude higher than the standard neutron matter shear viscosity in the relevant temperature range of $10^6-10^9$K and for heavier mass NSs ($M \geq 1.6M_{\odot}$) that contain a significant fraction of hyperons in their core, the bulk viscosity can heat up the stars upto $0.1 - 1$ MeV before the final merger. This "tidal heating" process also introduces a net phase shift of $10^{-3}-0.5$ rad, depending on the component mass, in the gravitational wave (GW) signal that can potentially be detected using current and future generation GW detectors. Such a detection would be the direct confirmation of the presence of hyperons inside the NS core, having a great significance for the study of dense matter under extreme condition.

Abstract: In the context of the Fab-Four theory of gravity in a Friedmann-Lema\^itre-Robertson-Walker background, in this work we use the cosmography approach to study a particular self-tuning filter solution focused on a zero-curvature fixed point to study the $H_0$ tension. In this scheme, the equations restrict the universe's evolution to certain scenarios, including radiation-like expansion, matter-like expansion, and late-time acceleration. Furthermore, we build the cosmographic series of the Fab-Four theory to obtain the kinematic parameters as the Hubble constant $H_0$ and the deceleration parameter $q_0$ for all the scenarios mentioned. Finally, we compare our results to find that it is possible to alleviate the current discrepancy on $H_0$ by considering specific requirements on the free parameters of the Fab-Four theory through a self-tuning filter.