General Relativity and Quantum Cosmology (gr-qc)

Abstract: By considering Kehagias-Sfetsos black hole in the framework of the Ho\v{r}ava-Lifshitz gravity, we study the optical appearance of such black holes surrounded by spherical accretion flow. For the static/infalling spherical accretion flow, we compute the observed specific intensity as a function of impact parameter. We also investigate the effect of the Ho\v{r}ava parameter and accreting matter on the luminosity of shadows and photon rings. It is found that an increase in the Ho\v{r}ava parameter decreases the shadow size, while the shadows and photon rings luminosities increase. Moreover, we constrain the Ho\v{r}ava parameter from the observational data reported by the Event Horizon Telescope for M87* and Sgr A*.

Abstract: This paper explores the detection capability of space-borne detectors to the anisotropic stochastic gravitational-wave background (SGWB) without relying on the low-frequency approximation. To assess the detection performance, we calculate the power-law integrated sensitivity (PLIS) curve. Our results demonstrate that a single detector has limited capabilities in detecting multipole moments beyond the monopole ($l=0$), quadrupole ($l=2$), and hexadecapole ($l=4$). However, when multiple detectors are combined, the presence of multiple pointing directions and the separation between detectors significantly enhance the detection capabilities for the other multipole moments. For instance, when considering the dipole ($l=1$), combining TianQin with TianQin II and LISA with TianQin significantly improves the detection sensitivity by 2-3 orders of magnitude, compared with using a single TianQin and a single LISA, respectively.

Abstract: Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system. In this study, the connection between the phase transition of a black hole and the winding number derived by the complex analysis is used to predict the type of the black hole phase transition. For the third-order Lovelock black holes, at the hyperbolic topology in any dimensions and the spherical topology in $7$ dimensions, we arrive at the winding numbers both are $W=3$ which predicts that the system will undergo both the first-order and second-order phase transitions. For the spherical topology in $7<d<12$ dimensions, the winding number is $W=4$ and the corresponding phase transition will occur in two situations: one with only pure second-order phase transition and the other with both first-order and second-order phase transitions. We further confirm the correctness and rationality of this prediction by placing the black hole thermodynamics system in the potential field.

Abstract: Recently, the mimetic gravitational theory has gained much attention in the frame of cosmology as well as in the domain of astrophysics. In this study, we show that in the frame of mimetic gravitation theory we are not able to derive an isotropic model. As a result, our focus shifts towards combining mimetic gravitational theory with the Lagrangian multiplier. The field equations of a static isotropic gravitational system that controls the geometry and dynamics of star structure are studied in the frame of mimetic theory coupled with a Lagrangian multiplier using a non-linear equation of state. An energy density is assumed from where all the other unknowns are fixed and a new isotropic model is derived. The physical analysis of this model is studied from different viewpoints and consistent results compatible with a realistic isotropic star are investigated analytically and graphically. Ultimately, we demonstrate the stability of the model in question by employing the adiabatic index technique.

Abstract: Non-commutativity is a key feature of spacetime geometry. The current article explores the traversable wormhole solutions in the framework of $f(R,L_m)$ gravity within non-commutative geometry. By using the Gaussian and Lorentzian distributions, we construct tideless wormholes for the nonlinear $f(R,L_m)$ model $f(R,L_m)=\dfrac{R}{2}+L_m^\alpha$. For both cases, we derive shape functions and discuss the required different properties with satisfying behavior. For the required wormhole properties, we develop some new constraints. The influence of the involved model parameter on energy conditions is analyzed graphically which provides a discussion about the nature of exotic matter. Further, we check the physical behavior regarding the stability of wormhole solutions through the TOV equation. An interesting feature regarding the stability of the obtained solutions via the speed of sound parameters within the scope of average pressure is discussed. Finally, we conclude our results.

Abstract: A gauge-invariant perturbation theory on a generic background spacetime is developing from 2003 and ``zero-mode problem'' for linear metric perturbations was proposed as the essential problem of this theory. In the perturbation theory on the Schwarzschild background spacetime, $l=0,1$ modes correspond to the above ``zero-mode'' and the gauge-invariant treatments of these modes is a famous non-trivial problem in perturbation theories on the Schwarzschild background spacetime. Due to this situation, a gauge-invariant treatment for these $l=0,1$-mode perturbations is proposed. Through this gauge-invariant treatment, the solutions to the linearized Einstein equation for these modes with a generic matter field are derived. In the vacuum case, the linearized version of uniqueness theorem of Kerr spacetime is confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable.

Abstract: Numerical simulation of strange quark stars (QSs) is challenging due to the strong density discontinuity at the stellar surface. In this paper, we report successful simulations of rapidly rotating QSs and study their oscillation modes in full general relativity. Building on top of the numerical relativity code \texttt{Einstein Toolkit}, we implement a positivity-preserving Riemann solver and a dust-like atmosphere to handle the density discontinuity at the surface. We demonstrate the robustness of our numerical method by performing stable evolutions of rotating QSs close to the Keplerian limit and extracting their oscillation modes. We focus on the quadrupolar $l=|m|=2$ $f$-mode and study whether they can still satisfy the universal relations recently proposed for rotating neutron stars (NSs). We find that two of the three proposed relations can still be satisfied by rotating QSs. For the remaining broken relation, we propose a new relation to unify the NS and QS data by invoking the dimensionless spin parameter $j$. The onsets of secular instabilities for rotating QSs are also studied by analyzing the $f$-mode frequencies. Same as the result found previously for NSs, we find that QSs become unstable to the Chandrasekhar-Friedman-Schutz instability when the angular velocity of the star $\Omega \approx 3.4 \sigma_0$ for sequences of constant central energy density, where $\sigma_0$ is the mode frequency of the corresponding nonrotating configurations. For the viscosity-driven instability, we find that QSs become unstable when $j\approx 0.881$ for both sequences of constant central energy density and constant baryon mass. Such a high value of $j$ cannot be achieved by realistic rotating NSs before reaching the Keplerian limit.

Abstract: We show that the transformation of a time-evolving spherically symmetric metric tensor into a Painleve-Gullstrand-Lemaitre form brings forth a few curious consequences. The time evolution describes a non-singular gravitational collapse, leading to a bounce and dispersal of all the clustered matter, or a wormhole geometry for certain initial conditions. The null convergence condition is violated only at the onset of bounce or the wormhole formation. As an example, the requirements to develop a Simpson-Visser wormhole/regular black-hole geometry is discussed. The solution can be regarded as a new time-evolving twin of sonic dumb holes found in analog gravity.

Abstract: We investigate a new type of Schwarzschild wormhole, which relies on a 3-dimensional spacetime defect with degenerate metrics. This particular wormhole is a solution of the vacuum Einstein equations. We also study the generalized Schwarzschild-type defect wormhole and discuss the Null Energy Condition. In particular, we investigate the geodesics and geodesic congruences of the generalized Schwarzschild-type defect wormhole. Additionally, we explore the optical appearance of these wormholes, shedding light on their observable features.

Abstract: In this letter we explore the foundations of entropic cosmology and highlight some important flaws which have emerged and adopted in the recent literature. We argue that, when applying entropy and temperature on the cosmological horizon by assuming the holographic principle for all thermodynamic approaches to cosmology and gravity, one must derive the consistent thermodynamic quantities following Clausius relation. One key assumption which is generally overlooked, is that in this process one must assume a mass-to-horizon relation, which is generally taken as a linear one. We show that, regardless of the type of entropy chosen on the cosmological horizon, when a thermodynamically consistent corresponding temperature is considered, all modified entropic force models are equivalent to and indistinguishable from the original entropic force models based on standard Bekenstein entropy and Hawking temperature. As such, they are also plagued by the same problems and inability to describe in a satisfactory qualitative and quantitative way the cosmological dynamics as it emerges from the probes we have. We also show that the standard accepted parameterization for Hawking temperature (including a $\gamma$ rescaling) is actually not correctly applied, namely, it is not related to entropy in a thermodynamically consistent way. Finally, we clearly state that the explicit form of the entropic force on cosmological horizons is mostly dictated by the assumption on the mass-to-horizon relation. As such, we discuss what should be done in order to fix all such issues, and what conceptually could be implied by its correct implementation in order to advance in the field.

Abstract: Examining the relativistic collapse of a spherical spacetime where gravity is coupled with a scalar field, this review provides a thorough analysis of some of the most relevant studies from both analytical and numerical perspectives. The discussion includes achievements made in this field, with a focus on those related to cosmic censorship, as well as recent perspectives on the topic.

Abstract: We examine the scenario of non-minimally coupled relativistic fluid and $k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker universe. By adding a non-minimal coupling term in the Lagrangian level, we study the variation of Lagrangian with respect to independent variables, which produces modified scalar field and Friedmann equations. Using dynamical stability approach in different types of interaction models with two types of scalar field potential, we explore this coupled framework. Implementing detailed analysis, we can conclude our models can able to produce stable late-time cosmic acceleration.

Abstract: In this paper, we discuss a general method to obtain exact cosmological solutions in modified gravity, to demonstrate the method it is employed to obtain exact cosmological solutions in $f(R,\phi)$ gravity. Here, we show that, given a particular evolution of the Universe, we could obtain different models of gravity that give that evolution, using the same construction. Further, we obtain an exact inflationary solution for Starobinsky action with a negligible cosmological constant. This analysis helps us to have a better understanding of Starobinsky inflation. With our analysis we could refine the parameter values and predictions of Starobinsky inflation. Also, we make an observation that there exist a no-go theorem for a bounce from Starobinsky action in the absence of scalar fields or a cosmological constant.

Abstract: Wave packets propagating in inhomogeneous media experience a coupling between internal and external degrees of freedom and, as a consequence, follow spin-dependent trajectories. These are known as spin Hall effects, which are well known in optics and condensed matter physics. Similarly, the gravitational spin Hall effect is expected to affect the propagation of gravitational waves on curved spacetimes. In this general-relativistic setup, the curvature of spacetime acts as impurities in a semiconductor or inhomogeneities in an optical medium, leading to a frequency- and polarization-dependent propagation of wave packets. In this letter, we study this effect for strong-field lensed gravitational waves generated in hierarchical triple black hole systems in which a stellar-mass binary merges near a more massive black hole. We calculate how the gravitational spin Hall effect modifies the gravitational waveforms and show its potential for experimental observation. If detected, these effects will bear profound implications for astrophysics and tests of general relativity.

Abstract: We explore the phase-space of a multiscalar-torsion gravitational theory within a cosmological framework characterized by a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker model. Our investigation focuses on teleparallelism and involves a gravitational model featuring two scalar fields, where one scalar field is coupled to the torsion scalar. We consider coupling in the two scalar fields' kinetic and potential components. We employ exponential functions for the scalar field potentials and analyse the field equations' stationary points to reconstruct the cosmological evolution. Remarkably, we discover many stationary points in this multiscalar field model, capable of describing various eras of cosmological evolution. Hence, this model can be used to describe the early and time acceleration phases of the universe and as a unification model for the elements of the dark sector of the universe.

Abstract: According to the Banados-Silk-West (BSW) process, rotating black holes can act as particle colliders capable of achieving arbitrarily high center-of-mass energy (CME), provided that a specific angular momentum of one of the particles is present. In this discussion, we demonstrate that both Kerr black holes and Schwarzschild black holes could serve as potential sources of high-energy particles in the polar region.