General Relativity and Quantum Cosmology (gr-qc)

Abstract: This article provides a discussion on the construction of conformal Gaussian gauge systems to study the evolution of solutions to the Einstein field equations with positive Cosmological constant. This is done by means of a gauge based on the properties of conformal geodesics. The use of this gauge, combined with the extended conformal Einstein field equations, yields evolution equations in the form of a symmetric hyperbolic system for which standard Cauchy stability results can be employed. This strategy is used to study the global properties of de Sitter-like spacetimes with constant negative scalar curvature. It is then adapted to study the evolution of the Schwarzschild-de Sitter spacetime in the static region near the conformal boundary. This review is based on Class. Quantum Grav. 38 145026 and Class. Quantum Grav. 40 145005.

Abstract: We revisit the vital issue of gauge dependence in the scalar-induced secondary gravitational waves (SIGWs), focusing on the radiation domination (RD) and matter domination (MD) eras. The energy density spectrum is the main physical observable in such induced gravitational waves. For various gauge choices, there has been a divergence in the energy density, $\Omega_{\text{GW}}$, of SIGWs. We calculate SIGWs in different gauges to quantify this divergence to address the gauge-dependent problem. In our previous studies, we had found that the energy density diverges in the polynomial power of conformal time (e.g., $\eta^6$ in uniform density gauge). We try to fix this discrepancy by adding a counter-term that removes the fictitious terms in secondary tensor perturbations. We graphically compare the calculations in various gauges and also comment on the physical origin of the observed gauge dependence.

Abstract: We present an ideal characterization of the family of four dimensional Lorentzian spacetimes that are conformally related to the Kerr vacuum solution.

Abstract: We have investigated an isotropic and homogeneous cosmological model of the universe in $f(R, T^{\phi})$ gravity, where $T^{\phi}$ is the trace of the energy-momentum tensor and $R$ is the Ricci scalar. We developed and presented exact solutions of field equations of the proposed model by taking the parametrization $q(z) =\alpha + \frac{\beta z}{1+z}$, where $\alpha$ and $\beta$ are arbitrary constants. The best possible values of the model's free parameters are estimated using the latest observational data sets of OHD, BAO, and Pantheon by applying the MCMC statistical technique. Some kinematic properties like density parameter $\rho_{\phi}$, pressure $p_{\phi}$, and equation of state parameter $\omega_{\phi}$ are derived. We have also discussed the behavior of the scalar potential $V(\phi)$ in the $f(R, T^{\phi})$ gravity theory. The behaviors of scalar fields for quintessence and phantom models are explored. Furthermore, we have discussed the behavior of energy conditions and sound speed in $f(R, T^{\phi})$ cosmology.

Abstract: In this paper, we model the bounce phase, stability and the reconstruction of the universe by non-minimal kinetic coupling. In the process, we obtained importance information about the energy density and the matter pressure of the universe in relation to the previous universe through the bounce quantum phase. The novelty of the work is that the scale factor is obtained directly from the model and is fitted with an exponential function, with this view we explore the process of the early universe even the bounce phase. After that, we plot the cosmological parameters in terms of time evolution. In what follows, we investigate the stability of the model by the dynamical system analysis in a phase plane. Finally, the phase space trajectories examine the stability of the universe, especially in the inflationary period.

Abstract: In the context of holography, the Einstein ring of an AdS black hole (BH) in massive gravity (MG) is depicted. An oscillating Gaussian source on one side of the AdS boundary propagates in bulk, and we impose a response function to explain it. Using a wave optics imaging system, we obtain the optical appearance of the Einstein ring. Our research reveals that the ring can change into a luminosity-deformed ring or light spots depending on the variation of parameters and observational positions. When observers are positioned at the north pole, the holographic profiles always appear as a ring with concentric stripe surroundings, and a bright ring appears at the location of the photon sphere of the BH. These findings are consistent with the radius of the photon sphere of the BH, which is calculated in geometrical optics. Our study contributes to a better understanding of the analytical studies of holographic theory, which can be used to evaluate different types of BHs for a fixed wave source and optical system.

Abstract: This study focuses on investigating a regular black hole within the framework of Verlinde's emergent gravity. In particular, we explore the classical aspects of the modified Simpson--Visser solution. Our analysis reveals the presence of a unique physical event horizon. Moreover, we study the thermodynamic properties, including the \textit{Hawking} temperature, the entropy, and the heat capacity. Based on these quantities, our results show several phase transitions. Geodesic trajectories for photon--like particles, encompassing photon spheres and the formation of black hole shadows, are also calculated to comprehend the behavior of light in the vicinity of the black hole. Furthermore, we investigate the quasinormal modes using third--order WKB approximation.

Abstract: We explore the use of the recently defined scalar charge which satisfies a Gauss law in stationary spacetimes, in the context of theories with a scalar potential. We find new conditions that this potential has to satisfy in order to allow for static, asymptotically-flat black-hole solutions with regular horizons and non-trivial scalar field. These conditions are equivalent to some of the known ``no-hair'' theorems (such as Bekenstein's). We study the extended thermodynamics of these systems, deriving a first law and a Smarr formula. As an example, we study the Anabal\'on-Oliva hairy black hole

Abstract: Understanding the evolution of entropy in the universe is a fundamental aspect of cosmology. This paper investigates the evolution of entropy in a spatially flat $K=0$ universe, focusing on the contributions of matter, radiation, and dark energy components. The study derives the rate of change of entropy with respect to cosmic time, taking into account the scaling relations of energy densities and temperatures for different components. The analysis reveals the dominance of radiation entropy at early times, transitioning to matter dominance as the universe expands. The constant contribution of dark energy entropy throughout cosmic time is also considered. The paper acknowledges the limitations of the simplified model and the omission of entropy generation processes, emphasizing the importance of future research to incorporate these aspects. The results highlight the complex interplay between different components and provide insights into the dynamics of entropy in the expanding universe. This study lays the foundation for further investigations into entropy evolution, urging the consideration of more comprehensive models and numerical techniques to achieve a deeper understanding of the universe's thermodynamic behavior.

Abstract: In this work, we consider a propagating scalar field on Kaluza-Klein-type cosmological background. It is shown that this geometrical description of the Universe resembles - from a Hamiltonian standpoint - a damped harmonic oscillator with mass and frequency, both time-dependents. In this scenario, we construct the squeezed coherent states (SCSs) for the quantized scalar field by employing the invariant operator method of Lewis-Riesenfeld (non-Hermitian) in a non-unitary approach. The non-classicality of SCSs has been discussed by examining the quadrature squeezing properties from the uncertainty principle. Moreover, we compute the probability density, which allows us to investigate whether SCSs can be used to seek traces of extra dimensions. We then analyze the effects of the existence of supplementary space on cosmological particle production in SCSs by considering different cosmological eras.

Abstract: This article deals with the thermodynamics of gravitational radiation arising from the Bondi-Sachs space-time. The equation of state found allows us to conclude that the dependence of the energy density on the temperature is a quadratic power of the latter. Such a conclusion is possible once the consequences of the first law of thermodynamics are analyzed. Then, in analogy to electromagnetic radiation, the same approach as used by Planck to obtain the quantum of energy of the gravitational radiation is proposed. An energy for the graviton proportional to the cubic frequency is found. The graviton is here understood as the quantum of gravitational energy.

Abstract: Within the context of energy-momentum squared gravity (EMSG), where non-linear matter contributions appear in the gravitational action, we derive the modified TOV equations describing the hydrostatic equilibrium of charged compact stars. We adopt two different choices for the matter Lagrangian density ($\mathcal{L}_m= p$ versus $\mathcal{L}_m= -\rho$) and investigate the impact of each one on stellar structure. Furthermore, considering a charge profile where the electric charge density $\rho_{\rm ch}$ is proportional to the standard energy density $\rho$, we solve numerically the stellar structure equations in order to obtain the mass-radius diagrams for the MIT bag model equation of state (EoS). For $\mathcal{L}_m= p$ and given a specific value of $\beta$ (including the uncharged case when $\beta= 0$), the maximum-mass values increase (decrease) substantially as the gravity model parameter $\alpha$ becomes more negative (positive). However, for uncharged configurations and considering $\mathcal{L}_m= -\rho$, our numerical results reveal that when we increase $\alpha$ (from a negative value) the maximum mass first increases and after reaching a maximum value it starts to decrease. Remarkably, this makes it a less trivial behavior than that caused by the first choice when we take into account the presence of electric charge ($\beta \neq 0$).

Abstract: We study the black hole spacetime structure of a model consisting of the standard Maxwell theory and a $p$-power-Yang-Mills term. This non-linear contribution introduces a non-Abelian charge into the global solution, resulting in a modified structure of the standard Reissner-Nordstr\"{o}m black hole. Specifically, we focus on the model with $p=1/2$, which gives rise to a new type of modified Reissner-Nordstr\"{o}m black hole. For this class of black holes, we compute the event horizon, the innermost stable circular orbit, and the conditions to preserve the weak cosmic censorship conjecture. The latter condition sets a well-established relation between the electric and the Yang-Mills charges. As a first astrophysical implication, the accretion properties of spherical steady flows are investigated in detail. Extensive numerical examples of how the Yang-Mills charge affects the accretion process of an isothermal fluid in comparison to the standard Reissner-Nordstr\"{o}m and Schwarzschild black holes are displayed. Finally, analytical solutions in the fully relativistic regime, along with numerical computations, of the mass accretion rate for a polytropic fluid in terms of the electric and Yang-Mills charges are obtained. As a main result, the mass accretion rate efficiency is considerably improved, with respect to the standard Reissner-Nordstr\"{o}m and Schwarzschild solutions, for negative values of the Yang-Mills charge.