General Relativity and Quantum Cosmology (gr-qc)

Abstract: In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein--Euler equations of general relativity based on a first order hyperbolic reformulation of the Z4 formalism. The first order Z4 system, which is composed of 59 equations, is analyzed and proven to be strongly hyperbolic for a general metric. The well-balancing is achieved for arbitrary but a priori known equilibria by subtracting a discrete version of the equilibrium solution from the discretized time-dependent PDE system. Special care has also been taken in the design of the numerical viscosity so that the well-balancing property is achieved. As for the treatment of low density matter, e.g. when simulating massive compact objects like neutron stars surrounded by vacuum, we have introduced a new filter in the conversion from the conserved to the primitive variables, preventing superluminal velocities when the density drops below a certain threshold, and being potentially also very useful for the numerical investigation of highly rarefied relativistic astrophysical flows. Thanks to these improvements, all standard tests of numerical relativity are successfully reproduced, reaching three achievements: (i) we are able to obtain stable long term simulations of stationary black holes, including Kerr black holes with extreme spin, which after an initial perturbation return perfectly back to the equilibrium solution up to machine precision; (ii) a (standard) TOV star under perturbation is evolved in pure vacuum ($\rho=p=0$) up to $t=1000$ with no need to introduce any artificial atmosphere around the star; and, (iii) we solve the head on collision of two punctures black holes, that was previously considered un--tractable within the Z4 formalism.

Abstract: Boundary term and Brown-York (BY) formalism, which is based on the Hamilton-Jacobi principle, are complimentary of each other as the gravitational actions are not, usually, well-posed. In scalar-tensor theory, which is an important alternative to GR, it has been shown that this complementarity becomes even more crucial in establishing the equivalence of the BY quasi-local parameters in the two frames which are conformally connected. Furthermore, Brown-York tensor and the corresponding quasi-local parameters are important from two important yet different aspects of gravitational theories: black hole thermodynamics and fluid-gravity correspondence. The investigation suggests that while the two frames are equivalent from the thermodynamic viewpoints, they are not equivalent from the perspective of fluid-gravity analogy or the membrane paradigm. In addition, the null boundary term and null Brown-York formalism are the recent developments (so far obtained only for GR) which is non-trivial owing to the degeneracy of the null surface. In the present analysis these are extended for scalar-tensor theory. The present analysis also suggests that, regarding the equivalence (or inequivalence) of the two frame, the null formalism draws the same inferences as of the timelike case, which in turn establishes the consistency of the newly developed null Brown-York formalism.

Abstract: The imaging by the Event Horizon Telescope (EHT) of the supermassive central objects at the heart of the M87 and Milky Way (Sgr A$^\star$) galaxies, has marked the first step into peering at the shadow and photon rings that characterize the optical appearance of black holes surrounded by an accretion disk. Recently, Vagnozzi et. al. [S.~Vagnozzi, \textit{et al.} arXiv:2205.07787 [gr-qc]] used the claim by the EHT that the size of the shadow of Sgr A$^\star$ can be inferred by calibrated measurements of the bright ring enclosing it, to constrain a large number of spherically symmetric space-time geometries. In this work we use this result to study some features of the first and second photon rings of a restricted pool of such geometries in thin accretion disk settings. The emission profile of the latter is described by calling upon three analytic samples belonging to the family introduced by Gralla, Lupsasca and Marrone, in order to characterize such photon rings using the Lyapunov exponent of nearly bound orbits and discuss its correlation with the luminosity extinction rate between the first and second photon rings. We finally elaborate on the chances of using such photon rings as observational discriminators of alternative black hole geometries using very long baseline interferometry.

Abstract: In Einstein-Gauss-Bonnet gravity, we study the quasi-normal modes (QNMs) of the tensor perturbation for the so-called Maeda-Dadhich black hole which locally has a topology $\mathcal{M}^n \simeq M^4 \times \mathcal{K}^{n-4}$. Our discussion is based on the tensor perturbation equation derived in~\cite{Cao:2021sty}, where the Kodama-Ishibashi gauge invariant formalism for Einstein gravity theory has been generalized to the Einstein-Gauss-Bonnet gravity theory. With the help of characteristic tensors for the constant curvature space $\mathcal{K}^{n-4}$, we investigate the effect of extra dimensions and obtain the scalar equation in four dimensional spacetime, which is quite different from the Klein-Gordon equation. Using the asymptotic iteration method and the numerical integration method with the Kumaresan-Tufts frequency extraction method, we numerically calculate the QNM frequencies. In our setups, characteristic frequencies depend on six distinct factors. They are the spacetime dimension $n$, the Gauss-Bonnet coupling constant $\alpha$, the black hole mass parameter $\mu$, the black hole charge parameter $q$, and two ``quantum numbers" $l$, $\gamma$. Without loss of generality, the impact of each parameter on the characteristic frequencies is investigated while fixing other five parameters. Interestingly, the dimension of compactification part has no significant impact on the lifetime of QNMs.

Abstract: We investigate the implications for cosmology of a phenomenological quantum gravity approach based on thermodynamics. We analyze in detail the corresponding primordial power spectrum. The considered modified cosmological scenario has similarities with Loop Quantum Cosmology. Actually, one recovers the same effective background dynamics by fixing the value of the free parameter of the modified approach. In particular, the background experiences a bounce that solves the initial singularity. Adopting background-dependent equations for the primordial perturbations like those derived in General Relativity, the studied model can be considered a generalization of the dressed metric formalism in Loop Quantum Cosmology. We focus our discussion on the spectrum of tensor perturbations. For these perturbations, we compute the exact form of the background-dependent effective mass that affects their propagation. Since there are background regimes in the modified cosmology that are far away from slow-roll inflation, we do not have at our disposal a privileged vacuum like the Bunch-Davies state. We then select the state of the perturbations by a recently proposed criterion that removes unwanted oscillations in the power spectrum. Finally, we numerically compute the spectrum of this vacuum and compare it with other spectra obtained in the literature, especially with one corresponding to an alternative quantization prescription in Loop Quantum Cosmology (called the hybrid prescription).

Abstract: General relativity (GR) will be imminently challenged by upcoming experiments in the strong gravity regime, including those testing the energy extraction mechanisms for black holes. Motivated by this, we explore magnetospheric models and black hole jet emissions in MOdified Gravity (MOG) scenarios. Specifically, we construct new power emitting magnetospheres in a Kerr-MOG background which are found to depend non-trivially on the MOG deformation parameter. This may allow for high-precision tests of GR. In addition, a complete set of analytic solutions for vacuum magnetic field configurations around static MOG black holes are explicitly derived, and found to comprise exclusively Heun polynomials.

Abstract: One of the main objectives of modern cosmology is to explain the origin and evolution of cosmic structures at different scales. The principal force responsible for the formation of such structures is gravity. In a general relativistic framework, we have shown that matter density contrasts do not grow over time at scales exceeding the cosmic screening length, which corresponds to a cosmological scale of the order of two to three gigaparsecs at the present time, at which gravitational interactions exhibit an exponential cut-off. This is a purely relativistic effect. To demonstrate the suppression of density growth, we have performed N-body simulations in a box with a comoving size of $5.632\,{\rm Gpc}/h$ and obtained the power spectrum of the mass density contrast. We have shown that it becomes independent of time for scales beyond the cosmic screening length as a clear manifestation of the cosmic screening effect.