General Relativity And Quantum Cosmology

Numerical relativity is central to the investigation of astrophysical sources in the dynamical and strong-field gravity regime, such as binary black hole and neutron star coalescences. Current challenges set by gravitational-wave and multi-messenger astronomy call for highly performant and scalable codes on modern massively-parallel architectures. We present GR-Athena++, a general-relativistic, high-order, vertex-centered solver that extends the oct-tree, adaptive mesh refinement capabilities of the astrophysical (radiation) magnetohydrodynamics code Athena++. To simulate dynamical space-times GR-Athena++ uses the Z4c evolution scheme of numerical relativity coupled to the moving puncture gauge. We demonstrate stable and accurate binary black hole merger evolutions via extensive convergence testing, cross-code validation, and verification against state-of-the-art effective-one-body waveforms. GR-Athena++ leverages the task-based parallelism paradigm of Athena++ to achieve excellent scalability. We measure strong scaling efficiencies above 95% for up to ??.2? 10 4 CPUs and excellent weak scaling is shown up to ??10 5 CPUs in a production binary black hole setup with adaptive mesh refinement. GR-Athena++ thus allows for the robust simulation of compact binary coalescences and offers a viable path towards numerical relativity at exascale.

It has recently been demonstrated that black holes with spatially regular horizons can support external scalar fields (scalar hairy configurations) which are non-minimally coupled to the Gauss-Bonnet invariant of the curved spacetime. The composed black-hole-scalar-field system is characterized by a critical existence line α=α(μ r H ) which, for a given mass of the supported scalar field, marks the threshold for the onset of the spontaneous scalarization phenomenon [here {α,μ, r H } are respectively the dimensionless non-minimal coupling parameter of the field theory, the proper mass of the scalar field, and the horizon radius of the central supporting black hole]. In the present paper we use analytical techniques in order to explore the physical and mathematical properties of the marginally-stable composed black-hole-linearized-scalar-field configurations in the eikonal regime μ r H ?? of large field masses. In particular, we derive a remarkably compact analytical formula for the critical existence-line α=α(μ r H ) of the system which separates bare Schwarzschild black-hole spacetimes from composed hairy (scalarized) black-hole-field configurations.

We discuss the "quantum deformed Schwarzschild spacetime" as originally introduced by Kazakov and Solodukhin in 1993, and investigate the precise sense in which it does and does not satisfy the desiderata for being a "regular black hole". We shall carefully distinguish (i) regularity of the metric components, (ii) regularity of the Christoffel components, and (iii) regularity of the curvature. We shall then embed the Kazakov-Solodukhin spacetime in a more general framework where these notions are clearly and cleanly separated. Finally we analyze aspects of the classical physics of these "quantum deformed Schwarzschild spacetimes". We shall discuss the surface gravity, the classical energy conditions, null and timelike geodesics, and the appropriate variant of Regge--Wheeler equation.

The general parametrization for spacetimes of spherically symmetric Lorentzian, traversable wormholes in an arbitrary metric theory of gravity is presented. The parametrization is similar in spirit to the post-Newtonian parametrized formalism, but with validity that extends beyond the weak field region and covers the whole space. Our method is based on a continued-fraction expansion in terms of a compactified radial coordinate. Calculations of shadows and quasinormal modes for various examples of parametrization of known wormhole metrics that we have performed show that, for most cases, the parametrization provides excellent accuracy already at the first order. Therefore, only a few parameters are dominant and important for finding potentially observable quantities in a wormhole background. We have also extended the analysis to the regime of slow rotation.

We consider the relativistic hydrodynamics of non-perfect fluids with the goal of determining a formulation that is suited for numerical integration in special-relativistic and general-relativistic scenarios. To this end, we review the various formulations of relativistic second-order dissipative hydrodynamics proposed so far and present in detail a particular formulation that is fully general, causal, and can be cast into a 3+1 flux-conservative form as the one employed in modern numerical-relativity codes. As an example, we employ a variant of this formulation restricted to a relaxation-type equation for the bulk viscosity in the general-relativistic magnetohydrodynamics code BHAC . After adopting the formulation for a series of standard and non-standard tests in 1+1-dimensional special-relativistic hydrodynamics, we consider a novel general-relativistic scenario, namely, the stationary, spherically symmetric viscous accretion onto a black hole. The newly developed solution ??which can exhibit even considerable deviations from the inviscid counterpart ??can be used as a testbed for numerical codes simulating non-perfect fluids on curved backgrounds.

Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing spatially homogeneous and isotropic cosmology in general relativity. These analogies are presented, together with their Lagrangian and Hamiltonian formulations and with an invariant of the Fibonacci sequence.

In this article, the generalized gravity theory with the curvature, torsion and nonmetricy was studied. For the FRW spacetime case, in particular, the Lagrangian, Hamilatonian and gravitational equations are obtained. The particular case F(R,T)=αR+βT+μQ+νT is investigated in detail. In quantum case, the corresponding Wheeler-DeWitt equation is obtained. Finally, some gravity theories with the curvature, torsion and nonmetricity are presented.

This paper concerned with the effect of generalized uncertainty principle (GUP) on the stochastic gravitational wave (SGW) background signal that produced during first order cosmological QCD phase transition in early universe. A modified formula of entropy is used to calculate the temporal evolution of temperature of the universe as a function of the Hubble parameter. The pressure that results from the recent lattice calculations, which provides parameterizations of the pressure due to u, d, s quarks and gluons, with trace anomaly is used to describe the equation of state around QCD epoch. A redshift in the peak frequency of SGW at current epoch is calculated. The results indicate an increase in the frequency peak due to GUP effect, which improves the ability to detect it. Taking into account bubble wall collisions (BWC) and turbulent magnetohydrodynamics (MHD) as a source of SGW, a fractional energy density is investigated. It is found that the GUP effect weakens the SGW signal generated during QCD phase transition in comparison to its counterpart in the absence of GUP. These results support understanding the cosmological QCD phase transition and test the effectiveness of the GUP theory.

The Geroch/Stephani transformation is a solution-generating transformation, and may generate spiky solutions. The spikes in solutions generated so far are either early-time permanent spikes or transient spikes. We want to generate a solution with a late-time permanent spike. We achieve this by applying the Stephani transformation with the rotational Killing vector field of the locally rotationally symmetric Jacobs solution. The late-time permanent spike occurs along the cylindrical axis. The generated solution also features a rich variety of transient structures. We introduce a new technique to analyse these structures. Our findings lead us to discover a transient behaviour, which we call the overshoot transition.

We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) in the Weyl type f(Q,T) gravity, in which the nonmetricity Q is represented in the standard Weyl form, fully determined by the Weyl vector, while T represents the trace of the matter energy-momentum tensor. The effects of the Weyl geometry and of the extra force induced by the nonmetricity-matter coupling are explicitly taken into account. The Newtonian limit of the theory is investigated, and the generalized Poisson equation, containing correction terms coming from the Weyl geometry, and from the geometry matter coupling, is derived. As a physical application of the geodesic deviation equation the modifications of the tidal forces, due to the nonmetricity-matter coupling, are obtained in the weak field approximation. The tidal motion of test particles is directly influenced by the gradients of the extra force, and of the Weyl vector. As a concrete astrophysical example we obtain the expression of the Roche limit (the orbital distance at which a satellite begins to be tidally torn apart by the body it orbits) in the Weyl type f(Q,T) gravity.