General Relativity and Gravitation最新文献

We investigate gravitational waves with an arbitrary potential within the framework of linearized Horndeski theory. We show that the minimum of the potential can play the role of an effective cosmological constant in this theory, which is usually neglected in previous studies of this subject. We first determine the background geometry in this setup by solving the weak field scalar and tensorial equations of linearized Horndeski theory. The solutions of linearized weak-field wave equations, in an appropriate gauge, are then obtained perturbatively to study the propagation and interactions of gravitational waves in this background. We compare our results with different realizations of the cosmological constant in Horndeski theory to compare the role of an arbitrary scalar potential with those of vacuum energy density and a linear potential. The results show that the background curvature arising from the minimum of the scalar potential effectively mimics a cosmological constant, producing distinct redshifts in the frequency and wave number that distinguish the tensor waves from massive scalar ones. We also find that the way the cosmological constant is introduced directly influences the speed and polarization of the scalar wave.

General relativity (GR) admits two alternative formulations with the same dynamics attributing the gravitational phenomena to torsion or nonmetricity of the manifold’s connection. They lead, respectively, to the teleparallel equivalent of general relativity (TEGR) and the symmetric teleparallel equivalent of general relativity (STEGR). In this work, we focus on STEGR and present its differences with the conventional, curvature-based GR. We exhibit the 3+1 decomposition of the STEGR Lagrangian in the coincident gauge and present the Hamiltonian, the Hamiltonian and momenta constraints, and Hamilton’s equations. For a particular case of spherical symmetry, we explicitly show the differences in the Hamiltonian and the Hamiltonian constraint between GR and STEGR. We finally discuss the implications that these differences, which represent genuine different features between the two formulations of gravity, might encompass to numerical relativity.

The existence of black hole shadows is one of the most interesting effects of the strong field regime of general relativity (GR). Recent observations by the Event Horizon Telescope (EHT) have provided high-resolution images of the vicinity of supermassive black holes, ushering in a new era for testing gravitation on astrophysical scales. In this work, we continue the investigation initiated by [1], focusing on shadows associated with generalized (k-n) black-bounce type spacetimes, which smoothly interpolate between regular black holes and wormholes. We consider a generalization of the metric with free parameters (a, k, n) that modify the mass function and enrich the possible phenomenology. We develop a semi-analytical study of photon orbits, obtaining the critical impact parameter and the shadow radius for different parameter combinations. Subsequently, we perform numerical ray-tracing simulations using the GYOTO code, incorporating optically thick accretion disks and varying the observation angle. Our results reveal characteristic signatures, including the formation of double-ring structures and deformations of the shadow radius, which can serve as observational discriminators between classical black holes and black-bounce solutions.

We extend the isolated horizon formalism to include rotating black holes arising in five dimensional Einstein- Gauss- Bonnet (EGB) theory of gravity, and derive the laws of black hole mechanics. This result allows us to show that the first law of black hole mechanics is modified, due to the Gauss- Bonnet term, so as to include corrections to (i) the area of horizon cross- sections and, to (ii) the expression of horizon angular momentum. Once these modifications are included, the Hamiltonian generates an evolution on the space of solutions of the EGB theory admitting isolated horizon as an internal boundary, the consequence of which is the first law of black hole mechanics. These boundary conditions may help in the search for exact solutions describing rotating black holes in this theory.

We present a spherically symmetric stellar model within the framework of seven dimensional third order Lovelock gravity for a neutral perfect fluid distribution. The third order Lovelock field equations are generated for such a fluid configuration by imposing pressure isotropy. This condition yields a first order nonlinear differential equation which is an extension of the Abel differential equation. This is due to the additional higher order curvature effects arising in third order Lovelock gravity. We demonstrate new exact solutions that can model a static spherically symmetric star. The energy density and pressure are both variable. We also show that a special case arises, which is a constant density model with a cosmological interpretation. Furthermore, we illustrate the matching conditions to generate a spherically symmetric stellar model in third order Lovelock gravity when the EGB and third order Lovelock coupling constants are related.

We show that in the spacetime dominated by a cosmological constant, given by de Sitter metric, a seed magnetic field can be generated in an ambient plasma (in a state of no magnetic field) by a general-relativistic battery. This cosmological battery depends on the interaction of spacetime curvature with inhomogeneous plasma thermodynamics. Thus, dark energy becomes a gravitational source for cosmic magnetic fields

We express the vacuum Einstein constraints in terms of differential forms—the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be always expressed locally as a system of first order PDE’s—this system is obtained by a special choice of coframe, which reduces to zero all second order terms in the scalar constraint. We also present a general formula for coframes, which allow for this simplification of the constraint and give it additionally a certain symmetric form.