A relativistic theory of the field II: Hamilton's principle and Bianchi's identities

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry. Thence emerges a relativistic theory of the field by generalization of the general relativity. The derivation presented shows how naturally we can extend general relativity theory to a non-symmetric field, and that the field-equations are really the generalizations of the gravitational equations. With curvature tensor and the variational principle, we will deduce the field equations and Bianchi's identities. In consecuense, the field equations will find from Bianchi's identities.

Hyperbolically symmetric sources in Palatini f(R) gravity

A thorough examination of static hyperbolically symmetric matter configuration in the context of Palatini f(R) gravitational theory has been carried out in this manuscript. Following the work of Herrera et al. (Phys. Rev. D 103: 024037, 2021) we worked out the modified gravitational equations and matching conditions using the Palatini technique of variation in Einstein–Hilbert action. It is found from the evaluations that the energy density along with the contribution of dark source terms is inevitably negative which is quite useful in explaining several quantum field effects, because negative energies are closely linked with the quantum field theory. Such negative energies may also assist in time-travel to the past and formation of artificial wormholes. Furthermore, we evaluated the algebraic expressions for the mass of interior hyperbolical geometry and total energy budget, i.e., the Tolman mass of the considered source. Also, the structure scalars are evaluated to analyze the properties of matter configuration. Few analytical techniques are also presented by considering several cases to exhibit the exact analytical static solutions of the modified gravitational equations.

Extended corner symmetry, charge bracket and Einstein’s equations

We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies, and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner.

Particle production in modified gravity in the early and present day universe

Gravitational equations of motion in modified theories of gravity have oscillating solutions, both in the early and in the present day universe. Particle production by such oscillations is analyzed and possible observational consequences are considered. This phenomenon has impact on energy spectrum of cosmic rays and abundance of dark matter particles.

Cosmological viscous fluid models describing infinite time singularities in f(T) gravity

In this paper we explore the state parameter behaviour of the interacting viscous dark energy in f(T) gravity. Using constant deceleration parameter we investigate the cosmological implications of the viscosity and interaction between the dark components (energy and matter) in terms of Redshift. So doing, the viscosity and the interaction between the two fluids are parameterized by constants $$\delta $$ δ and $$\xi $$ ξ respectively. In the later part of the paper, we explore some bulk viscosity models describing Little Rip and Pseudo Rip future singularities within f(T) modified gravity. We obtain gravitational equations of motion for viscous dark energy coupled with dark matter. Solving these equations, we found analytic expressions for characteristic properties of these cosmological models.

Post-Newtonian limit: second-order Jefimenko equations

The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

Viscous accelerating universe with nonlinear and logarithmic equation of state fluid

We describe the accelerated expansion of the late-time universe using a generalized equation of state (EoS) when account is taken of bulk viscosity. We assume a homogeneous and isotropic Friedmann–Robertson–Walker spacetime. Solutions of the gravitational equations for dark energy are obtained in implicit form. Characteristic properties of the universe evolution in the presence of the viscosity effects are discussed. Finally, the dynamics of the accelerated expansion of the viscous universe are discussed on the basis of a modified logarithmic-corrected EoS.

Regular black holes with $$\varLambda >0$$ and its evolution in Lovelock gravity

In this work it is shown that the thermodynamics of regular black holes with a cosmological horizon, which are solutions of Lovelock gravity, determines that they must evolve either into a state where the black hole and cosmological horizons have reached thermal equilibrium or into an extreme black hole geometry where the black hole and cosmological horizons have merged. This differs from the behavior of Schwarzschild de Sitter geometry which evolves into a de Sitter space, the ground state of the space of solutions. This occurs due to a phase transition of the heat capacity of the black hole horizon. To perform that analysis it is shown that at each horizon a local first law of thermodynamics can be obtained from the gravitational equations.