Related papers: Energy in Fourth Order Gravity
The discovery of cosmic acceleration has triggered a consistent body of theoretical work aimed at modeling its phenomenology and understanding its fundamental physical nature. In recent years, a powerful formalism that accomplishes both…
We establish a general relation between the canonical energy-momentum tensor of Lagrangian dynamics and the tensor that acts as the source of the gravitational field in Einstein's equations, and we show that there is a discrepancy between…
The fourth-gradient model for fluids-associated with an extended molecular mean-field theory of capillarity-is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is…
A exact de Sitter-like cosmological solution of quadratic gravitation with torsion has been found. In the limit of constant energy and pressure, it becomes a exact de Sitter spacetime. It exists in a wide class of quadratic gravity theories…
We consider whether local and causal non-conservation of energy may occur in generally covariant theories with long-ranged fields (analogs of Newton's gravity) whose source is energy--momentum. We find that such a possibility exists in…
Viewing gravitational energy momentum $p_G^\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\mu$ requires two different symmetries to account for their independent conservations - spacetime and inner…
The theory of quantum fields in classical backgrounds is re-examined for the cases in which the Lagrangian is quadratic in quantum fields. Various methods that describe particle production are discussed. It is found that all methods suffer…
Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system…
An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows…
The nonrenormalizable singularity of the gravitational 1/r potential at ralativistic and quantum levels is a longstanding problem of modern physics. The problem is discussed in Relativistic Lagrangean framework with the variable proper…
We present an energy conservative, quadrature based model reduction framework for the compressible Euler equations of Lagrangian hydrodynamics. Building on a finite element discretization of the governing equations, we develop reduced…
We generalize the $f(R)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the matter Lagrangian $L_m$. We obtain the gravitational field equations in the…
We first review the various definition of the total energy in the gravitational system. The naive definition has some defects, and we review how to modify the definition of the total energy. Then we explicitly demonstrate how to calculate…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
We start with the cosmic Friedmann equations, where we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that…
We present a simple "Wald-like" formula for gravitational energy about a constant curvature background spacetime. The formula is derived following the Abbott-Deser-Tekin approach for the definition of conserved asymptotic charges in…
The paper discusses the influences of velocity curl and field strength on some theorems in the electromagnetic field and gravitational field. With the characteristics of the algebra of quaternions, the theorem of linear momentum,…
We consider the higher-order gravity theory derived from the quadratic lagrangian $R+\epsilon R^2$ in vacuum as a first-order (ADM-type) system with constraints, and build time developments of solutions of an initial value formulation of…
We proposed a gravitation theory based on an analogy with electrodynamics on the basis of a vector field. For the first time, to calculate the basic gravitational effects in the framework of a vector theory of gravity, we use a Lagrangian…
We investigate the connection between dark energy and fourth order gravity by analyzing the behavior of scalar perturbations around a Friedmann-Robertson-Walker background. The evolution equations for scalar perturbation are derived using…