Maxwell-Lorentz without self-interactions: Conservation of energy and momentum

Since a classical charged point particle radiates energy and momentum it is argued that there must be a radiation reaction force. Here we present an action for the Maxwell-Lorentz without self interactions model, where each particle only responds to the fields of the other charged particles. The corresponding stress-energy tensor automatically conserves energy and momentum in Minkowski and other appropriate spacetimes. Hence there is no need for any radiation reaction.

Conharmonic Curvature Inheritance in Spacetime of General Relativity

The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conformal motion and conharmonic motion in general and Einstein spacetime. From the investigation of the kinematical and dynamical properties of the conformal Killing vector (CKV) with the Conh CI vector admitted by spacetime, it is found that they are quite physically applicable in the theory of general relativity. We obtain results on the symmetry inheritance for physical quantities (μ,p,ui,σij,η,qi ) of the stress-energy tensor in imperfect fluid, perfect fluid and anisotropic fluid spacetimes. Finally, we prove that the conharmonic curvature tensor of a perfect fluid spacetime will be divergence-free when a Conh CI vector is also a CKV.

The time traveler’s guide to the quantization of zero modes

We study the relationship between the quantization of a massless scalar field on the two-dimensional Einstein cylinder and in a spacetime with a time machine. We find that the latter picks out a unique prescription for the state of the zero mode in the Einstein cylinder. We show how this choice arises from the computation of the vacuum Wightman function and the vacuum renormalized stress-energy tensor in the time-machine geometry. Finally, we relate the previously proposed regularization of the zero mode state as a squeezed state with the time-machine warp parameter, thus demonstrating that the quantization in the latter regularizes the quantization in an Einstein cylinder.

Simulation of a rotating strong gravity that reverses time

In this research we simulated how time can be reversed with a rotating strong gravity. At first, we assumed that the time and the space can be distorted with the presence of a strong gravity, and then we calculated the angular momentum density of the rotating gravitational field. For this simulation we used Einstein’s field equation with spherical polar coordinates and the Euler’s transformation matrix to simulate the rotation. We also assumed that the stress-energy tensor that is placed at the end of the strong gravitational field reflects the intensities of the angular momentum, which is the normal (perpendicular) vector to the rotating axis. The result of the simulation shows that the angular momentum of the rotating strong gravity changes its directions from plus (the future) to minus (the past) and from minus (the past) to plus (the future), depending on the frequency of the rotation.

Physics in curved spacetime

Electromagnetic field theory, and the physics of continuous media (fluids, solids) in curved spacetime are discussed. Generalized Maxwell’s equations are written down and their justifaction is briefly presented. Then we turn to thermodynamics and continuous media. The concept of energy and momentum conservation is carefully expounded, and then the equations for fluid flow (continuity equation and Euler equation) are developed from the divergence of the energy tensor. The Bernoulli equation and the equation for hydrostatic equilibrium are obtained. The chapter then goes on to a general discussion of how general relativity operates and how gravitational phenomena are calculated and observed. The relation between gravity and other aspects of physics such as particle physics is discussed, along with the notion of general covariance.

Lagrangian mechanics for fields

An introduction to Lagrangian methods for classical fields in flat spacetime and then in curved spacetime. The Euler-Lagrange equations for Lagrangian densities are obtained, and applied to the wave, Klein-Gordan, Weyl, Dirac, Maxwell and Proca equations. The canonical energy tensor is obtained. Conservation laws and Noether’s theorem are described. An example of the treatment of Interactions is given by presenting the the QED Lagrangian. Finally, covariant Lagrangian methods are described, and the Einstein field eqution is derived from the Einstein-Hilbert action.