Nonconservative Unimodular Gravity: Gravitational Waves

Unimodular gravity is characterized by an extra condition with respect to general relativity, i.e., the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation: The symmetry properties of unimodular gravity are governed by the transverse diffeomorphisms. Nevertheless, if the conservation of the energy–momentum tensor is imposed in unimodular gravity, the general relativity theory is recovered with an additional integration constant which is associated to the cosmological term Λ. However, if the energy–momentum tensor is not conserved separately, a new geometric structure appears with potentially observational signatures. In this text, we consider the evolution of gravitational waves in a nonconservative unimodular gravity, showing how it differs from the usual signatures in the standard model. As our main result, we verify that gravitational waves in the nonconservative version of unimodular gravity are strongly amplified during the evolution of the universe.

Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

Einstein’s Notational Equation of Electro-Magnetic Field Equation in Rindler spacetime

We find Einstein’s notational equation of the electro-magnetic field equation and the electromagneticfield in Rindler space-time. Because, electromagnetic fields of the accelerated frame include in general relativity theory.

Spherical Solution of Classical Quantum Gravity

In the general relativity theory, using Einstein’s gravity field equation, we discover the spherical solution of the classical quantum gravity. The careful point is that this theory is different from the other quantum theory. This theory is made by the Einstein’s classical field equation.

Electromagnetic Wave Functions of CMB and Schwarzschild Space-Time

In the general relativity theory, we find electro-magnetic wave functions of Cosmic Microwave Background and Schwarzschild space-time. Specially, this article is that electromagnetic wave equations are treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

Electromagnetic Wave Function and Equation, Lorentz Force in Rindler Spacetime

In the general relativity theory, we find the electro-magnetic wave function and equation in Rindlerspace-time. Specially, this article is that electromagnetic wave equation is corrected by the gauge fixingequation in Rindler space-time. We define the force in Rindler space-time We find Lorentz force(electromagnetic force) by electro-magnetic field transformations in Rindler space-time. In the inertial frame, Lorentz force is defined as 4-dimensional force. Hence, we had to obtain 4-dimensional force in Rindler space-time. We define energy-momentum in Rindler space-time.

Reissner-Nodstrom Solution and Energy-Momentum Density’s Conservation Law

We find Reissner-Nodstrom solution hold by the energy-momentum density’s conservation law(Noether’s theorem) of electromagnetic field in general relativity theory.

New Gravity Field Equation is derived by Einstein Field Equation in General Relativity Theory

We found the 4-order curvature term satisfied the co-variant derivative. Einstein gravity fieldequation is consist of 2-order curvature terms. Hence, the 4-order curvature term and 2-order curvature termsmake new gravity field equation. In this point, Einstein’s gravity field equation can be modified by new 4-order curvature term because gravity field equation’s term doesn’t have to be 2-order term. Indeed, Einsteinhimself was like that, 0-order term, the cosmological term. Therefore, our theory is based on legitimate facts.