Session AAA02: V: Alternative Theories of Gravity

Spacetimes between Einstein and Kaluza-Klein

Extended general relativity is the extension of general relativity from the tensor algebra to its own universal covering algebra. The universal covering algebra involves all direct sums of tensors of different rank, elements called tensor multinomials. Focusing on a subalgebra consisting of direct sums of scalar, vector, and second rank tensor fields only, results in geometric objects as spacious as those in five-dimensional Kaluza-Klein spacetimes while remaining defined over only four space-time dimensions, hence may be thought of as being between the theories of Einstein and Kaluza and Klein. It is possible to deduce the equivalent of Christoffel symbols from the equivalent geodesic equation, and from the Christoffel symbols, the extended Ricci curvature. The extended Ricci curvature yields the Ricci tensor of general relativity, Maxwell's electromagnetism, and a Kaluza-Klein scalar field equation as components of a single second-rank tensor multinomial equation. The scalar field couples naturally to the square of the electric charge, leading to a new force that may be significant only in collapsed matter or in a cosmological setting. There are numerous possible new Lagrangians unique to this formalism, and rich new ways of introducing scalar fields and accelerated cosmological expansion. In one of many such solutions, a scalar field source that falls off with expanding volume forces a dark energy equation of state.   

On the Emission of the Gravitational Radiation by Light via Gravitational Redshift

In this research, it has been shown that the energy difference during the redshift is equal to the energy difference emitted by a massless field wave moving away from a central mass. Therefore, gravitational redshift is explained to be a phenomenon caused by gravitational waves emitted by a photon moving away from the gravitational field. Using the definition of the gravitational waves according to the Teleparallel Equivalent of General Relativity (TEGR), it has been shown that the energy difference due to gravitational redshift which usually explained as the energy difference due to gravitational time dilation experienced by observers at different distances from the gravitating object. Hence, it is shown that the difference between the two observed energies of the gravitational redshift of light is calculated and is the same as the value obtained in TEGR. Since gravitational waves in TEGR is equivalent to General Relativity, gravitational redshift might be one of the oldest, therefore the first indirect experimental proof of the existence of gravitational waves.    

Compensator fields in dimensional reduction and compactification without truncation — Part III: Einstein Gravity

In dimensionally reduced theories with gauge or diffeomorphism invariance, consistency of the Kaluza-Klein ansatz requires the introduction of compensator fields. The compensator fields project gauge-variant field fluctuations to their physical horizontal components, which in turn determine the gauge-invariant moduli space metric that appears in kinetic terms of the lower dimensional theory. The compensator fields must be introduced "by hand" in dimensional reduction (i.e., compactification truncated to zero modes), but arise automatically in the full untruncated theory. Warming up with gauge theory, and then focusing on pure Einstein gravity compactified on an arbitrary compact manifold, we re-express the full untruncated parent theory in lower dimensional language, and identify the compensator fields. One of their known geometric interpretations features prominently. The moduli space of metrics on the compact manifold can be regarded as a fiber bundle whose fiber is the space of diffeomorphisms. The compensator fields arise as a repackaging of the connection on this bundle.   

Violation of the Equivalence Principle for some Macroscopic Quantum Bodies

We consider macroscopic ensembles of the hydrogen atoms in a weak post-Newtonian gravitation field in the presence of quantum effects. We show that for the most ensembles the Einstein’s Equivalence Principle is valid in the above mentioned quantum case. On the other hand, it is shown to be broken for some special macroscopic ensembles [1] – the coherent quantum superpositions of the stationary quantum states. We discuss how such ensembles (which we call “Gravitational demons”) can be created using laser technique in the Earth’s laboratories and how the violation of the Equivalence Principle can be observed.

[1] A.G. Lebed, Editor, Breakdown of Einstein’s Equivalence Principle (World Scientific, Singapore, 2023).

    

Concept of quantum space-time structure- Initial stage (Basic framework)

This paper's aim is to showcase a possible fundamental structure of space-time, which is done by using the basic concepts of quantum time crystal i.e. discrete time transitional symmetry. I am able to comprehend the structural description of space-time in a way that elucidates the origin of gravity and may describe the working of quantum gravity. This paper provides an alternate framework to understand gravity in a more thorough way, to get one step closer to completing the "Theory of Everything".   

Gravitational wave energy-momentum tensor and radiated power in a strongly curved background

Allowing for the possibility of extra dimensions, there are two paradigms: either the extra dimensions are hidden from observations by being compact and small as in Kaluza-Klein scenarios, or the extra dimensions are large/non-compact and undetectable due to a large warping as in the Randall-Sundrum scenario. In the latter case, the five-dimensional background has a large curvature, and Isaacson's construction of the gravitational energy-momentum tensor, which relies on the assumption that the wavelength of the metric fluctuations is much smaller than the curvature length of the background spacetime, cannot be used. In this work, we construct the gravitational energy-momentum tensor in a strongly curved background such as Randall-Sundrum. We perform a scalar-vector-tensor decomposition of the metric fluctuations with respect to the $SO(1,3)$ background isometry and construct the covariantly-conserved gravitational energy-momentum tensor out of the gauge-invariant metric fluctuations. We also give a formula for the radiated power.