We profit by a recent paper of Visser claiming that Rastall gravity is equivalent to Einstein gravity to compare the two gravitational theories in a general way. Our conclusions are different from Visser’s ones. We indeed argue that these two theories are not equivalent. In fact, Rastall theory of gravity is an “open” theory when compared to Einstein general theory of relativity. Thus, it is ready to accept the challenges of observational cosmology and quantum gravity.

/pdf/einstein-and-rastall-theories-of-gravitation-in-comparison-35tc92vomv.pdf

Einstein and Rastall theories of gravitation in comparison

We profit by a recent paper of Visser claiming that Rastall gravity is equivalent to Einstein gravity to compare the two gravitational theories in a general way. Our conclusions are different from Visser's ones. We indeed argue that these two theories are not equivalent. In fact, Rastall theory of gravity is an "open" theory when compared to Einstein general theory of relativity. Thus, it is ready to accept the challenges of observational cosmology and quantum gravity.

/pdf/einstein-and-rastall-theories-of-gravitation-in-comparison-53mladrccs.pdf

Einstein and Rastall Theories of Gravitation in Comparison

A prototype of Rastall’s theory of gravity, in which the divergence of the energy-momentum tensor is proportional to the gradient of the scalar curvature, is shown to be derivable from a variational principle. Both the proportionality factor and the unrenormalized gravitational constant are found to be covariantly constant, but not necessarily constant. The prototype theory is, therefore, a gravitational theory with variable gravitational constant.

Variational principle for a prototype Rastall theory of gravitation

We explore the thermodynamic analysis at the apparent horizon in the framework of Rastall theory of gravity. We take different entropies such as the Bakenstein, logarithmic corrected, power law corrected, and the Renyi entropies. We investigate the first law and generalized second law of thermodynamics analytically for these entropies which hold under certain conditions. Furthermore, the behavior of the total entropy in each case is analyzed. As a result, it is implied that the generalized second law of thermodynamics is satisfied. We also check whether the thermodynamic equilibrium condition for these entropies is met at the present horizon.

/pdf/thermodynamics-in-rastall-gravity-with-entropy-corrections-578gwiy9le.pdf

Thermodynamics in Rastall gravity with entropy corrections

Comparative analysis of Einstein gravity and Rastall gravity for the compact objects

The proper framework for testing Rastall's theory and its generalizations is in the case of non-negligible (i.e. discernible) gravitational effects such as gravity gradients. These theories have conserved integral four-momentum and angular momentum. The Nordtvedt effect then provides limits on the parameters which arise as the result of the non-zero divergence of the energy-momentum tensor.

http://iopscience.iop.org/article/10.1088/0305-4470/16/10/014/pdf

L. L. Smalley

Papers

Rastall's and related theories are conservative gravitational theories although physically inequivalent to general relativity