Energy-Momentum Squared Gravity

Understand

A new covariant generalization of Einstein's general relativity is developed which allows the existence of a term proportional to $T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory ($T_{\alpha\beta}$ is the energy-momentum tensor).

• Consequently the relevant field equations are different from general relativity only in the presence of matter sources.
• In the case of a charged black hole, we find exact solutions for the field equations.
• Applying this theory to a homogeneous and isotropic space-time, we find that there is a maximum energy density $\rho_{\text{max}}$, and correspondingly a minimum length $a_{\text{min}}$, at early universe.