Introduction to General Relativity

Rotating charged black hole solution in heterotic string theory

“…Rotating charge neutral black hole solutions can also be constructed in string theory, and are identical to the Kerr solution [2] of ordinary Einstein gravity with the dilaton taking a constant value. Recently, rotating charged black hole solutions in these theories have been analyzed [3] in the limit of small angular momentum.…”

More about scalar gravity

“…(the minus sign at the RHS is because of our conventions on the curvature tensor [21]). This reformulation is due to Einstein and Fokker [22].…”

“…In our conventions [21] the Minkowski metric written in Cartesian coordinates is mostly minus: η µν = diag(1, −1, −1, −1), but it can be written in any coordinate system. The hypothesis that the matter fields are minimally coupled to the physical metric g µν warrants the validity of the weak equivalence principle.…”

“…It is immediate to verify that To study what happens at the surface ρ = 3 √ 3M (aka r = 3M ) let us briefly examine the radial timelike geodesics. The geodesic equation relative to the time coordinate t can be integrated as usual [21]:…”

Slightly Bimetric Gravitation

“…(From the flat spacetime viewpoint, this equation is best regarded as a force law, not a conservation equation.) If coordinate-dependent expressions are admitted, then one can write τ µν , µ = 0, where τ µν is some nontensorial complex that includes gravitational as well as matter energy-momentum [45,46]. But these objects behave oddly under coordinate transformations [47][48][49][50][51][52][53].…”