Asymptotic safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity, the idea of a nontrivial fixed point providing a possible UV completion...

The Schwarzschild solution describes spacetime under influence by a non-rotating massive spherically-symmetric object. Of the solutions to the Einstein field equations, it is considered by some to be one of the simplest and most useful. == Assumptions and notation == Working in a coordinate chart with coordinates ( r , θ , ϕ , t ) {\displaystyle \left(r,\theta ,\phi ,t\right)} labelled 1 to 4 respectively, we begin with...

In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. These are distinct from the electrovacuum solutions, which take into account the electromagnetic field in addition to the gravitational field. Vacuum solutions are also distinct from the lambdavacuum solutions, where the only term in the stress–energy tensor is the cosmological constant term (and thus, the lambdavacuums...