General relativity 

Einstein field equations
Equations 

Linearized Gravity
PostNewtonian formalism Einstein field equations
Friedmann equations
ADM formalism
BSSN formalism 
Advanced theories 

Kaluza–Klein Quantum gravity 
Solutions 

Schwarzschild
ReissnerNordström · Gödel
Kerr · KerrNewman
Kasner · TaubNUT · Milne · RobertsonWalker
ppwave 


Quantum gravity is an area of research in physics. Right now, physics is able to describe gravity of reallife sized objects using general relativity. Physicists can also describe the universe on a microscopic scale with quantum mechanics. The goal of quantum gravity is to develop a theory which contains both general relativity and quantum mechanics. However, combining the theories of the big and the small is very difficult in practice.
Physicists are working on a number of ways to write down a theory of quantum gravity. One approach is to search for a unified field theory. Physicists also try to develop theories at an even more fundamental level, like string theory, loop quantum gravity, or other methods, to find out why our current theories of gravity and quantum mechanics cannot be combined.
Images for kids

Gravity Probe B (GPB) has measured spacetime curvature near Earth to test related models in application of Einstein's general theory of relativity.


Projection of a Calabi–Yau manifold, one of the ways of compactifying the extra dimensions posited by string theory