An Introduction to Loop Quantum Gravity and Its Application to Black Holes

This paper provides a brief introduction to Loop Quantum Gravity which is the main competitor of String Theory for a quantized theory of gravity. It is formulated on the basis of a Hamiltonian formalism of General Relativity with quantization performed in a non-perturbative and background independent manner. Coupling to matter fields as they appear in the Standard Model is also considered. Canonically quantizing General Relativity, it is shown that spacetime is discretized at Planckian scales and such a result leads to applying Loop Quantum Gravity to calculations of black hole entropy values. An alternative method to the Hamiltonian formalism of Loop Quantum Gravity called the spin foam formalism is also discussed.