Determining the Minimal Length Scale of the Generalized Uncertainty Principle from the Entropy-Area Relationship

Understand

We derive the formula of the black hole entropy with a minimal length of the Planck size by counting quantum modes of scalar fields in the vicinity of the black hole horizon, taking into account the generalized uncertainty principle (GUP).

• This formula is applied to some intriguing examples of black holes - the Schwarzschild black hole, the Reissner-Nordstrom black hole, and the magnetically charged dilatonic black hole.
• As a result, it is shown that the GUP parameter can be determined by imposing the black hole entropy-area relationship, which has a Planck length scale and a universal form within the near-horizon expansion.