Minimal length effects in black hole thermodynamics from tunneling formalism

Abstract

The tunneling formalism in the Hamilton-Jacobi approach is adopted to study Hawking radiation of massless Dirac particles from spherically symmetric black hole spacetimes incorporating the effects of the generalized uncertainty principle. The Hawking temperature is found to contain corrections from the generalized uncer-tainty principle. Further, we show from this result that the ratio of the GUP cor-rected energy of the particle to the GUP corrected Hawking temperature is equal to the ratio of the corresponding uncorrected quantities. This result is then exploited to compute the Hawking temperature for more general forms of the uncertainty principle having infinite number of terms. Choosing the coefficients of the terms in the series in a specific way enables one to sum the infinite series exactly. This leads to a Hawking temperature for the Schwarzschild black hole that agrees with the result which accounts for the one loop back reaction effect. The entropy is finally computed and yields the area theorem upto logarithmic corrections. The existence of a minimal observable length is a common feature of all candidate theories of quantum gravity such as string theory [1]-[3], loop quantum gravity [4] and noncom-mutative geometry [5]. The consequence of this is the modification of the Heisenberg uncertainty principle to the so called generalized uncertainty principle (GUP) ∆x∆p ≥ h