Hawking Radiation As Tunneling

345

322

Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.

Section: Radial Null Geodesic Method: a Brief Reviewmentioning

confidence: 99%

Section: Jhep06(2008)095mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum tunneling beyond semiclassical approximation

Banerjee

Majhi

2008

345

322

“…(4.4) reproduces the familiar relation. The single particle distribution can be understood by interpreting the occupation of states as arising from a tunnelling probability [53,54]. From the single particle number density (eq.…”

Section: Jhep10(2005)053mentioning

confidence: 99%

Black hole remnants at the LHC

Koch

Bleicher

Hossenfelder

2005

104

110

Within the scenario of large extra dimensions, the Planck scale is lowered to values soon accessible. Among the predicted effects, the production of TeV mass black holes at the LHC is one of the most exciting possibilities. Though the final phases of the black hole's evaporation are still unknown, the formation of a black hole remnant is a theoretically well motivated expectation. We analyze the observables emerging from a black hole evaporation with a remnant instead of a final decay. We show that the formation of a black hole remnant yields a signature which differs substantially from a final decay. We find the total transverse momentum of the black hole event to be significantly dominated by the presence of a remnant mass providing a strong experimental signature for black hole remnant formation.

“…There are great deal of works in the literature to study and to discuss the black hole's temperature β −1 (e.g., see [6] [9]- [15]). We employ the methods of Damour-Ruffini [9] and of Sannan [10] to do so.…”

mentioning

confidence: 99%

Remarks on 't Hooft's brick wall model

Bai

Yan

2003

A semi-classical reasoning leads to the non-commutativity of the space and time coordinates near the horizon of Schwarzschild black hole. This non-commutativity in turn provides a mechanism to interpret the brick wall thickness hypothesis in 't Hooft's brick wall model as well as the boundary condition imposed for the field considered. For concreteness, we consider a noncommutative scalar field model near the horizon and derive the effective metric via the equation of motion of noncommutative scalar field. This metric displays a new horizon in addition to the original one associated with the Schwarzschild black hole. The infinite red-shifting of the scalar field on the new horizon determines the range of the noncommutativ space and explains the relevant boundary condition for the field. This range enables us to calculate the entropy of black hole as proportional to the area of its original horizon along the same line as in 't Hooft's model , and the thickness of the brick wall is found to be proportional to the thermal average of the noncommutative space-time range. The Hawking temperature has been derived in this formalism. The study here represents an attempt to reveal some physics beyond the brick wall model. The brick wall model proposed by 't Hooft has been used for the purpose of deriving the entropy of black hole and other quantities [1] [2], and has been extensively studied (an incomplete list, see Refs.[3] [4]). In the model, the thickness of the brick wall near the horizon of Schwarzschild black hole was set to bewhere r H is the radius at which the horizon is located, l p = √ G (in this letterh = c = 1) the Planck length and N ′ the number of the multiplet of the quantum field in the model. Eq. (1) is a prior hypothesis of the brick wall model. Actually, only under this hypothesis, the thermodynamic properties of a black hole can be reproduced correctly. Namely, this model can lead to the correct Bekenstein-Hawking entropy formulawhere S BH is Bekenstein-Hawking entropy [5] [6] and A is the horizon area . In this letter, we try to derive the brick wall thickness by a semi-classical argument and to reveal some underlying physics related to this hypothesis. For the sake of definiteness, we study the 3 + 1 dimensional Schwarzschild black hole. In this case, ∂ t is the time Killing vector. Its global energy (or the mass of the black hole) is E BH = M = r H /2G. Rather than thinking black hole as a classical object, we treat it as a quantum state with high degeneracy and its degrees of freedom are located near by the horizon. Treating the energy E BH and its conjugate time coordinate as operators, quantum mechanics tells that these two quantities can not be measured simultaneously. In other words, E BH and t satisfy Heisenberg