Hawking radiation in κ-spacetime

Abstract

In this paper, we analyze the Hawking radiation of a κ-deformed-Schwarzschild black hole and obtain the deformed Hawking temperature. For this, we first derive deformed metric for the κ-spacetime, which in the generic case, is not a symmetric tensor and also has a momentum dependence. We show that the Schwarzschild metric obtained in the κ-deformed spacetime has a dependence on energy. We use the fact that the deformed metric is conformally flat in the 1 + 1 dimensions to solve the κ-deformed Klein-Gordon equation in the background of the Schwarzschild metric. The method of Bogoliubov coefficients is then used to calculate the thermal spectrum of κ-deformed-Schwarzschild black hole and show that the Hawking temperature is modified by the noncommutativity of the κ-spacetime.

Superdense star in a spacetime with minimal length

“…Here also we notice that the deformed tangential pressure gets scaled by (1 + 4ak 0 ) factor. The positivity condition for tangential pressure and the expression for central density yield a limit on deformation parameter given by |a| > 10 −16 m and this is in agreement with the bound obtained in [22]. The negative value of bound on deformation parameter a is seen in [43] also.…”

“…In this section, first we summerise the construction of metric in the κdeformed space-time [22]. Then we use deformed metric as well as deformed energy-momentum tensor and derive κ-deformed Einstein field equations, which form the basis of our analysis.…”

“…We demand that ŷµ also can be written in terms of commutative coordinate and momenta as ŷµ = x α φ α µ (p). The κ-deformed metric can be obtained [22] from Eq. (3.2) as…”

“…A detailed behaviour of black holes in Moyal space-time has been studied in [16]. In the present work, we will use another non-commutative space-time, called κ-deformed space-time, whose coordinates obey a Lie algebra type commutation relation between the space and time coordinates [17,18,19,20,21,22]. Theoretical studies of black hole in κ-space-time have been reported in [23,24,25] and properties of compact stars in κ-deformed space-time is studied [26].…”

Maximal acceleration in non-commutative space-time and its implications

“…We have derived κ-deformed corrections to the Hawking temperature from the deformed Schwarzschild metric using imaginary time method. The κ-deformed correction, expressed in terms of a, is the same as that in [48], where the κ-deformed correction to the Hawking temperature is obtained using the method of Bogoliubov coefficients. Using the deformed Hawking temperature we have derived deformed entropy and heat capacity, which involve deformed maximal acceleration.…”