Entropy of Hawking radiation for two-sided hyperscaling violating black branes

Abstract

Abstract In this paper, we study the von Neumann entropy of Hawking radiation S R for a d + 2-dimensional Hyperscaling Violating (HV) black brane which is coupled to two Minkowski spacetimes as the thermal baths. We consider two different situations for the matter fields: first, they are described by a CFT d+2 whose central charge c is very large. Second, they are described by a d+2 dimensional HV QFT which has a holographic gravitational theory that is a HV geometry at zero temperature. For both cases, we calculate the Page curve of the Hawking radiation as well as the Page time t Page. For the first case, S R grows linearly with time before the Page time and saturates after this time. Moreover, t Page is proportional to 2 S th cT $$ \frac{2{S}_{\mathrm{th}}}{cT} $$ , where S th and T are the thermal entropy and temperature of the black brane. For the second case, when the hyperscaling violation exponent θ m of the matter fields is zero, the results are very similar to those for the first case. However, when θ m ≠ 0, the entropy of Hawking radiation grows exponentially before t Page and saturates after this time. Furthermore, the Page time is proportional to log 1 G N , r $$ \left(\frac{1}{G_{\mathrm{N},\mathrm{r}}}\right) $$ , where G N,r is the renormalized Newton’s constant. It was also observed that for both cases, t Page is a decreasing and an increasing function of the dynamical exponent z and hyperscaling violation exponent θ of the black brane geometry, respectively. Moreover, for the second case, t Page is independent of z m , and for θm ≠ 0, it is a decreasing function of θ m .

Keywords

• AdS-CFT Correspondence
• Gauge-Gravity Correspondence