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

Abstract

In this paper, we study the von Neumann entropy of Hawking radiation SR 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 CFTd+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 tPage. For the first case, SR grows linearly with time before the Page time and saturates after this time. Moreover, tPage is proportional to frac{2{S}_{mathrm{th}}}{cT} , where Sth and T are the thermal entropy and temperature of the black brane. For the second case, when the hyperscaling violation exponent θm of the matter fields is zero, the results are very similar to those for the first case. However, when θm ≠ 0, the entropy of Hawking radiation grows exponentially before tPage and saturates after this time. Furthermore, the Page time is proportional to log left(frac{1}{G_{mathrm{N},mathrm{r}}}right) , where GN,r is the renormalized Newton’s constant. It was also observed that for both cases, tPage 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, tPage is independent of zm, and for θm ≠ 0, it is a decreasing function of θm.