Flat-space holography and stress tensor of Kerr black hole

Abstract

We propose a stress tensor for the Kerr black hole written in the Boyer-Lindquist coordinate. To achieve this, we use the dictionary of the Flat/CCFT correspondence and take the flat-space limit from the quasi-local stress tensor of the four-dimensional Kerr-AdS black hole. The proposed stress tensor yields the correct values for the mass and angular momentum of the Kerr black hole at spatial infinity. We also calculate some components of the energy momentum tensor of the three dimensional CCFT and show that they are consistent with the holographic calculation of the Kerr black hole. The calculation we present in this paper is another confirmation for the Flat/CCFT proposal.

Stress tensor correlators of $$\hbox {CCFT}_2$$ CCFT 2 using flat-space holography

“…Our results in this paper are consistent with [12]. This method has also been used previously for the quasi-local stress tensor of the Kerr black hole [14] and the results are consistent with the ones obtained through taking the flatspace limit.…”

Flat-space holography and correlators of Robinson–Trautman stress tensor

“…Our approach in this paper is similar to [10,11,12,13]. We start from some asymptotically flat solutions and find the asymptotically AdS spacetimes whose flat-space limit leads to the original asymptotically flat metric.…”

“…We have used the above approach for BMSFT 2 in papers [10,11,13] and for the quasi-local stress tensor of the Kerr black hole in [12]. In this paper we apply our method for a class of fourdimensional asymptotically flat spacetimes known as Robinson-Trautman (RT) solutions [20] (see also [21] ).…”

“…Although, taking the flat-space limit from the metric components is straightforward but stress tensor components are either zero or singular after taking the naive flat-space limit. Hence, similar to [10,11,12,13], we first multiply appropriate powers of AdS radius and then take the flat-space limit. In order to show that our proposed stress tensor is correct, we shall use it to compute the conserved charges of symmetry generators.…”

Complexity growth in flat spacetimes

“…The interesting point is that this formula yields the entropy of three-dimensional flat space cosmology (FSC), which is given by taking the flat space limit from the Banados, Teitelboim and Zanelli (BTZ) black holes. The universal structure of the correlation functions of BMSFT 2 and BMSFT 3 has been studied in [9][10][11][12]. The entanglement entropy formula and also the holographic interpretation of this formula in the context of flat/BMSFT have been studied in [13][14][15][16][17][18][19][20].…”