Thermal one point functions, large d and interior geometry of black holes

Abstract

We study thermal one point functions of massive scalars in AdSd+1 black holes. These are induced by coupling the scalar to either the Weyl tensor squared or the Gauss-Bonnet term. Grinberg and Maldacena argued that the one point functions sourced by the Weyl tensor exponentiate in the limit of large scalar masses and they contain information of the black hole geometry behind the horizon. We observe that the one point functions behave identically in this limit for either of the couplings mentioned earlier. We show that in an appropriate large d limit, the one point function for the charged black hole in AdSd+1 can be obtained exactly. These black holes in general contain an inner horizon. We show that the one point function exponentiates and contains the information of both the proper time between the outer horizon to the inner horizon as well as the proper length from the inner horizon to the singularity. We also show that Gauss-Bonnet coupling induced one point functions in AdSd+1 black holes with hyperbolic horizons behave as anticipated by Grinberg-Maldacena. Finally, we study the one point functions in the background of rotating BTZ black holes induced by the cubic coupling of scalars.

Boundary signature of singularity in the presence of a shock wave

“…In this section, we present the calculations that lead to our main result (17). In Section 4.1, we first derive a general expression for the two-point function via a mode expansion and study some of its properties.…”

“…In Section 4.3, we discuss the analytic continuation of the large mass expression to complex frequencies, which reveals a concrete relation between the two-point function and geodesics in the shock wave spacetime. 10 Finally in Section 4.4, we Fourier transform the large mass expression in one of the frequencies to time and obtain the result (17).…”

“…Since Z(u L , u R ) depends on r c (u), one might expect branch cuts of r c (u) to remain branch cuts of Z(u L , u R ). 17 These considerations determines that the branch cut from the 4 branch points of r c (u) should extend radially outward to infinity.…”

“…See also[15][16][17][18][19][20] for recent works related to these approaches 2. Throughout this paper we assume the bulk time t increases toward the future in the right exterior, and increases…”

Holographic three-point correlators at finite density and temperature

“…the square of the Weyl tensor W 2 ) between the scalar field and the gravitons. Furthermore, one-point thermal functions in the limit of large dimensions and large spin have been considered in [22,23]. Subsequently, it was argued that a similar mechanism is at work, but now for the thermal two-point function [14].…”