Abstract
We develop a new test that provides a necessary condition for a quantum state to be smooth in the vicinity of a null surface: “near-horizon modes” that can be defined locally near any patch of the null surface must be correctly entangled with each other and with their counterparts across the surface. This test is considerably simpler to implement than a full computation of the renormalized stress-energy tensor. We apply this test to Reissner-Nordström black holes in asymptotically anti-de Sitter space and provide numerical evidence that the inner horizon of such black holes is singular in the Hartle-Hawking state. We then consider BTZ black holes, where we show that our criterion for smoothness is satisfied as one approaches the inner horizon from outside. This results from a remarkable conspiracy between the properties of mode-functions outside the outer horizon and between the inner and outer horizon. Moreover, we consider the extension of spacetime across the inner horizon of BTZ black holes and show that it is possible to define modes behind the inner horizon that are correctly entangled with modes in front of the inner horizon. Although this provides additional suggestions for the failure of strong cosmic censorship, we lay out several puzzles that must be resolved before concluding that the inner horizon will be traversable.
Highlights
Receive radiation from all the events outside the black hole, which stretch out for an infinite amount of time [1]
We develop a new test that provides a necessary condition for a quantum state to be smooth in the vicinity of a null surface: “near-horizon modes” that can be defined locally near any patch of the null surface must be correctly entangled with each other and with their counterparts across the surface
This corresponds to the fact that if we set the local temperature of the field correctly near the outer horizon, it is automatically red-shifted by the geometry so that the local temperature of the modes near the inner horizon coincides exactly with the temperature of the inner horizon! This is in contrast to what we found numerically in the previous section for the AdS-RN black hole in higher dimensions
Summary
To test whether the spacetime in the vicinity of a surface is smooth, we can test whether it is possible to transmit “messages” in that region by turning on a source for a field at one point and measuring the response of the field at another. We define some modes by integrating the field over a very short distance on both sides of the U = 0 surface and for a very short distance over the transverse coordinates. In the limit where s(ω) is very sharply peaked around ω = 0, and using the normalization condition (2.11), the two-point function just reduces to e−πω0 Ψ|aa|Ψ = 1 − e−2πω0 This gives us the universal form of entanglement for short distance modes on opposite sides of the horizon. The analysis above tells us that this coefficient must be universal and cannot be changed by a smooth deformation We will elucidate this point further in our analysis of the Reissner-Nordström black hole below, where we discuss global modes and explicitly relate them to the near-horizon modes defined above
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
