Hawking radiation inside a Schwarzschild black hole

TL;DR

This paper investigates the nature of Hawking radiation inside a Schwarzschild black hole, revealing that the quantum energy-momentum diverges near the singularity and is driven by the illusory horizon perceived by observers.

Contribution

It provides a detailed analysis of Hawking radiation and quantum energy-momentum inside a black hole, emphasizing the role of the illusory horizon and isotropic acceleration near the singularity.

Findings

Quantum energy-momentum diverges as r^{-6} near the singularity.

Hawking radiation inside the black hole is isotropic and power-law in character.

Quantum back reaction exacerbates the singularity.

Abstract

The boundary of any observer's spacetime is the boundary that divides what the observer can see from what they cannot see. The boundary of an observer's spacetime in the presence of a black hole is not the true (future event) horizon of the black hole, but rather the illusory horizon, the dimming, redshifting surface of the star that collapsed to the black hole long ago. The illusory horizon is the source of Hawking radiation seen by observers both outside and inside the true horizon. The perceived acceleration (gravity) on the illusory horizon sets the characteristic frequency scale of Hawking radiation, even if that acceleration varies dynamically, as it must do from the perspective of an infalling observer. The acceleration seen by a non-rotating free-faller both on the illusory horizon below and in the sky above is calculated for a Schwarzschild black hole. Remarkably, as an infaller approaches the singularity, the acceleration becomes isotropic, and diverging as a power law. The isotropic, power-law character of the Hawking radiation, coupled with conservation of energy-momentum, the trace anomaly, and the familiar behavior of Hawking radiation far from the black hole, leads to a complete description of the quantum energy-momentum inside a Schwarzschild black hole. The quantum energy-momentum near the singularity diverges as $r^{-6}$, and consists of relativistic Hawking radiation and negative energy vacuum in the ratio $3 : -2$. The classical back reaction of the quantum energy-momentum on the geometry, calculated using the Einstein equations, serves merely to exacerbate the singularity. All the results are consistent with traditional calculations of the quantum energy-momentum in 1+1 spacetime dimensions.