Interior of Schwarzschild in semiclassical gravity

Abstract

In Einstein gravity, matter with an arbitrarily small density can be a black hole. Pressure in the star diverges if size of the star is smaller than 9/8 of the Schwarzschild radius, implying the gravitational collapse into a black hole. By taking quantum effects of matter, however, pressure is bounded from above, and a core with negative energy appears instead. Density of matter increases and eventually reaches the cut-off scale as size of the star approaches the Schwarzschild radius. This result implies that density must be very large as the Planck scale if the star is put inside the Schwarzschild radius.

Figures (1)

• Figure 1: As the radius of the star $r_s$ approaches the Schwarzschild radius $r_h = 2 G M$, the amount of negative energy in the semiclassical core $A$ increases. The radius $r_s$ goes to the Schwarzschild radius in $A\to\infty$.