Abstract
In the Painleve–Gullstrand (PG) reference frame, the description of elementary particles in the background of a black hole (BH) is similar to the description of non-relativistic matter falling toward the BH center. The velocity of the fall depends on the distance to the center, and it surpasses the speed of light inside the horizon. Another analogy to non-relativistic physics appears in the description of the massless fermionic particle. Its Hamiltonian inside the BH, when written in the PG reference frame, is identical to the Hamiltonian of the electronic quasiparticles in type II Weyl semimetals (WSII) that reside in the vicinity of a type II Weyl point. When these materials are in the equilibrium state, the type II Weyl point becomes the crossing point of the two pieces of the Fermi surface called Fermi pockets. It was previously stated that there should be a Fermi surface inside a black hole in equilibrium. In real materials, type II Weyl points come in pairs, and the descriptions of the quasiparticles in their vicinities are, to a certain extent, inverse. Namely, the directions of their velocities are opposite. In line with the mentioned analogy, we propose the hypothesis that inside the equilibrium BH there exist low-energy excitations moving toward the exterior of the BH. These excitations are able to escape from the BH, unlike ordinary matter that falls to its center. The important consequences to the quantum theory of black holes follow.
Highlights
In the Painleve–Gullstrand (PG) coordinate frame, the Schwarzschild black hole solution [1,2] has a form such that the description of matter resembles the description of liquid motion [3,4]
This is why we suppose that the Fermi surface that appears in the equilibrium state within the black hole (BH) interior is closed
We rely on the description of the black hole in Einstein’s theory of gravity, which enables the use of the Painleve–Gullstrand reference frame, where the metric has the especially simple form of Equation (1)
Summary
In the Painleve–Gullstrand (PG) coordinate frame, the Schwarzschild black hole solution [1,2] has a form such that the description of matter resembles the description of liquid motion [3,4]. The low-energy excitations near one piece of the Fermi surface move only toward the center of the BH, while the low-energy excitations near the other piece of the Fermi surface move only toward the exterior of the black hole This hypothesis has been illustrated by a particular lattice model, which belongs to a class of the analogue gravity models (for discussion of the analogue gravity models, see, for example, [28] and references therein). We only deal with the dynamics of matter in the presence of a fixed gravitational background and completely neglect the back reaction This allows us to seriously take into account the analogy with type II Weyl semimetals while considering the motion of elementary particles. We rely only on the compactness and finiteness of the Fermi surface formed inside the black hole according to the scenario of [13]
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