Why Quantum Fields Equalize Horizon Temperatures ✛ ✦

Original: "Nontrivial self-consistent backreaction of quantum fields in 2D dilaton gravity"
arXiv:2401.07645 · 2024-01-15 · CC BY 4.0 · 1 min
Quantum fields in a spacetime with two horizons at different temperatures force them to equalize.

Two vessels of water at different temperatures are connected by a partition. Remove the partition, and the temperatures begin to equalize until they match. A similar process occurs in a spacetime with two black hole horizons when quantum fields are present.

A horizon is a boundary beyond which light cannot escape. A black hole can have two horizons, and they have different temperatures: the outer one has a nonzero temperature, while the inner one is at zero. Quantum fields filling the space between the horizons behave like a gas of particles, but their energy depends on the curvature of spacetime. Near the horizon with nonzero temperature, this energy becomes infinite.

Infinite energy means that quantum fields strongly affect the geometry, curving it even further. This is called backreaction.

When backreaction was taken into account, the geometry changed: the dilaton field became constant, and the metric function took an exponential form. The new geometry has two horizons at infinities, and both horizons have zero temperature. Thus, quantum fields equalize the temperatures of the horizons by restructuring spacetime itself.

In two-dimensional gravity, the horizon temperature is proportional to its surface gravity, and for the horizon at r = 0 it is zero, even though the horizon exists. This resembles an extreme black hole, but here the zero temperature arises from the degeneracy of the metric function.

ds^2 = -[a^2 r^2 - a^4 r^4] dt^2 + \frac{dr^2}{a^2 r^2 - a^4 r^4}
Metric of two-dimensional spacetime with two horizons, where a is a parameter related to the cosmological constant λ.
T = \begin{cases} \frac{a}{2\pi}, & r \to 1/a, \\ 0, & r \to 0. \end{cases}
Canonical temperatures at the two horizons: at the outer horizon the temperature is proportional to a, at the inner horizon it is zero.
-\langle :T^{matter}_{tt}: \rangle = \frac{\pi}{6\beta^2} + \frac{e^{2\nu(X)}}{24\pi} [\nu'(X)^2 + 2\nu''(X)]
Regularized energy density of the thermal scalar field, including the thermal contribution and the conformal anomaly contribution.
Scientists
Stephen HawkingJacob BekensteinFritz ZwickyEmmy NoetherBernhard RiemannJoseph Weber
Concepts
backreaction analogue black holes schwarzschild metric quantum corrections black hole thermodynamics quantum nature of gravity horizon area particle antiparticle pair white hole semiclassical gravity gravitational instanton logarithmic correction kerr metric tidal charge remnant Hawking radiation antiquark Einstein field equations gravitational decoherence mirror symmetry