Heavy Fields and Gravity

TL;DR

This paper investigates how heavy fields influence 4D spacetimes with various asymptotics, deriving higher derivative corrections to gravity, analyzing their effects on black hole properties, and assessing the reliability of these corrections within effective field theory.

Contribution

It provides a detailed calculation of higher derivative corrections from heavy fields on black hole solutions and entropy, demonstrating the robustness of black hole properties against these corrections.

Findings

Higher derivative operators modify black hole horizons and thermodynamics.

Scalar and fermion fields increase entropy bounds, vectors decrease them.

Many corrections are below the effective field theory's resolving power, questioning their physical significance.

Abstract

We study the effects of heavy fields on 4D spacetimes with flat, de Sitter and anti-de Sitter asymptotics. At low energies, matter generates specific, calculable higher derivative corrections to the GR action which perturbatively alter the Schwarzschild-$(A)dS$ family of solutions. The effects of massive scalars, Dirac spinors and gauge fields are each considered. The six-derivative operators they produce, such as $\sim R^{3}$ terms, generate the leading corrections. The induced changes to horizon radii, Hawking temperatures and entropies are found. Modifications to the energy of large $AdS$ black holes are derived by imposing the first law. An explicit demonstration of the replica trick is provided, as it is used to derive black hole and cosmological horizon entropies. Considering entropy bounds, it's found that scalars and fermions increase the entropy one can store inside a region bounded by a sphere of fixed size, but vectors lead to a decrease, oddly. We also demonstrate, however, that many of the corrections fall below the resolving power of the effective field theory and are therefore untrustworthy. Defining properties of black holes, such as the horizon area and Hawking temperature, prove to be remarkably robust against higher derivative gravitational corrections.