Gravitational Field of a Rotating Mass on an Expanding Universe

Abstract

We present a new exact solution to Einstein's field equations that unifies the Kerr black hole with Friedmann-Lemaître-Robertson-Walker cosmology. This metric reduces to Kerr-de Sitter in the appropriate limit and accounts for cosmological expansion dynamics both inside and outside the black hole. The model predicts a stationary mass, as well as a contracting ergosphere and event horizon with respect to the expanding cosmic rest frame. This result correctly generalises the McVittie metric to rotating masses or Kerr-de Sitter to arbitrary scale factors $a(t)$. Additionally, we find that the ergosphere tends to fade away with respect to the universe's expansion and no further interactions of dark energy with respect to the black hole's rotation.

References in corpus (6)

• Dynamics of dark energy
• Generating rotating regular black hole solutions without complexification
• Cosmological expansion and local physics
• Observational evidence for cosmological coupling of black holes and its implications for an astrophysical source of dark energy
• Black holes in the presence of dark energy
• Black holes as the source of dark energy: a stringent test with high-redshift JWST AGNs