2024/02/16 by Maeda, Hideki, Martinez, Cristian · 3 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2402.11012
Without specifying a matter field nor imposing energy conditions, we study Killing horizons in n(≥ 3)-dimensional static solutions in general relativity with an (n-2)-dimensional Einstein base manifold. Assuming linear relations p\rm r≃χ\rm r ρ and p2≃χ\rm t ρ near a Killing horizon between the energy density ρ, radial pressure p\rm r, and tangential pressure p2 of the matter field, we prove that any non-vacuum solution satisfying χ\rm r<-1/3 (χ\rm r≠ -1) or χ\rm r>0 does not admit a horizon as it becomes a curvature singularity. For χ\rm r=-1 and χ\rm r∈[-1/3,0), non-vacuum solutions admit Killing horizons, on which there exists a matter field only for χ\rm r=-1 and -1/3, which are of the Hawking-Ellis type~I and type~II, respectively. Differentiability of the metric on the horizon depends on the value of χ\rm r, and non-analytic extensions beyond the horizon are allowed for χ\rm r∈[-1/3,0). In particular, solutions can be attached to the Schwarzschild-Tangherlini-type vacuum solution at the Killing horizon in at least a C1,1 regular manner without a lightlike thin shell. We generalize some of those results in Lovelock gravity with a maximally symmetric base manifold.