Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes

TL;DR

This paper explores null geodesics and causal structure in Lorentzian-Euclidean black holes, showing photons cannot cross the horizon and analyzing matter accretion, with implications for singularity avoidance.

Contribution

It introduces a detailed analysis of null geodesics and causal structure in Lorentzian-Euclidean black holes, extending previous work on radial trajectories and singularity avoidance.

Findings

Photon orbits cannot cross the event horizon.

The causal structure is characterized with a Penrose diagram.

Matter accretion in the outer region is analyzed.

Abstract

Recently, we introduced the Lorentzian-Euclidean black hole, a static and spherically symmetric solution of vacuum Einstein equations that exhibits a change in metric signature across the event horizon. In this framework, the analysis of radial trajectories of freely falling bodies proves that the central singularity can be avoided via a mechanism we interpret as atemporality, which is responsible for the shift of the time variable from real to imaginary values. In this paper, we further explore this model by first examining the behavior of null geodesics. Our investigation requires a set of signature-adaptive coordinate changes that generalize the local Lorentz transformations underlying General Relativity. We find that photon orbits, like their massive counterparts, cannot traverse the event horizon, thereby strengthening the previous result on the impossibility to reach the $r=0$ singularity. Additionally, we discuss the causal structure of the spacetime, provide the corresponding Penrose diagram, and analyze the process of matter accretion in the outer region of the black hole.