Imaging a semi-classical horizonless compact object with strong redshift

Abstract

The recent advancements in black hole imaging have opened a new era of probing horizon-scale physics with electromagnetic radiation. However, a feature of the observed images, a bright ring encircling a relatively dark region, has not sufficiently proved the existence of event horizons. It thus requires extreme care when studying the possibility of using such image features to examine quantum effects that may change the classical picture of black holes slightly or drastically. In this work, we investigate the image of a horizonless compact object, whose interior metric satisfies the 4D semi-classical Einstein equation non-perturbatively for the Planck constant, and whose entropy agrees with the Bekenstein-Hawking formula. Although the absence of an event horizon allows light rays to pass through the dense interior, the extremely strong redshift significantly darkens the image, making it almost identical to the classical black-hole image. In particular, if there is light emission a bit inside the surface of the object, the intensity around the inner shadow is slightly enhanced, which could be a future observable prediction to characterize the object. We also find through a phenomenological parameter that the image is further darkened due to interactions inside. Thus, the image is consistent with current observations, and the object could be a candidate for black holes in quantum theory.