Ringing and echoes from black bounces surrounded by the string cloud

Abstract: In the string theory, the fundamental blocks of nature are not particles but one-dimensional strings. Therefore, a generalization of this idea is to think of it as a cloud of strings. Rodrigues et al. embedded the black bounces spacetime into the string cloud, which demonstrates that the existence of the string cloud makes the Bardeen black hole singular, while the black bounces spacetime remains regular. On the other hand, the echoes are the correction to the late stage of the quasinormal ringing for a black hole, which is caused by the deviation of the spacetime relative to the initial black hole spacetime geometry in the near-horizon region. In this work, we study the gravitational wave echoes of black bounces spacetime surrounded by a cloud of strings under scalar field and electromagnetic field perturbation to explore the effects caused by a string cloud in the near-horizon region. The ringing of the regular black hole and traversable wormhole with string cloud are presented. Our results demonstrate that the black bounce spacetime with strings cloud is characterized by gravitational wave echoes as it transitions from regular black holes to wormholes, i.e. the echoes signal will facilitate us to distinguish between black holes and the wormholes in black bounces surrounded by the string cloud.