Effects of spontaneous Lorentz Symmetry breaking on Letelier-AdS charged black boles within Kalb-Ramond gravity

TL;DR

The paper investigates spontaneous Lorentz symmetry breaking in Kalb–Ramond gravity for a static Letelier-AdS black hole surrounded by a cloud of strings. It analyzes photon geodesics, photon-sphere structure, and BH shadows, deriving how the KR parameter $\ell$ and string-cloud parameter $\alpha$ modify the effective potentials, topological properties, and asymptotics, with constraints derived from EHT observations of M87* and Sgr A*. The study extends to neutral test-particle dynamics, ISCO shifts, and the fundamental frequencies related to QPOs, showing measurable deviations from GR predictions and outlining observational tests. It also develops the KR–CoS framework with a nonminimal coupling to the Ricci tensor, derives the modified field equations, and compares the resulting Letelier–AdS–KR solutions to global monopole scenarios, highlighting potential signatures in BH imaging and timing data.

Abstract

In this study, we investigate the geodesic motion of massless particles -- specifically photons -- in the spacetime of a charged anti-de Sitter (AdS) black hole (BH) surrounded by a cloud of strings (CoS) within the framework of Kalb-Ramond (KR) gravity. We analyze the effective potential that governs photon trajectories, explore the properties and location of the photon sphere (PS), and examine the effective radial force acting on photons. The resulting BH shadow is also studied, highlighting the roles of both the CoS parameter $α$ and the KR field parameter $\ell$ in shaping its geometry. We constrain these parameters using observational data from M87* and Sgr A* obtained by the Event Horizon Telescope (EHT). Furthermore, we extend our investigation to the motion of neutral test particles in the same gravitational background. By examining the impact of the CoS and KR field, we show how these additional fields modify the dynamics relative to standard charged BH scenarios. Finally, we study the fundamental frequencies associated with quasiperiodic oscillations (QPOs) of test particles, demonstrating how these frequencies are affected by the presence of the CoS and KR field. Our results reveal the rich structure of AdS-BH spacetimes influenced by string clouds and antisymmetric tensor fields, with potential observational consequences in gravitational wave and BH imaging astronomy.

Figures (21)

• Figure 1: Behavior of the metric function $f(r)$ for a charged BH. Here $Q/M=0.5,\,\,\Lambda=-0.001/M^2$.
• Figure 2: A comparison of the metric function $f(r)$ for charged BHs in different configurations. Here $Q/M=0.5,\,\,\Lambda=-0.001/M^2$.
• Figure 3: The radial profiles of the Ricci scalar for various values of KR field parameter $\ell$ and CoS parameter $\alpha$ with $\Lambda=-0.001/M^2$.
• Figure 6: Behavior of the effective potential $V_\text{eff}(r)$ as a function of $r/M$ for different values of KR field parameter $\ell$ and CoS parameter $\alpha$. Here $Q/M=0.5,\,\,\mathrm{L}/M=1,\,\,\Lambda=-0.001/M^2$.
• Figure 7: A comparison of the effective potential $V_\text{eff}(r)$ of the null geodesics as a function of $r/M$ for charged BHs in different configurations. Here $Q/M=0.5,\,\,\mathrm{L}/M=1,\,\,\Lambda=-0.001/M^2$.