Shadow of Extreme Compact Charged Objects in Consistent 4-Dimensional Einstein-Gauss-Bonnet Gravity

TL;DR

The paper analyzes Extreme Compact Charged Objects in regularized 4D Einstein–Gauss–Bonnet gravity to connect high-curvature corrections with near-horizon optics. By deriving null geodesics, shadow Radius $r_s$, energy emission rate, and deflection angle in terms of the Gauss–Bonnet coupling $\alpha$ and charge $q$, it shows that larger $\alpha$ generally shrinks the shadow and lowers the light deflection while increasing evaporation rate, and it constrains $\alpha$ by comparing with the M87* shadow from the EHT. The study finds substantial agreement with EHT data for $0 \le \alpha < 0.5$, making this range compatible with current strong-field tests and supporting the viability of 4D EGB gravity as a cf alternative to GR in strong gravity regimes. These results provide a pathway to bound higher-curvature corrections with horizon-scale imaging and motivate further multifaceted observational tests of regularized 4D EGB gravity.

Abstract

In order to better describe gravitational phenomena on both very small and cosmological scales, there have been constant attempts to generalize and expand the theory of General Relativity (GR) since its inception. The Einstein Gauss Bonnet (EGB) theory is one such extension that adds spacetime corrections related to curvature. Since the standard Gauss Bonnet term is purely topological, it does not contribute to the field equations in four dimensions. To get around this restriction, however, an invariant four dimensional limit has been developed. In this work, we study Extreme Compact Charged Objects (ECCOs), which can resemble black holes, in a gravity framework that is compatible with Einstein Gauss Bonnet in four dimensions. Our main goal is to compare theoretical predictions with Event Horizon Telescope (EHT) observational data in order to constrain the Gauss Bonnet coupling constant α. In order to achieve this, we investigate important optical characteristics like the shadow, light bending angle, and other associated observables, as well as the geodesic structure of ECCO spacetimes in EGB gravity. Finally, we apply these findings to constrain the Gauss Bonnet constant.

Figures (7)

• Figure 1: The radial variation of the effective potential of the Extreme Chgarged Compact Object in 4D Einstein-Gauss-Bonnet gravity for various values of $\alpha$ and $q$, where we set $L = 5$ and $E = K = M = 1$.
• Figure 2: The celestial coordinates on the distant observer's sky are shown. The observer's position is $(R_o, \tilde{\theta}_o)$, and $(\lambda, \psi)$ gives the image's apparent position.
• Figure 3: Geometrical shape of the shadow of the Extreme chgarged compact object in 4D Einstein-Gauss-Bonnet gravity (with $M = 1$).
• Figure 4: Geometrical shape of the shadow of the Extreme Chgarged Compact Cbject in 4D Einstein-Gauss-Bonnet gravity( with $M = 1$).
• Figure 5: The energy emission rate as a function of $\varpi$ for different values of $q$ and $\alpha$ for a Extreme Compact Charged Object in 4D EGB gravity.