Exploring Tidal Force Effects and Shadow Constraints for Schwarzschild-like Black Hole in Starobinsky-Bel-Robinson Gravity

TL;DR

This paper investigates the tidal forces, geodesic deviations, and shadow sizes of a Schwarzschild-like black hole in Starobinsky-Bel-Robinson gravity, constraining parameters with observational data from M87* and Sgr A*.

Contribution

It introduces a detailed analysis of tidal effects and shadow constraints for this black hole model, comparing it with Schwarzschild black holes and fitting observational data.

Findings

Radial and angular tidal forces switch from stretching to compressing near the horizon.

Geodesic deviation exhibits oscillatory behavior for certain initial conditions.

Shadow diameters are smaller than Schwarzschild black holes but consistent with EHT observations.

Abstract

The current manuscript deals with the tidal force effects, geodesic deviation, and shadow constraints of the Schwarzschild-like black hole theorised in Starobinsky-Bel-Robinson gravity exhibiting M-theory compactification. In the current analysis, we explore the radial and angular tidal force effects on a radially in-falling particle by the central black hole, which is located in this spacetime. We also numerically solve the geodesic deviation equation and study the variation of the geodesic separation vector with the radial coordinate for two nearby geodesics using suitable initial conditions. All the obtained results are tested for Sag A* and M87* by constraining the value of the stringy gravity parameter $\beta$ using the shadow data from the event horizon telescope observations. All the results are compared with Schwarzschild black hole spacetime. In our study, we found that both the radial and angular tidal forces experienced by a particle switch their initial behaviour and turn compressive and stretching, respectively, before reaching the event horizon. The geodesic deviation shows an oscillating trend as well for the chosen initial condition. For the constrained value of $\beta$, we see that the spacetime geometry generated by Sag A* and M87* is effectively same for both Schwarzschild and Starobinsky-Bel-Robinson black hole. Furthermore, we also calculated the angular diameter of the shadow in Starobinsky-Bel-Robinson black hole and compared with the Schwarzschild black hole. It is observed that the angular diameter of shadow for M87* and Sgr A* in Starobinsky-Bel-Robinson black hole is smaller than the Schwarzschild black hole. The calculated results satisfy the event horizon telescope observational constraints. Finally, we have concluding remarks.