arXiv:2402.16922v1 Announce Type: new
Abstract: A novel class of Buchdahl-inspired metrics with closed-form expressions was recently obtained based on Buchdahl’s seminal work on searching for static, spherically symmetric metrics in ${cal R}^{2}$ gravity in vacuo. Buchdahl-inspired spacetimes provide an interesting framework for testing predictions of ${cal R}^{2}$ gravity models against observations. To test these Buchdahl-inspired spacetimes, we consider observational constraints imposed on the deviation parameter, which characterizes the deviation of the asymptotically flat Buchdahl-inspired metric from the Schwarzschild spacetime. We utilize several recent solar system experiments and observations of the S2 star in the Galactic center and the black hole shadow. By calculating the effects of Buchdahl-inspired spacetimes on astronomical observations both within and outside of the solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, shadow, and geodetic precession, we determine observational constraints on the corresponding deviation parameters by comparing theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the Cassini mission’s measurement of gravitational time delay.
A recent study has obtained closed-form expressions for a novel class of Buchdahl-inspired metrics based on Buchdahl’s work on static, spherically symmetric metrics in ${cal R}^{2}$ gravity. These metrics provide an interesting framework for testing predictions of ${cal R}^{2}$ gravity models against observations. In order to test these metrics, the authors consider observational constraints on the deviation parameter, which quantifies the difference between the Buchdahl-inspired metric and the Schwarzschild spacetime. In this article, we will examine the constraints imposed by recent solar system experiments and observations of astronomical objects such as the S2 star in the Galactic center and the black hole shadow. By comparing theoretical predictions with observational data, we can determine the tightest observational constraints on the deviation parameters.
Observational Constraints
To evaluate the Buchdahl-inspired spacetimes, several astronomical observations and experiments are considered:
- Deflection Angle of Light by the Sun: The bending of light around massive objects like the Sun is a well-known phenomenon. By studying the deflection angle of light passing close to the Sun, we can determine the constraints on the deviation parameter.
- Gravitational Time Delay: The delay in the arrival time of light due to gravitational effects can be measured and compared with theoretical predictions. The Cassini mission’s measurement of gravitational time delay provides one of the tightest constraints on the deviation parameter.
- Perihelion Advance: The shift in the perihelion of an orbiting object provides valuable information about the underlying gravitational theory. By studying the perihelion advance, we can obtain constraints on the deviation parameter.
- Shadow: The shadow cast by a black hole can reveal information about spacetime geometry. Observations of the black hole shadow can help determine the constraints on the deviation parameter.
- Geodetic Precession: The precession of a gyroscope’s spin axis in a gravitational field is known as geodetic precession. By studying the geodetic precession, we can establish constraints on the deviation parameter.
Future Roadmap
Building upon the recent progress in obtaining closed-form expressions for Buchdahl-inspired metrics, future research can focus on the following aspects:
- Refining Observational Techniques: To further tighten the constraints on the deviation parameters, more accurate measurements and observations of astronomical phenomena should be conducted. Advancements in observational techniques, such as higher resolution imaging and better instruments, can contribute to this refinement.
- Exploring Other Astronomical Objects: While the S2 star in the Galactic center and the black hole shadow have provided valuable constraints, studying other astronomical objects can offer additional insights. For example, observations of other stars, pulsars, or galaxies can help broaden our understanding of Buchdahl-inspired spacetimes.
- Theoretical Extensions: Investigating theoretical extensions of Buchdahl-inspired spacetimes can uncover new avenues for research. Exploring different parameterizations or modifications of the metrics can lead to a deeper understanding of ${cal R}^{2}$ gravity and its predictions.
- Numerical Simulations: Conducting numerical simulations of the dynamics of objects in Buchdahl-inspired spacetimes can provide complementary insights to observational data. These simulations can help validate theoretical predictions and further refine the constraints on the deviation parameters.
While there are challenges in obtaining more precise constraints and exploring different aspects of Buchdahl-inspired spacetimes, the opportunities for uncovering new physics and testing the limits of our current understanding are abundant. By combining theoretical insights, observational data, and advancements in technology, we can continue to refine our knowledge of ${cal R}^{2}$ gravity and its implications for the universe.