Testing General Relativity with Present and Future Astrophysical Observations

TL;DR

This work surveys why and how General Relativity should be tested in strong-field regimes, focusing on black holes, neutron stars, binary systems, pulsars, cosmology, and gravitational waves. It outlines a comprehensive taxonomy of beyond-GR theories, highlighting scalar-tensor, f(R), quadratic-curvature, Lorentz-violating, massive gravity, and auxiliary-field frameworks, and discusses how each modifies compact-object structure, dynamics, and radiation. The authors synthesize analytic and numerical methods (PN, NR, EFT) across theories, summarize current empirical bounds from binary pulsars, cosmology, and GW observations, and emphasize model-independent strategies like I-Love-Q universality and PPE/TIGER-type tests for robust gravity tests. They emphasize the crucial role of upcoming facilities (FAST, SKA, eLISA/LISA, ET) and the need to carefully account for astrophysical systematics and environmental effects to realize precise tests of gravity in the strong-field regime. Overall, the paper provides a detailed roadmap for exploiting present and future astrophysical observations to constrain GR and reveal possible new gravitational physics.

Abstract

One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

Figures (46)

• Figure 2.1: This diagram illustrates how Lovelock's theorem serves as a guide to classify modified theories of gravity. Each of the yellow boxes connected to the circle represents a class of modified theories of gravity that arises from violating one of the assumptions underlying the theorem. A theory can, in general, belong to multiple classes. See Table \ref{['tab:theories']} for a more precise classification.
• Figure 3.1: Domain of existence of hairy BHs for $n=0$, $m=1$ in $M$-$\omega$ space (shaded blue region). The black solid curve corresponds to extremal Kerr BHs, which obey $M={1}/(2\Omega_H)$; Kerr BHs exist below it. For $q=0$, the domain of existence connects to Kerr solutions (dotted blue line). For $q=1$, $R_H$ vanishes and hairy BHs reduce to boson stars (red solid line). The final line that delimits the domain of existence of the hairy BHs (dashed green line) corresponds to extremal BHs, i.e. with zero temperature. (Inset) Boson star curves for $m=1,2$. The units in the axes are normalized to the scalar field mass $\mu$. [Adapted from Herdeiro:2014goa.]
• Figure 3.2: Left panel: The metric functions in \ref{['ansatz_hairy']} for a Kerr BH in the region of nonuniqueness. We have chosen its mass and angular momentum to be $M=0.415$, $J=0.172$; this corresponds to $r_H= 0.066$. Right panel: The metric and scalar field functions for a hairy BH in the region of nonuniqueness with the same $M,J$ as the Kerr BH. This hairy BH is Kerr-like and has $\omega=0.975$ and $r_H=0.2$. The value of the scalar field profile function has been multiplied by a factor of 100.
• Figure 3.3: The domain of existence of EDBG BHs (shaded area). We plot the scaled horizon area $a_{\rm H}=A_{\rm H}/M^2$ (left panel) and the scaled quadrupole moment $\hat{Q}=Q M/J^2$ (right panel) as functions of the scaled angular momentum $j=J/M^2$. Different curves correspond to families of EDBG BHs with fixed scaled horizon angular velocity $\Omega_{\rm H} \alpha_3^{1/2}$. [From Kleihaus:2011tgKleihaus:2014lba.]
• Figure 3.4: The scaled moment of inertia $\hat{I} = J/(\Omega_{\rm H} M^3)$ is shown versus the scaled quadrupole moment $\hat{Q}$ for fixed values of $j$. The Kerr BHs are indicated by the fat dots on the $\hat{I}$-axis. The straight dotted lines represent the perturbative results of Ayzenberg:2014aka. The critical BHs are represented by the dotted curve. [From Kleihaus:2014lba.]