Black Hole Based Tests of General Relativity (1602.02413v2)

Abstract: General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is in systems that contain one or more black holes. Black holes are the most compact objects in the universe, providing probes of the strongest-possible gravitational fields. We are motivated to study strong-field gravity since many theories give large deviations from general relativity only at large field strengths, while recovering the weak-field behavior. In this article, we review how one can probe general relativity and various alternative theories of gravity by using electromagnetic waves from a black hole with an accretion disk, and gravitational waves from black hole binaries. We first review model-independent ways of testing gravity with electromagnetic/gravitational waves from a black hole system. We then focus on selected examples of theories that extend general relativity in rather simple ways. Some important characteristics of general relativity include (but are not limited to) (i) only tensor gravitational degrees of freedom, (ii) the graviton is massless, (iii) no quadratic or higher curvatures in the action, and (iv) the theory is 4 dimensional. Altering a characteristic leads to a different extension of general relativity: (i) scalar-tensor theories, (ii) massive gravity theories, (iii) quadratic gravity, and (iv) theories with large extra dimensions. Within each theory, we describe black hole solutions, their properties, and current and projected constraints on each theory using black hole-based tests of gravity. We close this review by listing some of the open problems in model-independent tests and within each specific theory.

Black Hole Based Tests of General Relativity

This paper, authored by Kent Yagi and Leo C. Stein, explores novel methodologies for testing the robustness of General Relativity (GR) by using black holes as a primary tool. While GR has been exceptionally successful in predicting solar system behavior and neutron star interactions, areas with intense gravitational fields, such as those involving black holes, present unique opportunities to investigate potential deviations.

Testing Framework and Theoretical Models

The paper begins by delineating black holes as extremely compact entities which allow access to strong-field gravitational conditions. In strong gravitational fields, many theoretical models predict significant deviations from GR, unlike the weak-field scenarios where GR predictions remain consistent. By focusing on black-hole systems—especially those with electromagnetic emissions from accretion disks or gravitational wave outputs—this paper is positioned to offer insights into the behavior of gravity under such conditions.

Categorization of Alternative Theories

The paper categorizes deviations from GR into several extensions based on modifications to its fundamental characteristics:

• Scalar-Tensor Theories: These involve additional scalar fields alongside tensor fields. GR's formulation only considers tensor fields, but scalar-tensor theories like Brans-Dicke models introduce scalar fields interacting with gravity.
• Massive Gravity Theories: Modifications include the introduction of finite mass to gravitons, deviating from the massless graviton assumption in GR. Despite the theoretical consistency, these models often face challenges like the Boulware-Deser ghost.
• Quadratic Gravity Theories: Here, gravitational theory incorporates terms quadratic in curvature, as represented in dynamic scalar fields coupled specifically to Gauss-Bonnet and Chern-Simons densities.
• Extra Dimension Theories: Randall-Sundrum models demonstrate theories where our universe is embedded in a higher-dimensional space, with gravity potentially leaking into these extra dimensions.

Black Hole Dynamics and Observational Techniques

Black hole dynamics in alternative theories predominantly focus on solutions assuming non-standard attributes:

• Accessory Fields and Hair: While GR posits that black holes are identified only by mass and spin, known as "no-hair", alternative theories propose extra fields or "hair" which could alter observable radiation signatures.
• Gravitational Waves (GWs): Binary systems involving black holes serve as sources of GWs. Studying waveform perturbations allows quantification of theoretical deviations. The paper discusses various analytical methods such as post-Einsteinian frameworks and Bayesian inference that help fit or contrast observational data with theoretical predictions.

Observational Methods

The paper highlights electromagnetic observational methods in tandem with gravitational wave studies. Important techniques include:

• X-ray Spectrum Analysis: Examining emissions from accretion disks helps estimate properties like spin and angular momentum that could deviate in alternative models.
• Fe Line Emissions and Black Hole Shadows: These fine spectral lines can reveal deviations from GR via their broadening influenced by strong gravity.
• Quasi-Periodic Oscillations (QPOs): Frequencies of oscillations observed in data could correspond directly to theoretical predictions diverging from GR.

Implications and Future Research

The challenges and prospects of constraining GR via black hole-based tests span not only technical measurement accuracy but also the interpretation under competing models. The future of gravitational science involves expanding detection capabilities and analytical frameworks to capture subtle deviations that mainstream GR might overlook.

This research agenda outlines important practical implications and theoretical exploration opportunities. By cross-referencing gravitational wave signals with electromagnetic observations across diverse cosmic scenarios, physicists can either verify the precision of GR or uncover new realms that require innovative gravitational paradigms. Moving forward, the continued combination of advanced detectors and simulation tools will bring clarity to these fundamental aspects of universal laws.