Classical Tests, Black Holes, and Gravitational Waves
Observational pillars
Classical tests
General relativity explains Mercury’s perihelion advance, gravitational redshift, and the bending of light near massive bodies. In weak fields, the metric can be approximated by , linking relativity to Newtonian gravity via the potential .
Black hole spacetimes
The Schwarzschild solution describes the exterior of a static, spherically symmetric mass. Its horizon at marks a causal boundary, and the interior reveals the necessity of global causal analysis.
Gravitational waves
Linearized perturbations around a background metric propagate as waves at the speed of light, carrying energy and angular momentum. Their detection opened a new observational window on compact binary coalescence.
Strong-field gravity
Binary black holes, neutron stars, and extreme-mass-ratio systems probe highly nonlinear regimes where post-Newtonian theory, numerical relativity, and effective-one-body methods complement one another.
What physical quantity is directly associated with the horizon radius of a non-rotating black hole?
The Schwarzschild radius is .
Correct answer:
Why are gravitational waves transverse and propagating at in linearized general relativity?
This is the relativistic analog of radiation in gauge theories.
Correct answer: Because small metric perturbations satisfy a wave equation on the background spacetime and the gauge-fixed physical degrees of freedom are transverse-traceless modes propagating causally.
Classic predictions and observations
| Phenomenon | GR prediction |
|---|---|
| Perihelion precession | Extra advance beyond Newtonian theory |
| Light bending | Deflection by curved spacetime |
| Gravitational redshift | Frequency shift in gravitational potential |
| Binary inspiral | Orbital decay from wave emission |
What is the causal significance of an event horizon?
The horizon is a global causal boundary, not merely a local surface.
Correct answer: No future-directed causal signal from inside the horizon can reach distant observers outside it.