### 3.3 Probing versus testing strong-field gravity

The parameter space shown in Figure 1 is useful in identifying the strength of the gravitational field
probed by a particular test of gravity. However, it is important to emphasize that probing a gravitational
field of a given strength is not necessarily the same as testing general relativity in that regime. I discuss
bellow the difference with two examples from scalar-tensor gravity that illustrate the two opposite
extremes.
First, a phenomenon that occurs in a weak gravitational field may actually be testing the strong-field
regime of gravity. In general relativity, Birkhoff’s theorem states that the external spacetime of a
spherically-symmetric object is described by the Schwarzschild metric, independent of the properties of the
object itself. Birkhoff’s theorem, however, does not apply to a variety of gravity theories, such as
scalar-tensor or non-linear (e.g., ) theories. In fact, in these theories, the spacetime at any point
around a spherically-symmetric object depends on the mass distribution that generates the spacetime,
which may itself lie in a strong gravitational field and, therefore, probe that regime of the theory. For
example, in Brans–Dicke gravity, which is a special case of scalar-tensor theories, the evolution of the binary
orbit in a system with two neutron stars due to the emission of gravitational waves depends on the
coupling of matter to the scalar field, which occurs in the strong gravitational field of each
neutron star [54, 182, 40]. As a result, even though the gravitational field that corresponds to
a double-neutron star orbit is rather weak (see Figure 2), observations of the orbital decay
of the binary actually test general relativity against scalar-tensor theories in the strong-field
regime [40].

In the opposite extreme, phenomena that probe strong gravitational fields may not necessarily be used
in testing general relativity in this regime. Analytical and numerical studies strongly suggest that the end
state of the collapse of a star in Brans–Dicke gravity is a black hole described by the Kerr spacetime of
general relativity [165, 13, 71, 142, 130]. Therefore, the observation of a phenomenon that occurs even
just above the horizon of a black hole cannot be used in testing general relativity against Brans–Dicke
gravity in the strong-field regime, because both theories make the exact same prediction for that
phenomenon.

In the following, I will distinguish attempts to probe phenomena that occur exclusively in the
strong-field regime of general relativity from those that aim to test the strong-field predictions of the theory
against various alternatives.