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3.3 Probing versus testing strong-field gravity

The parameter space shown in Figure 1View Image 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., 2 R + R) 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 [54Jump To The Next Citation Point182Jump To The Next Citation Point40Jump To The Next Citation Point]. As a result, even though the gravitational field that corresponds to a double-neutron star orbit is rather weak (see Figure 2View Image), observations of the orbital decay of the binary actually test general relativity against scalar-tensor theories in the strong-field regime [40Jump To The Next Citation Point].

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 [165Jump To The Next Citation Point13Jump To The Next Citation Point71Jump To The Next Citation Point142Jump To The Next Citation Point130Jump To The Next Citation Point]. 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.

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