80
M. Burgay et al.
to find a pulsar orbiting a black hole!), for which the spacetime curvature is high
and which can be approximated to be a point-like mass (therefore simplifying the
description). We are also especially interested in pulsars with high timing stability,
usually rapidly-spinning millisecond pulsars with a narrow pulse, since they allow
the precise testing of general relativity’s effects.
General relativity and most alternative theories of gravity are both in the class of
metric theories of gravity [75], however in alternative theories of gravity, additional
fields are present. In these theories, while matter only responds to the curvature
described by the spacetime metric (like in general relativity), the spacetime metric
itself is influenced by these additional fields (whether of the scalar, vector or tensor
form), which are associated with tunable parameters. These parameters can in turn
be constrained by observations in the strong-field regime [73–75].
2.5.1 Tests Using PPN Parameters
Metric theories of gravity, whether general relativity or alternative theories of
gravity, can be tested using the parametrized post-Newtonian (PPN) formalism.
The post-Newtonian terms correspond to deviations from Newtonian physics; there
are ten so-called PPN parameters [74] that can be constrained and that correspond
to different physical effects such as the existence of preferred frames, preferred
locations, the non-conservation of momentum, the non-linear superposition of gravitational effects or the spacetime curvature created by a unit mass. The formalism
was initially used to constrain the weak-field limit of gravity in the Solar System
[73–76]. It was extended to the strong-field limit (e.g. in the environment around
compact objects where ( ∼ 0.2)), for a class of tensor-scalar gravity theories
[77, 78] with a partial redefinition of the original ten parameters.
Tests of the Strong Equivalence Principle (SEP) are particularly interesting: the
SEP is satisfied by general relativity, meaning any violation of the SEP implies a
violation of general relativity [73]. The SEP consists of both the Weak Equivalence
Principle (WEP) and the Einstein Equivalence Principle (EEP). WEP corresponds
to the universality of free fall, that is the trajectory of a free-falling body in a
gravitational field should not depend on its internal structure. On the other hand,
EEP corresponds to the Lorentz and positional invariance of non-gravitational
experiments (i.e. the outcomes of these experiments should not depend on the time
and place where they take place, or on the velocity of the reference frame). The
SEP can be tested by monitoring the trajectories of two masses in a gravitational
field, and check for any differences. The SEP would be violated if differences, or
“polarizations” were detected due to different self-energies of the two bodies (as
predicted in alternative theories of gravity), as for example the orbital trajectories
of the Earth and the Moon in the gravitational field of the Sun: this is called
the Nordtvedt effect or gravitational Stark effect [79]. Strong constraints on PPN
parameters have been achieved in the Solar System using Lunar Laser Ranging
(LLR) experiments. However this can be tested in the strong-field limit of gravity
M. Burgay et al.
to find a pulsar orbiting a black hole!), for which the spacetime curvature is high
and which can be approximated to be a point-like mass (therefore simplifying the
description). We are also especially interested in pulsars with high timing stability,
usually rapidly-spinning millisecond pulsars with a narrow pulse, since they allow
the precise testing of general relativity’s effects.
General relativity and most alternative theories of gravity are both in the class of
metric theories of gravity [75], however in alternative theories of gravity, additional
fields are present. In these theories, while matter only responds to the curvature
described by the spacetime metric (like in general relativity), the spacetime metric
itself is influenced by these additional fields (whether of the scalar, vector or tensor
form), which are associated with tunable parameters. These parameters can in turn
be constrained by observations in the strong-field regime [73–75].
2.5.1 Tests Using PPN Parameters
Metric theories of gravity, whether general relativity or alternative theories of
gravity, can be tested using the parametrized post-Newtonian (PPN) formalism.
The post-Newtonian terms correspond to deviations from Newtonian physics; there
are ten so-called PPN parameters [74] that can be constrained and that correspond
to different physical effects such as the existence of preferred frames, preferred
locations, the non-conservation of momentum, the non-linear superposition of gravitational effects or the spacetime curvature created by a unit mass. The formalism
was initially used to constrain the weak-field limit of gravity in the Solar System
[73–76]. It was extended to the strong-field limit (e.g. in the environment around
compact objects where ( ∼ 0.2)), for a class of tensor-scalar gravity theories
[77, 78] with a partial redefinition of the original ten parameters.
Tests of the Strong Equivalence Principle (SEP) are particularly interesting: the
SEP is satisfied by general relativity, meaning any violation of the SEP implies a
violation of general relativity [73]. The SEP consists of both the Weak Equivalence
Principle (WEP) and the Einstein Equivalence Principle (EEP). WEP corresponds
to the universality of free fall, that is the trajectory of a free-falling body in a
gravitational field should not depend on its internal structure. On the other hand,
EEP corresponds to the Lorentz and positional invariance of non-gravitational
experiments (i.e. the outcomes of these experiments should not depend on the time
and place where they take place, or on the velocity of the reference frame). The
SEP can be tested by monitoring the trajectories of two masses in a gravitational
field, and check for any differences. The SEP would be violated if differences, or
“polarizations” were detected due to different self-energies of the two bodies (as
predicted in alternative theories of gravity), as for example the orbital trajectories
of the Earth and the Moon in the gravitational field of the Sun: this is called
the Nordtvedt effect or gravitational Stark effect [79]. Strong constraints on PPN
parameters have been achieved in the Solar System using Lunar Laser Ranging
(LLR) experiments. However this can be tested in the strong-field limit of gravity