2 General Relativity Measurements from Pulsars
79
gravitational fields) [74, 75]. As we probe astrophysical systems with yet stronger
gravitational fields, we could continue to confirm general relativity (and achieve a
higher precision in that confirmation) or find a breakdown of the theory.
Why consider a breakdown of general relativity? Since general relativity is, at
a fundamental level, not compatible with quantum mechanics, one could expect
for it to break down at small scales, or alternatively in strong gravitational fields.
The idea is that an overarching theory (a theory of everything) could explain all
forces of nature, including the electromagnetic, the weak and strong nuclear forces,
and gravity. Since this overarching theory is still largely unknown, we cannot
directly know what the ‘correct’ theory of gravity looks like. Instead, a number of
alternative theories of gravity, some of them inspired by efforts to unify the forces of
nature, have been proposed through the years and been constrained by observations
(alternative theories contain additional parameters that are not present in general
relativity, therefore this additional parameter space can be constrained). Some of
these theories have been excluded entirely since they didn’t pass observational
tests. Other theories have not been excluded but their parameter space has been
constrained by observations.
As mentioned earlier, general relativity has been extensively tested and confirmed
in the weak-field limit; thus alternative theories of gravity need to be behaving like
general relativity in that limit. General relativity could instead break down in the
strong-field limit. In order to further test general relativity and alternative theories
of gravity, we thus need to probe gravity in the strong-field limit (where is closer
to one), that is in extreme gravity scenarios. Indeed, there exist alternative theories
that pass all tests in the weak-field limit but could be excluded or constrained in the
strong-field limit.
Relativistic binary pulsars, in particular where the pulsar is a recycled millisecond pulsar, can be great tools for probing gravity theories. Since the separation
between the neutron star and its companion is large (as compared to the neutron
star radius) in known binary pulsar systems, the orbital motion of any of the
two components takes place in the weak gravitational field of the other binary
component. While in general relativity, the orbital motion in these systems does not
depend on the gravitational binding energy (or self-energy) of the components, that
is no longer true in most alternative theories of gravity. Therefore the effects of these
alternate theories can be detected in systems where the self-energy is large, which
is the case at the neutron star surface (of the order of ∼ 0.2), therefore orbital
motions involving neutron stars are ideal for testing strong gravity. In addition,
pulsars, especially millisecond pulsars, are neutron stars that rotate with extreme
precision, and their radio wave emission constitutes a stable clock with which to
measure the orbital motion of the binary, using the timing methods described in
Sect. 2.4. The combination of a large self-energy at the neutron star surface and
the possibility of very precisely measuring orbital motions using pulsar timing
techniques, makes binary pulsars perfect laboratories for testing strong gravity.
The best binary pulsars for testing strong gravity involve those with short orbital
periods (meaning high orbital velocities), as well as those whose companion is
also a compact object (e.g. DNS or NS–WD binaries; ideally, one would also like
79
gravitational fields) [74, 75]. As we probe astrophysical systems with yet stronger
gravitational fields, we could continue to confirm general relativity (and achieve a
higher precision in that confirmation) or find a breakdown of the theory.
Why consider a breakdown of general relativity? Since general relativity is, at
a fundamental level, not compatible with quantum mechanics, one could expect
for it to break down at small scales, or alternatively in strong gravitational fields.
The idea is that an overarching theory (a theory of everything) could explain all
forces of nature, including the electromagnetic, the weak and strong nuclear forces,
and gravity. Since this overarching theory is still largely unknown, we cannot
directly know what the ‘correct’ theory of gravity looks like. Instead, a number of
alternative theories of gravity, some of them inspired by efforts to unify the forces of
nature, have been proposed through the years and been constrained by observations
(alternative theories contain additional parameters that are not present in general
relativity, therefore this additional parameter space can be constrained). Some of
these theories have been excluded entirely since they didn’t pass observational
tests. Other theories have not been excluded but their parameter space has been
constrained by observations.
As mentioned earlier, general relativity has been extensively tested and confirmed
in the weak-field limit; thus alternative theories of gravity need to be behaving like
general relativity in that limit. General relativity could instead break down in the
strong-field limit. In order to further test general relativity and alternative theories
of gravity, we thus need to probe gravity in the strong-field limit (where is closer
to one), that is in extreme gravity scenarios. Indeed, there exist alternative theories
that pass all tests in the weak-field limit but could be excluded or constrained in the
strong-field limit.
Relativistic binary pulsars, in particular where the pulsar is a recycled millisecond pulsar, can be great tools for probing gravity theories. Since the separation
between the neutron star and its companion is large (as compared to the neutron
star radius) in known binary pulsar systems, the orbital motion of any of the
two components takes place in the weak gravitational field of the other binary
component. While in general relativity, the orbital motion in these systems does not
depend on the gravitational binding energy (or self-energy) of the components, that
is no longer true in most alternative theories of gravity. Therefore the effects of these
alternate theories can be detected in systems where the self-energy is large, which
is the case at the neutron star surface (of the order of ∼ 0.2), therefore orbital
motions involving neutron stars are ideal for testing strong gravity. In addition,
pulsars, especially millisecond pulsars, are neutron stars that rotate with extreme
precision, and their radio wave emission constitutes a stable clock with which to
measure the orbital motion of the binary, using the timing methods described in
Sect. 2.4. The combination of a large self-energy at the neutron star surface and
the possibility of very precisely measuring orbital motions using pulsar timing
techniques, makes binary pulsars perfect laboratories for testing strong gravity.
The best binary pulsars for testing strong gravity involve those with short orbital
periods (meaning high orbital velocities), as well as those whose companion is
also a compact object (e.g. DNS or NS–WD binaries; ideally, one would also like