The gravitational acceleration of massive bodies toward other bodies is dependent on the nonlinear
properties of gravity within metric theories of gravity [48]. Tracking this acceleration provides a
measurement of how gravity pulls on the gravitational binding energy and how gravitational binding energy
affects inertia. This probe of nonlinear gravity is explicitly singled out in measurements of the
Parameterized Post-Newtonian parameter
discussed below, but it is also implicitly contained within the
Einstein Equivalence Principle.
The Equivalence Principle (EP), which states the equality of gravitational and inertial mass, is central to the theory of GR. The EP comes in two flavors: the weak (WEP) and the strong (SEP). The WEP pertains to nongravitational contributions to mass: namely, Standard Model contributions of nuclear and electromagnetic energy, gluons, plus quark masses and their kinetic energies. Nucleons of differing fractional electro-weak and nuclear binding energies might exhibit different couplings to gravity in the case of a WEP violation. The SEP extends the WEP to include gravitational self-energy of a body, addressing the question of how gravity pulls on itself and, therefore, accessing the nonlinear aspect of gravity.
While the EP must hold true in GR, nearly all alternative theories of gravity predict a violation of the
EP at some level. Efforts to formulate a quantum description of gravity generally introduce
new scalar or vector fields that violate the EP [13, 14]. These violations manifest themselves
in the equations of motion for massive self-gravitating bodies, as well as preferred frame and
preferred-location effects on the gravitational constant. GR may be the only metric theory of gravity that is
dependent on the SEP holding true [72], distinguishing it from all other theories of gravity.
Therefore, probing the validity of the EP is one of the strongest ways of testing GR. This test is
often considered one of the most powerful ways to search for new physics beyond the standard
model [12].
Precision tests of the EP generally test the Universality of Free Fall (UFF): all test bodies
have the same gravitational acceleration in a uniform gravitational field. Tests of the UFF are
performed by comparing the gravitational accelerations and
of different test bodies:
In the late 1960s, Nordtvedt recognized that the SEP could be tested by comparing the gravitational acceleration of two massive bodies [48, 47]. For each body, the gravitational to inertial mass ratio can be written as:
where For a uniform sphere of radius ,
. However, due to their complex
interior structure, the gravitational self-energy for astronomical bodies is generally computed
numerically. An Earth model based on the model described in [25] yields a self-energy of [78]:
http://www.livingreviews.org/lrr-2010-7 |
Living Rev. Relativity 13, (2010), 7
![]() This work is licensed under a Creative Commons License. E-mail us: |