Relativistic gravity, compact objects and strong-field gravity

This is a semi-technical presentation of the succession of events that led Einstein to formulate his theory of general relativity. We present an overview of the field of relativistic astrophysics and motivate the study of compact objects (such as neutrons stars and black holes) as strong-field gravity probes for testing possible modifications to general relativity. 1 A PANORAMA OF PHYSICS BEFORE 1915 General relativity is the theory of space, time and gravity, formulated in final form by Albert Einstein in 1915. The theory superseded the gravitational theory of Isaac Newton, formulated in the mid-17th century, which had so accurately explained gravitational phenomena on a vast scale, from the falling objects on Earth to the motion of celestial bodies in the sky. Newtonian gravity is based on the idea that any two bodies in the Universe attract each other with a force whose magnitude is proportional to the product of their masses and inversely proportional to their distance squared. Together with Newton’s three laws of motion and the equality between inertial and passive gravitational masses1, Newtonian gravity developed greatly through 17th and 19th centuries [24] culminating in Laplace’s Mecánique Céleste (published between 1798 and 1827), the prediction of a new trans-uranic planet by Le Verrier, and the subsequent observational confirmation of what became known as Neptune by Galle in 1846. By the end of the 19th century, physics found itself in a privileged position among sciences, for it was thought that all of its fundamental aspects had been understood. At this time, the motion and dynamics of bodies could be formulated in the Newtonian mechanics framework. Electromagnetic phenomena (including the description of light) could be understood through Maxwell’s electrodynamics, and the study of heat and temperature could be formulated within the theory of thermodynamics and kinetic theory of gases. This set of theories is what we now call classical physics [22]. Nevertheless, in 1900 Lord Kelvin pointed out that “the beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds [...]” [11]. The two clouds were (i) the failure in detecting the luminiferous ether, the hypothetical supporting medium for light propagation, and (ii) the correct description of the blackbody radiation which thermodynamical and electromagnetic considerations failed to explain. As we now know, the blackbody radiation led Planck (1900) to introduce the idea that energy is quantized, which paved the road for the development of quantum mechanics. The absence of the ether is tightly related with Einstein’s 1905 special theory of relativity. If an ether existed, in principle it should be possible to detect small changes in the travel time of light using an interferometer as Earth orbited the Sun. This detection never happened. The failure in measuring any such modifications in the experiments by Michelson and Morley provided evidence for the constancy of the speed of light, as postulated in special relativity. The special theory relativity has as a second postulate: the equivalence of the laws of physics for any two inertial reference frames. This notion of a covariance of the equations of physics demanded a relativistic extension of Newtonian mechanics to a relativistic mechanics2, which must be used to correctly describe the dynamics of bodies at velocities comparable to the speed of light. 1The inertial mass of an object quantifies its resistance to be accelerate when acted upon by a force. The passive gravitational mass quantifies the gravitational force felt by an object in presence of another. The equality between these two masses is known as the weak equivalence principle and has been verified experimentally with very high precision. 2Maxwell’s electromagnetism was already invariant under the set of transformations relating to inertial observers known as the Lorentz transformations. The laws of thermodynamics are also invariant. The application of thermodynamics to relativistic systems was developed by Einstein and Planck in 1907-1908 [25]. This is not a straightfoward task however, see [4].