Gravity as Presented by Relativity

• Introduction
• What is Gravity
• What Came Before Relativity
• Timeline of Gravity Discovery
• Explanation of Scientific Evidence Collected to Prove Relativistic Gravity
• Mathematics of Gravity
• Summary

This article explores how gravity is conceptualized in the framework of relativistic physics, emphasizing its departure from force-based interactions and its compatibility with the principles of modern cosmology and high-energy astrophysics.

In Einstein’s General Theory of Relativity (1915), gravity is no longer treated as an invisible force acting across space. Instead, it is interpreted as the curvature of spacetime caused by mass and energy. Massive objects distort the geometry around them, and this curvature dictates the motion of other bodies.

“Matter tells spacetime how to curve; spacetime tells matter how to move.” — John Archibald Wheeler

This geometric interpretation of gravity replaces Newton's instantaneous action-at-a-distance with a local description of motion along curved paths called geodesics. All objects, regardless of mass, follow these geodesics unless acted upon by non-gravitational forces.

Gravity in relativity is:

• Not a force, but a geometric deformation.
• Dependent on mass, energy, pressure, and stress (via the energy-momentum tensor).
• Universal and attractive, though technically neutral (massless particles like photons also follow curved paths).

Before Einstein, gravity was universally explained through Newtonian mechanics. However, several unresolved phenomena hinted at deeper complexities:

• Perihelion precession of Mercury: Newtonian gravity could not fully account for Mercury’s orbital drift.
• Invariance of the speed of light: Maxwell's equations predicted a constant light speed, incompatible with Galilean relativity.
• Equivalence principle: Inertial mass and gravitational mass were known to be identical, but this had no explanation within Newtonian theory.

In 1905, Einstein's Special Relativity redefined space and time as intertwined and relative to observers. This paved the way for his General Theory of Relativity, where gravity emerges from spacetime itself, rather than being superimposed upon it.

Year	Contributor	Contribution
1687	Isaac Newton	Law of Universal Gravitation
1905	Albert Einstein	Special Relativity; spacetime introduced as a unified concept
1907	Einstein (Equivalence)	Weak equivalence principle articulated (uniform acceleration = gravity)
1915	Einstein	General Relativity formulated; field equations published
1919	Eddington’s Expedition	Confirmed light bending by gravity during solar eclipse
1974–Present	Various (LIGO, GPS, etc.)	Confirmations via time dilation, gravitational waves, GPS corrections

Einstein’s theory, though abstract, has withstood more than a century of experimental validation. Key pieces of evidence include:

1. Perihelion Advance of Mercury

Mercury’s elliptical orbit precesses slightly with each revolution. Newton’s laws explain most of this, but General Relativity accounts for the remaining 43 arcseconds per century, matching observation perfectly.

2. Deflection of Starlight

In 1919, Arthur Eddington measured the bending of starlight around the Sun during a total solar eclipse. The observed angular deflection matched Einstein’s predictions, establishing gravity’s influence on light and spacetime curvature.

3. Gravitational Time Dilation

Atomic clocks on satellites tick faster than those on Earth due to lower gravity. This effect, predicted by General Relativity, must be corrected in GPS systems to maintain positional accuracy within meters.

4. Gravitational Redshift

Light escaping from a massive object loses energy and shifts toward the red end of the spectrum. This was first observed in white dwarf stars and later confirmed in laboratory experiments.

5. Gravitational Waves

Ripples in spacetime caused by massive accelerating bodies (e.g., merging black holes) were directly detected by LIGO in 2015, 100 years after Einstein predicted them.

These observations collectively affirm that mass and energy warp spacetime, and that bodies move not because of a "force" but because the fabric of spacetime directs them.

The mathematical core of General Relativity is the Einstein Field Equations (EFEs):

$$ G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} $$

Where:

• $G_{\mu\nu}$ is the Einstein tensor (curvature of spacetime)
• $\Lambda$ is the cosmological constant
• $g_{\mu\nu}$ is the metric tensor (geometry of spacetime)
• $T_{\mu\nu}$ is the stress-energy tensor (matter and energy content)
• $G$ is the gravitational constant
• $c$ is the speed of light

Key Concepts:

• Geodesics: The equivalent of straight lines in curved spacetime; objects in freefall follow these naturally.
• Spacetime curvature: Visualized by embedding 2D analogs like rubber sheets, though real curvature occurs in four dimensions.
• Black holes: Solutions to EFEs where spacetime curvature becomes infinite (singularity), confirmed through X-ray observations and gravitational wave detections.

The mathematics is nonlinear and tensorial, requiring differential geometry and the language of manifolds for full comprehension.

In the relativistic view, gravity is not a force between masses, but a manifestation of curved spacetime. Mass and energy distort the geometry of spacetime, and all objects follow the curved paths dictated by this geometry. This framework elegantly explains phenomena that Newtonian gravity could not, from the orbit of Mercury to gravitational waves.

While mathematically complex, General Relativity offers a deeper, more accurate description of the universe, essential for high-precision systems (like GPS) and the study of black holes, neutron stars, and cosmology.

Yet, in the domain of moderate masses and velocities, Newtonian gravity remains a valid and useful approximation. The relativistic model does not invalidate Newton—it simply expands the view, just as Newton once expanded upon Galileo.