About this guide: This step-by-step tutorial breaks down the lapse-first formulation of General Relativity into digestible chapters. Each chapter builds on the previous one, gradually developing your understanding of how gravity emerges from temporal geometry.
Discover what the temporal potential Φ represents physically - the "depth" of gravitational wells that control how time flows. Learn how this single scalar field encodes the essence of gravity.
Understand why we use the exponential relationship N = e^Φ and the profound benefits of working with the logarithmic form. See how this choice simplifies the mathematics and clarifies the physics.
Learn how the ADM formalism splits spacetime into space plus time, introducing the lapse function, shift vector, and spatial metric. Understand the conveyor belt analogy for frame-dragging.
Explore the heart of lapse-first GR: the flux law that connects energy flow to temporal evolution. See how only actual energy flux can change the flow of time.
Discover how the value of Φ is determined by mass distributions and energy flows. Learn about the Poisson equation for static contributions and the flux law for dynamic evolution.
See lapse-first GR in action with concrete examples from GPS satellites to black holes. Understand the numerical values and why they matter for technology and astrophysics.
Compare the lapse-first approach with traditional GR formulations. Understand why this perspective simplifies physics and hints at deeper connections to quantum gravity.