Question 1

What is the Schwarzschild radius and what happens at the event horizon?

Accepted Answer

The Schwarzschild radius (r_s = 2GM/c²) is the physical boundary where the escape velocity of a spherical, non-rotating mass equals the speed of light. Inside this boundary, all future-directed light cones tilt toward the central singularity, making escape impossible for both matter and electromagnetic radiation.

Question 2

Why do GPS satellites need Einstein's General and Special Relativity?

Accepted Answer

GPS satellites orbit Earth at an altitude of 20,200 km where gravity is weaker, causing satellite clocks to tick faster by +45.9 microseconds per day due to general relativity. Simultaneously, their orbital speed of 3.87 km/s causes kinematic time dilation, ticking slower by -7.2 microseconds per day due to special relativity. The combined net drift is +38.7 microseconds per day. Without relativistic corrections, GPS navigation would accumulate approximately 11.6 kilometers of error every day.

Question 3

What is the photon sphere of a black hole?

Accepted Answer

The photon sphere is a spherical boundary at radius r = 1.5 r_s (for a Schwarzschild black hole) where gravity is so strong that photons of light can travel in unstable circular orbits. Any light beam aimed inside this radius inevitably falls into the event horizon.

Question 4

How did gravitational lensing prove General Relativity?

Accepted Answer

In 1919, Sir Arthur Eddington measured the deflection of starlight grazing the Sun during a total solar eclipse. The observed deflection of ~1.75 arcseconds perfectly matched Einstein's General Relativistic prediction (α = 4GM/c²R), which was exactly twice the Newtonian prediction (α = 2GM/c²R), confirming that space itself is curved by mass.

Question 5

What is the Ergosphere and can energy be extracted from a spinning black hole?

Accepted Answer

In a rotating Kerr black hole, the ergosphere is an oblate region outside the event horizon where spacetime itself is dragged into corotation at speeds exceeding the speed of light (frame dragging). In 1969, Roger Penrose demonstrated that a particle entering the ergosphere can split into two pieces, with one fragment falling in on a negative-energy trajectory while the other escapes with more energy than the original particle entered with, extracting rotational energy from the black hole.

Question 6

What causes spaghettification and why can you safely cross a supermassive black hole horizon?

Accepted Answer

Spaghettification is caused by the differential tidal gravitational force between an object's head and feet (Δa = 2GM·Δr / r³). Because the Schwarzschild radius scales linearly with mass (r_s ∝ M), the tidal acceleration at the event horizon scales inversely with the square of mass (Δa_horizon ∝ M / M³ = 1/M²). For a 10 solar mass black hole, tidal forces at the horizon exceed 100,000,000 g's (instantly ripping biological tissue into a stream of atoms). However, for a 4 million solar mass black hole like Sagittarius A*, tidal forces at the event horizon are less than 0.0001 g, allowing an astronaut to cross the event horizon completely unharmed.

Question 7

What are gravitational waves and what was observed in GW150914?

Accepted Answer

Gravitational waves are ripples in the fabric of spacetime produced by accelerating quadrupole mass distributions, propagating at the speed of light. In 2015, the LIGO interferometers made the historic first direct detection (GW150914) from two colliding black holes (36 M☉ and 29 M☉). In the final fractions of a second, 3.0 solar masses were converted directly into pure gravitational wave energy, radiating a peak luminosity exceeding that of all stars in the observable universe combined.

Question 8

What is a Penrose-Carter diagram and how does it illustrate causality?

Accepted Answer

A Penrose-Carter diagram is a two-dimensional conformal representation of spacetime that maps infinite distances and times into a finite diamond while strictly preserving the 45-degree angle of light cones. It visually reveals causal boundaries: future and past null infinity (ℐ⁺, ℐ⁻), spatial infinity (i⁰), the 45-degree event horizon, and the spacelike singularity at r = 0, proving that once inside the horizon, hitting the singularity is as inevitable as moving forward in time.

GeneralRelativity&SpacetimeCurvature

Use this studio like a real-time physics workbench

What is general relativity & spacetime curvature?

Experiment Execution & Governing Equations