The Latest Nobel Prize in Physics: Black holes (Roger Penrose)
Benjamin J. Owen
TTU P&A Colloquium 4/13/21 Sir Roger Penrose
Image: Penn State
Image: Phys. Rev. Lett. Image: B. Crowell
Image: A. M. de Campos TTU P&A Colloquium 4/13/21 What’s the big deal?
• Prize motivation: "for the discovery that black hole formation is a robust prediction of the general theory of relativity.” • Well, singularities really. • And event horizons are probably robust.
Event horizon: Once you go in, you can Singularity: never get out Infinite curvature
TTU P&A Colloquium 4/13/21 Before Penrose came along, people…
• Found a solution for a spherical, eternal black hole (Schwarzschild 1916) • Took decades to figure out the event horizon • Got hung up on coordinates • Lost track of causality • Found a solution for a spherically collapsing cow dust cloud (Oppenheimer & Snyder 1939) • Had no robust arguments
TTU P&A Colloquium 4/13/21 Penrose, Phys. Rev. Lett. 14, 57–59 (1965)
• Existence of a trapped surface means a singularity will form – Defined purely in geometric terms (null geodesics = paths light will take) – Purely local criterion, don’t need to wait an eternity to be sure nothing comes out – Doesn’t assume any particular shape – Physically assumes only Einstein field equations (locally relating curvature to mass- energy) and weak energy condition (no negative energy density) Image: Phys. Rev. Lett.
TTU P&A Colloquium 4/13/21 Minkowski (1908)
• Einstein’s math professor, showed that special relativity could be interpreted geometrically • First drew (special relativistic) spacetime diagrams ct • E.g. spherical symmetry timelike • Light rays are null geodesics world line • Matter moves on timelike geodesic lines, might be geodesics • Matter stays inside the light timelike cone of the starting point LIGHT CONE ingoing outgoing null null geodesic geodesic r TTU P&A Colloquium 4/13/21 Light rays coming from a surface
• Think of a spherical surface, for simplicity. Doesn’t matter! • In flat space, light rays (congruence of null geodesics) diverge from it like spikes from a ball…
TTU P&A Colloquium 4/13/21 Image: CDC
TTU P&A Colloquium 4/13/21 Light rays coming from a surface
• Think of a spherical surface, for simplicity. Doesn’t matter! • In flat space, light rays (congruence of null geodesics) diverge from it like spikes from a ball… • But in positively curved spacetime, null geodesics can converge (divergence of tangent vector field is negative) • Einstein equations involve 2nd derivatives, those and weak energy condition tell you null geodesics keep converging • After some time, they intersect. Timelike, too. Singularity! • Also known as a caustic
TTU P&A Colloquium 4/13/21 Later consequences
• Can use trapped surfaces to define apparent horizon • Sufficient but not necessary for event horizon to exist • Cosmic censorship conjecture (robust nonexistence of “naked singularities” (w/o horizons)) technically remains open
Image: Caltech TTU P&A Colloquium 4/13/21