STRONG COSMIC Wenceslao Santiago-Germán Postdoctoral fellow, UC Davis STRONG COSMIC Sponsored by UC MEXUS -CONACYT t he role of nearly extreme nonrotating black holes CENSORSHIP: t he role of nearly extreme nonrotating black holes SEPTEMBER 2005 [SEPTEMBER 2005 \ QGo5

Singularity Theorems, 1965 Under certain fairly physical situations of unstoppable gravitational collapse space- time singularities, in the sense of causal geodesic incompletness, must occur.

Cosmic Censorship Conjecture (Penrose 1969) “The topology of the spacetime is ” Weak cosmic censorship “the generic gravitational collapse of an isolated physical system, starting from perfectly physically reasonable nonsingular initial state, cannot produce spacetime singularities that can be seen from infinity, even though observations from infinity are allowed to continue indefinitely” Strong cosmic censorship ``Every inextendible spacetime M which evolves according to classical general relativity with physically reasonable matter satisfying appropriated energy conditions from a generic nonsingular initial data on a complete spacelike hypersurface, is globally hyperbolic.”

“Subtle is the Lord... in theory, naked singularities do form dynamically from regular initial data satisfying the usual energy conditions.” If the answer to Penrose’s riddle is in the affirmative: a)What is, one may ponder, the theoretical precise meaning of the qualificationsGENERIC, PHYSICALLY MATTER, AND PHYSICALLY REASONBLE MATTER, AND APPROPIATED ENERGY CONDITIONS that are essential to the validity and proper formulation of the conjecture? b) How do they fit together in a mathematical description of, say, the inner workings of the strong cosmic censorship principle?

“….At the border where the null energy condition would start to be violated” “Penrose diagram of Reissner- Nordstrom BH ” “The stability of Lorentzian traversable wormholes require exotic matter violating the average null energy condition”

de Sitter Instability of black-hole Cauchy horizons in asymptotically de Sitter spacetimes

“Main line of argument…” -Surface gravity estimates. “Implicit function theorem cannot be applied at the bifurcation point p, when ” “Introduce new expansion at p, classify the universe of solutions” “Then, use Einstein’s equations”

Internal instabilities: BH’s, once called dark stars Chadrasekhar (1964) “ In the post-Newtonian approximation, where GM/R <<1, a global adiabatic radial instability sets in for the core of a nonrotating star of mass M and radius R when the pressure-average adiabatic index governing the perturbations, satisfies the inequality where K is a constant of order unity, depending on the structure of the star. ” For nearly extreme static nonrotating black holes in the vicinity of p : (a) “The blueshift instability criteria implies (b) If in addition, is a sufficiently small positive constant, then the necessary condition for inner Cauchy horizon stability implies and vice versa” Cold Matter Cold Black Holes BH Cauchy horizon -NEW- Internal core

A Mathematical Riddle How to formulate strong cosmic censorship? --version of the SCC conjecture: Every generic four-dimensional space-time M containing a black hole with regular event horizon and satisfying the following four conditions, has a maximal future development which is locally inextendible in a manner inside the hole: (a)M arises from the evolution of nonsingular asymptotically flat or de Sitter initial data given in a complete space-like hypersurface S (b)the initial data evolves in a manner according to classical general relativity, (c)at late times the corresponding hole asymptotically approaches to a `nearly' extreme spherically symmetric static configuration with nonnegative mass. (d)at the event horizon of static spherically symmetric black holes with zero surface gravity, the matter sources are such that to satisfy the following inequality: and in addition STABILITY ENERGY CONDITIONSREASONABLE EQUATIONS OF STATE Other stories: Limits, by Jorge Luis. Borges. “….the pawn of that Someone who fixes in advance the omnipotent laws, tracing a secret and unyielding graph of all the dreams, the forms, and the shadows which thread and unthread the texture of this life..”

“Le Chatelier- Braun principle and cosmic censorship. Le Chatelier-Braun Principle (1884, 1888): “Every physical system in stable equilibrium under the influence of an external force (a change in an environmental property A) which tends to alter an intensive characteristic B of the system (temperature, pressure, concentration, number density of molecules, etc.) every where or just in some parts. Can only experience interior changes-- the secondary effect---in some other parameter of state C of the system, usually extensive (entropy, volume, number of particles of a specific kind, etc. ) producing a current (or flow) that causes a feedback effect B of opposite sign to that resulting from the exterior force. a)Maxwell b)Born-Infeld c)Born-Infeld modified “Dominant Energy condition satisfied” “Blueshift stable for mini BH’s with a positive cosmological constant small enough”

Outline of future research “Find a mathematically precise connection between blue shift instability and the occurrence of the phenomenon of mass inflation.” “Work out the generalization of the mathematical scheme to include nearly extreme rotating holes.” “Explore the following question: If every physical theory about matter, every cosmological premise, and so on, to be successful need to be compatible with the strong cosmic censorship principle in the limit when Does cosmic censorship constrain the size of the cosmological constant?

STRONG COSMIC Wenceslao Santiago-German Postdoctoral fellow, UC Davis STRONG COSMIC Sponsored by UC MEXUS CONACYT t he role of nearly extreme rotating black holes CENSORSHIP t he role of nearly extreme rotating black holes THE END