Wenceslao SantiagoGermn Postdoctoral fellow, UC Davis STRONG COSMIC

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Wenceslao Santiago-Germán Postdoctoral fellow,
UC DavisSTRONG COSMIC
CENSORSHIPthe role of nearly
extremenonrotating black holes
SEPTEMBER 2005 \
QGo5

• Sponsored by UC MEXUS -CONACYT

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Singularity Theorems, 1965

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

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CosmicCensorship Conjecture(Penrose 1969)
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
The topology of the spacetime is

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.
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Subtle is the Lord ... in theory, naked
singularities do form dynamically from regular
initial data satisfying the usual energy
conditions.

• If the answer to Penroses riddle is in the
  affirmative
• a)What is, one may ponder, the theoretical
  precise meaning of the qualifications
• GENERIC,
• 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?

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Penrose diagram of Reissner-Nordstrom BH
.At the border where the null energy condition
would start to be violated
The stability of Lorentzian traversable
wormholes require exotic matter violating the
average null energy condition
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Instability of black-hole Cauchy horizons in
asymptotically de Sitter spacetimes
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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 Einsteins equations
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Internal instabilities BHs, once called dark
stars

• Chadrasekhar (1964) In the post-Newtonian
  approximation, where GM/R 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
Internal core
Cold Black Holes
-NEW-
BH Cauchy horizon
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A Mathematical RiddleHow to formulate strong
cosmic censorship?
STABILITY
ENERGY CONDITIONS
REASONABLE EQUATIONS OF STATE

• --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
• M arises from the evolution of nonsingular
  asymptotically flat or de Sitter initial data
  given in a complete space-like hypersurface S
• the initial data evolves in a manner
  according to classical general relativity,
• at late times the corresponding hole
  asymptotically approaches to a nearly' extreme
  spherically symmetric static configuration with
  nonnegative mass.
• 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

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..
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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
Blueshift stable for mini BHs with a positive
cosmological constant small enough
Dominant Energy condition satisfied
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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?
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Wenceslao Santiago-German Postdoctoral fellow,
UC DavisSTRONG COSMIC
CENSORSHIPthe role of nearly extreme rotating
black holes
THE END

• Sponsored by UC MEXUS CONACYT